示例#1
0
def test_panel_lb():
    for model in [
            'plate_clt_donnell_bardell', 'plate_clt_donnell_bardell_w',
            'cpanel_clt_donnell_bardell', 'kpanel_clt_donnell_bardell'
    ]:
        print('Linear buckling for model {0}'.format(model))
        # ssss
        p = Panel()
        p.m = 12
        p.n = 13
        p.stack = [0, 90, -45, +45]
        p.plyt = 0.125e-3
        p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
        p.model = model
        p.a = 1.
        p.b = 0.5
        p.r = 1.e8
        p.alphadeg = 0.
        p.Nxx = -1
        k0 = p.calc_k0(silent=True)
        kG0 = p.calc_kG0(silent=True)
        eigvals, eigvecs = lb(k0, kG0, silent=True)
        if '_w' in model:
            assert np.isclose(eigvals[0], 88.47696, atol=0.1, rtol=0)
        else:
            assert np.isclose(eigvals[0], 85.2912, atol=0.1, rtol=0)

        p.Nxx = 0
        p.Nyy = -1
        k0 = p.calc_k0(silent=True)
        kG0 = p.calc_kG0(silent=True)
        eigvals, eigvecs = lb(k0, kG0, silent=True)
        if '_w' in model:
            assert np.isclose(eigvals[0], 26.45882, atol=0.1, rtol=0)
        else:
            assert np.isclose(eigvals[0], 25.17562, atol=0.1, rtol=0)

        # ssfs
        p = Panel()
        p.u2ty = 1
        p.v2ty = 1
        p.w2ty = 1
        p.u2ry = 1
        p.v2ry = 1
        p.m = 12
        p.n = 13
        p.stack = [0, 90, -45, +45]
        p.plyt = 0.125e-3
        p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
        p.model = model
        p.a = 1.
        p.b = 0.5
        p.r = 1.e8
        p.alphadeg = 0.
        p.Nxx = -1
        k0 = p.calc_k0(silent=True)
        kG0 = p.calc_kG0(silent=True)
        eigvals, eigvecs = lb(k0, kG0, silent=True)
        if '_w' in model:
            assert np.isclose(eigvals[0], 17.14427, atol=0.1, rtol=0)
        else:
            assert np.isclose(eigvals[0], 15.842356, atol=0.1, rtol=0)

        p.u2tx = 1
        p.v2tx = 1
        p.w2tx = 1
        p.u2rx = 1
        p.v2rx = 1
        p.u2ty = 0
        p.v2ty = 0
        p.w2ty = 0
        p.u2ry = 0
        p.v2ry = 0
        p.Nxx = 0
        p.Nyy = -1
        k0 = p.calc_k0(silent=True)
        kG0 = p.calc_kG0(silent=True)
        eigvals, eigvecs = lb(k0, kG0, silent=True)
        if '_w' in model:
            assert np.isclose(eigvals[0], 15.809986, atol=0.1, rtol=0)
        else:
            assert np.isclose(eigvals[0], 13.9421988, atol=0.1, rtol=0)
示例#2
0
    def add_panel(self, y1, y2, stack=None, plyts=None, plyt=None,
            laminaprops=None, laminaprop=None, model=None, mu=None, **kwargs):
        """Add a new panel to the current panel bay

        Parameters
        ----------
        y1 : float
            Position of the first panel edge along `y`.
        y2 : float
            Position of the second panel edge along `y`.
        stack : list, optional
            Panel stacking sequence. If not given the stacking sequence of the
            bay will be used.
        plyts : list, optional
            Thicknesses for each panel ply. If not supplied the bay ``plyts``
            attribute will be used.
        plyt : float, optional
            Unique thickness to be used for all panel plies. If not supplied
            the bay ``plyt`` attribute will be used.
        laminaprops : list, optional
            Lamina properties for each panel ply.
        laminaprop : list, optional
            Unique lamina properties for all panel plies.
        model : str, optional
            Not recommended to pass this parameter, but the user can use a
            different model for each panel. It is recommended to defined
            ``model`` for the bay object.
        mu : float, optional
            Panel material density. If not given the bay density will be used.

        Notes
        -----
        Additional parameters can be passed using the ``kwargs``.

        """
        p = Panel()
        p.m = self.m
        p.n = self.n
        p.a = self.a
        p.b = self.b
        p.r = self.r
        p.y1 = y1
        p.y2 = y2
        p.d = 0.
        p.model = model if model is not None else self.model
        p.stack = stack if stack is not None else self.stack
        p.plyt = plyt if plyt is not None else self.plyt
        p.plyts = plyts if plyts is not None else self.plyts
        p.laminaprop = laminaprop if laminaprop is not None else self.laminaprop
        p.laminaprops = laminaprops if laminaprops is not None else self.laminaprops
        p.mu = mu if mu is not None else self.mu

        p.u1tx = self.u1tx
        p.u1rx = self.u1rx
        p.u2tx = self.u2tx
        p.u2rx = self.u2rx
        p.v1tx = self.v1tx
        p.v1rx = self.v1rx
        p.v2tx = self.v2tx
        p.v2rx = self.v2rx
        p.w1tx = self.w1tx
        p.w1rx = self.w1rx
        p.w2tx = self.w2tx
        p.w2rx = self.w2rx
        p.u1ty = self.u1ty
        p.u1ry = self.u1ry
        p.u2ty = self.u2ty
        p.u2ry = self.u2ry
        p.v1ty = self.v1ty
        p.v1ry = self.v1ry
        p.v2ty = self.v2ty
        p.v2ry = self.v2ry
        p.w1ty = self.w1ty
        p.w1ry = self.w1ry
        p.w2ty = self.w2ty
        p.w2ry = self.w2ry

        for k, v in kwargs.items():
            setattr(p, k, v)

        self.panels.append(p)
示例#3
0
def tstiff2d_1stiff_freq(a,
                         b,
                         ys,
                         bb,
                         bf,
                         defect_a,
                         mu,
                         plyt,
                         laminaprop,
                         stack_skin,
                         stack_base,
                         stack_flange,
                         r=None,
                         m=8,
                         n=8,
                         mb=None,
                         nb=None,
                         mf=None,
                         nf=None):
    r"""Frequency T-Stiffened Panel with possible defect at middle

    For more details about each parameter and the aerodynamic formulation see
    Ref. [castro2016FlutterPanel]_ .

    For more details about the theory involved on the assembly of panels, see
    [castro2017AssemblyModels]_.

    The panel assembly looks like::

        skin
         _________ _____ _________
        |         |     |         |
        |         |     |         |
        |   p01   | p02 |   p03   |
        |         |     |         |
        |_________|_____|_________|
        |   p04   | p05 |   p06   |
        |_________|_____|_________|
        |         |     |         |
        |         |     |         |
        |   p07   | p08 |   p09   |
        |         |     |         |
        |         |     |         |
        |_________|_____|_________|

                  base            flange
                   _____           _____
                  |     |         |     |
                  |     |         |     |
                  | p10 |         | p11 |
                  |     |         |     |
                  |_____|         |_____|
                  | p12 |         | p13 |
                  |_____|         |_____|
                  |     |         |     |
                  |     |         |     |
                  | p14 |         | p15 |
                  |     |         |     |
                  |     |         |     |
                  |_____|         |_____|

    Parameters
    ----------

    a : float
        Total length of the assembly (along `x`).
    b : float
        Total width of the assembly (along `y`).
    ys : float
        Position of the stiffener along `y`.
    bb : float
        Stiffener's base width.
    bf : float
        Stiffener's flange width.
    defect_a : float
        Debonding defect/assembly length ratio.
    mu : float
        Material density.
    plyt : float
        Ply thickness.
    laminaprop : list or tuple
        Orthotropic lamina properties: `E_1, E_2, \nu_{12}, G_{12}, G_{13}, G_{23}`.
    stack_skin : list or tuple
        Stacking sequence for the skin.
    stack_base : list or tuple
        Stacking sequence for the stiffener's base.
    stack_flange : list or tuple
        Stacking sequence for the stiffener's flange.
    r : float or None, optional
        Radius of the stiffened panel.
    m, n : int, optional
        Number of terms of the approximation function for the skin.
    mb, nb : int, optional
        Number of terms of the approximation function for the stiffener's base.
    mf, nf : int, optional
        Number of terms of the approximation function for the stiffener's
        flange.

    Examples
    --------

    The following example is one of the test cases:

    .. literalinclude:: ../../../../../compmech/panel/assembly/tests/test_tstiff2d_assembly.py
        :pyobject: test_tstiff2d_1stiff_freq


    """
    defect = defect_a * a
    has_defect = True if defect > 0 else False
    defect = 0.33 * a if defect == 0 else defect  # to avoid weird domains
    aup = (a - defect) / 2.
    alow = (a - defect) / 2.
    bleft = b - ys - bb / 2.
    bright = ys - bb / 2.
    mb = m if mb is None else mb
    nb = n if nb is None else nb
    mf = m if mf is None else mf
    nf = n if nf is None else nf
    # skin panels
    p01 = Panel(group='skin',
                x0=alow + defect,
                y0=ys + bb / 2.,
                a=aup,
                b=bleft,
                r=r,
                m=m,
                n=n,
                plyt=plyt,
                stack=stack_skin,
                laminaprop=laminaprop,
                mu=mu)
    p02 = Panel(group='skin',
                x0=alow + defect,
                y0=ys - bb / 2.,
                a=aup,
                b=bb,
                r=r,
                m=m,
                n=n,
                plyt=plyt,
                stack=stack_skin,
                laminaprop=laminaprop,
                mu=mu)
    p03 = Panel(group='skin',
                x0=alow + defect,
                y0=0,
                a=aup,
                b=bright,
                r=r,
                m=m,
                n=n,
                plyt=plyt,
                stack=stack_skin,
                laminaprop=laminaprop,
                mu=mu)
    # defect
    p04 = Panel(group='skin',
                x0=alow,
                y0=ys + bb / 2.,
                a=defect,
                b=bleft,
                r=r,
                m=m,
                n=n,
                plyt=plyt,
                stack=stack_skin,
                laminaprop=laminaprop,
                mu=mu)
    p05 = Panel(group='skin',
                x0=alow,
                y0=ys - bb / 2.,
                a=defect,
                b=bb,
                r=r,
                m=m,
                n=n,
                plyt=plyt,
                stack=stack_skin,
                laminaprop=laminaprop,
                mu=mu)
    p06 = Panel(group='skin',
                x0=alow,
                y0=0,
                a=defect,
                b=bright,
                r=r,
                m=m,
                n=n,
                plyt=plyt,
                stack=stack_skin,
                laminaprop=laminaprop,
                mu=mu)
    #
    p07 = Panel(group='skin',
                x0=0,
                y0=ys + bb / 2.,
                a=alow,
                b=bleft,
                r=r,
                m=m,
                n=n,
                plyt=plyt,
                stack=stack_skin,
                laminaprop=laminaprop,
                mu=mu)
    p08 = Panel(group='skin',
                x0=0,
                y0=ys - bb / 2.,
                a=alow,
                b=bb,
                r=r,
                m=m,
                n=n,
                plyt=plyt,
                stack=stack_skin,
                laminaprop=laminaprop,
                mu=mu)
    p09 = Panel(group='skin',
                x0=0,
                y0=0,
                a=alow,
                b=bright,
                r=r,
                m=m,
                n=n,
                plyt=plyt,
                stack=stack_skin,
                laminaprop=laminaprop,
                mu=mu)

    # stiffeners
    p10 = Panel(group='base',
                x0=alow + defect,
                y0=ys - bb / 2.,
                a=aup,
                b=bb,
                r=r,
                m=mb,
                n=nb,
                plyt=plyt,
                stack=stack_base,
                laminaprop=laminaprop,
                mu=mu)
    p11 = Panel(group='flange',
                x0=alow + defect,
                y0=0,
                a=aup,
                b=bf,
                m=mf,
                n=nf,
                plyt=plyt,
                stack=stack_flange,
                laminaprop=laminaprop,
                mu=mu)
    # defect
    p12 = Panel(group='base',
                x0=alow,
                y0=ys - bb / 2.,
                a=defect,
                b=bb,
                r=r,
                m=mb,
                n=nb,
                plyt=plyt,
                stack=stack_base,
                laminaprop=laminaprop,
                mu=mu)
    p13 = Panel(group='flange',
                x0=alow,
                y0=0,
                a=defect,
                b=bf,
                m=mf,
                n=nf,
                plyt=plyt,
                stack=stack_flange,
                laminaprop=laminaprop,
                mu=mu)
    #
    p14 = Panel(group='base',
                x0=0,
                y0=ys - bb / 2.,
                a=alow,
                b=bb,
                r=r,
                m=mb,
                n=nb,
                plyt=plyt,
                stack=stack_base,
                laminaprop=laminaprop,
                mu=mu)
    p15 = Panel(group='flange',
                x0=0,
                y0=0,
                a=alow,
                b=bf,
                m=mf,
                n=nf,
                plyt=plyt,
                stack=stack_flange,
                laminaprop=laminaprop,
                mu=mu)

    # boundary conditions
    p01.u1tx = 1
    p01.u1rx = 1
    p01.u2tx = 0
    p01.u2rx = 1
    p01.v1tx = 1
    p01.v1rx = 1
    p01.v2tx = 0
    p01.v2rx = 1
    p01.w1tx = 1
    p01.w1rx = 1
    p01.w2tx = 0
    p01.w2rx = 1
    p01.u1ty = 1
    p01.u1ry = 1
    p01.u2ty = 0
    p01.u2ry = 1
    p01.v1ty = 1
    p01.v1ry = 1
    p01.v2ty = 0
    p01.v2ry = 1
    p01.w1ty = 1
    p01.w1ry = 1
    p01.w2ty = 0
    p01.w2ry = 1

    p02.u1tx = 1
    p02.u1rx = 1
    p02.u2tx = 0
    p02.u2rx = 1
    p02.v1tx = 1
    p02.v1rx = 1
    p02.v2tx = 0
    p02.v2rx = 1
    p02.w1tx = 1
    p02.w1rx = 1
    p02.w2tx = 0
    p02.w2rx = 1
    p02.u1ty = 1
    p02.u1ry = 1
    p02.u2ty = 1
    p02.u2ry = 1
    p02.v1ty = 1
    p02.v1ry = 1
    p02.v2ty = 1
    p02.v2ry = 1
    p02.w1ty = 1
    p02.w1ry = 1
    p02.w2ty = 1
    p02.w2ry = 1

    p03.u1tx = 1
    p03.u1rx = 1
    p03.u2tx = 0
    p03.u2rx = 1
    p03.v1tx = 1
    p03.v1rx = 1
    p03.v2tx = 0
    p03.v2rx = 1
    p03.w1tx = 1
    p03.w1rx = 1
    p03.w2tx = 0
    p03.w2rx = 1
    p03.u1ty = 0
    p03.u1ry = 1
    p03.u2ty = 1
    p03.u2ry = 1
    p03.v1ty = 0
    p03.v1ry = 1
    p03.v2ty = 1
    p03.v2ry = 1
    p03.w1ty = 0
    p03.w1ry = 1
    p03.w2ty = 1
    p03.w2ry = 1

    p04.u1tx = 1
    p04.u1rx = 1
    p04.u2tx = 1
    p04.u2rx = 1
    p04.v1tx = 1
    p04.v1rx = 1
    p04.v2tx = 1
    p04.v2rx = 1
    p04.w1tx = 1
    p04.w1rx = 1
    p04.w2tx = 1
    p04.w2rx = 1
    p04.u1ty = 1
    p04.u1ry = 1
    p04.u2ty = 0
    p04.u2ry = 1
    p04.v1ty = 1
    p04.v1ry = 1
    p04.v2ty = 0
    p04.v2ry = 1
    p04.w1ty = 1
    p04.w1ry = 1
    p04.w2ty = 0
    p04.w2ry = 1

    p05.u1tx = 1
    p05.u1rx = 1
    p05.u2tx = 1
    p05.u2rx = 1
    p05.v1tx = 1
    p05.v1rx = 1
    p05.v2tx = 1
    p05.v2rx = 1
    p05.w1tx = 1
    p05.w1rx = 1
    p05.w2tx = 1
    p05.w2rx = 1
    p05.u1ty = 1
    p05.u1ry = 1
    p05.u2ty = 1
    p05.u2ry = 1
    p05.v1ty = 1
    p05.v1ry = 1
    p05.v2ty = 1
    p05.v2ry = 1
    p05.w1ty = 1
    p05.w1ry = 1
    p05.w2ty = 1
    p05.w2ry = 1

    p06.u1tx = 1
    p06.u1rx = 1
    p06.u2tx = 1
    p06.u2rx = 1
    p06.v1tx = 1
    p06.v1rx = 1
    p06.v2tx = 1
    p06.v2rx = 1
    p06.w1tx = 1
    p06.w1rx = 1
    p06.w2tx = 1
    p06.w2rx = 1
    p06.u1ty = 0
    p06.u1ry = 1
    p06.u2ty = 1
    p06.u2ry = 1
    p06.v1ty = 0
    p06.v1ry = 1
    p06.v2ty = 1
    p06.v2ry = 1
    p06.w1ty = 0
    p06.w1ry = 1
    p06.w2ty = 1
    p06.w2ry = 1

    p07.u1tx = 0
    p07.u1rx = 1
    p07.u2tx = 1
    p07.u2rx = 1
    p07.v1tx = 0
    p07.v1rx = 1
    p07.v2tx = 1
    p07.v2rx = 1
    p07.w1tx = 0
    p07.w1rx = 1
    p07.w2tx = 1
    p07.w2rx = 1
    p07.u1ty = 1
    p07.u1ry = 1
    p07.u2ty = 0
    p07.u2ry = 1
    p07.v1ty = 1
    p07.v1ry = 1
    p07.v2ty = 0
    p07.v2ry = 1
    p07.w1ty = 1
    p07.w1ry = 1
    p07.w2ty = 0
    p07.w2ry = 1

    p08.u1tx = 0
    p08.u1rx = 1
    p08.u2tx = 1
    p08.u2rx = 1
    p08.v1tx = 0
    p08.v1rx = 1
    p08.v2tx = 1
    p08.v2rx = 1
    p08.w1tx = 0
    p08.w1rx = 1
    p08.w2tx = 1
    p08.w2rx = 1
    p08.u1ty = 1
    p08.u1ry = 1
    p08.u2ty = 1
    p08.u2ry = 1
    p08.v1ty = 1
    p08.v1ry = 1
    p08.v2ty = 1
    p08.v2ry = 1
    p08.w1ty = 1
    p08.w1ry = 1
    p08.w2ty = 1
    p08.w2ry = 1

    p09.u1tx = 0
    p09.u1rx = 1
    p09.u2tx = 1
    p09.u2rx = 1
    p09.v1tx = 0
    p09.v1rx = 1
    p09.v2tx = 1
    p09.v2rx = 1
    p09.w1tx = 0
    p09.w1rx = 1
    p09.w2tx = 1
    p09.w2rx = 1
    p09.u1ty = 0
    p09.u1ry = 1
    p09.u2ty = 1
    p09.u2ry = 1
    p09.v1ty = 0
    p09.v1ry = 1
    p09.v2ty = 1
    p09.v2ry = 1
    p09.w1ty = 0
    p09.w1ry = 1
    p09.w2ty = 1
    p09.w2ry = 1

    # base up
    p10.u1tx = 1
    p10.u1rx = 1
    p10.u2tx = 1
    p10.u2rx = 1
    p10.v1tx = 1
    p10.v1rx = 1
    p10.v2tx = 1
    p10.v2rx = 1
    p10.w1tx = 1
    p10.w1rx = 1
    p10.w2tx = 1
    p10.w2rx = 1
    p10.u1ty = 1
    p10.u1ry = 1
    p10.u2ty = 1
    p10.u2ry = 1
    p10.v1ty = 1
    p10.v1ry = 1
    p10.v2ty = 1
    p10.v2ry = 1
    p10.w1ty = 1
    p10.w1ry = 1
    p10.w2ty = 1
    p10.w2ry = 1

    # flange up
    p11.u1tx = 1
    p11.u1rx = 1
    p11.u2tx = 0
    p11.u2rx = 1
    p11.v1tx = 1
    p11.v1rx = 1
    p11.v2tx = 0
    p11.v2rx = 1
    p11.w1tx = 1
    p11.w1rx = 1
    p11.w2tx = 0
    p11.w2rx = 1
    p11.u1ty = 1
    p11.u1ry = 1
    p11.u2ty = 1
    p11.u2ry = 1
    p11.v1ty = 1
    p11.v1ry = 1
    p11.v2ty = 1
    p11.v2ry = 1
    p11.w1ty = 1
    p11.w1ry = 1
    p11.w2ty = 1
    p11.w2ry = 1

    # base mid
    p12.u1tx = 1
    p12.u1rx = 1
    p12.u2tx = 1
    p12.u2rx = 1
    p12.v1tx = 1
    p12.v1rx = 1
    p12.v2tx = 1
    p12.v2rx = 1
    p12.w1tx = 1
    p12.w1rx = 1
    p12.w2tx = 1
    p12.w2rx = 1
    p12.u1ty = 1
    p12.u1ry = 1
    p12.u2ty = 1
    p12.u2ry = 1
    p12.v1ty = 1
    p12.v1ry = 1
    p12.v2ty = 1
    p12.v2ry = 1
    p12.w1ty = 1
    p12.w1ry = 1
    p12.w2ty = 1
    p12.w2ry = 1

    # flange mid
    p13.u1tx = 1
    p13.u1rx = 1
    p13.u2tx = 1
    p13.u2rx = 1
    p13.v1tx = 1
    p13.v1rx = 1
    p13.v2tx = 1
    p13.v2rx = 1
    p13.w1tx = 1
    p13.w1rx = 1
    p13.w2tx = 1
    p13.w2rx = 1
    p13.u1ty = 1
    p13.u1ry = 1
    p13.u2ty = 1
    p13.u2ry = 1
    p13.v1ty = 1
    p13.v1ry = 1
    p13.v2ty = 1
    p13.v2ry = 1
    p13.w1ty = 1
    p13.w1ry = 1
    p13.w2ty = 1
    p13.w2ry = 1

    # base low
    p14.u1tx = 1
    p14.u1rx = 1
    p14.u2tx = 1
    p14.u2rx = 1
    p14.v1tx = 1
    p14.v1rx = 1
    p14.v2tx = 1
    p14.v2rx = 1
    p14.w1tx = 1
    p14.w1rx = 1
    p14.w2tx = 1
    p14.w2rx = 1
    p14.u1ty = 1
    p14.u1ry = 1
    p14.u2ty = 1
    p14.u2ry = 1
    p14.v1ty = 1
    p14.v1ry = 1
    p14.v2ty = 1
    p14.v2ry = 1
    p14.w1ty = 1
    p14.w1ry = 1
    p14.w2ty = 1
    p14.w2ry = 1

    # flange low
    p15.u1tx = 0
    p15.u1rx = 1
    p15.u2tx = 1
    p15.u2rx = 1
    p15.v1tx = 0
    p15.v1rx = 1
    p15.v2tx = 1
    p15.v2rx = 1
    p15.w1tx = 0
    p15.w1rx = 1
    p15.w2tx = 1
    p15.w2rx = 1
    p15.u1ty = 1
    p15.u1ry = 1
    p15.u2ty = 1
    p15.u2ry = 1
    p15.v1ty = 1
    p15.v1ry = 1
    p15.v2ty = 1
    p15.v2ry = 1
    p15.w1ty = 1
    p15.w1ry = 1
    p15.w2ty = 1
    p15.w2ry = 1

    conn = [
        # skin-skin
        dict(p1=p01, p2=p02, func='SSycte', ycte1=0, ycte2=p02.b),
        dict(p1=p01, p2=p04, func='SSxcte', xcte1=0, xcte2=p04.a),
        dict(p1=p02, p2=p03, func='SSycte', ycte1=0, ycte2=p03.b),
        dict(p1=p02, p2=p05, func='SSxcte', xcte1=0, xcte2=p05.a),
        dict(p1=p03, p2=p06, func='SSxcte', xcte1=0, xcte2=p06.a),
        dict(p1=p04, p2=p05, func='SSycte', ycte1=0, ycte2=p05.b),
        dict(p1=p04, p2=p07, func='SSxcte', xcte1=0, xcte2=p07.a),
        dict(p1=p05, p2=p06, func='SSycte', ycte1=0, ycte2=p06.b),
        dict(p1=p05, p2=p08, func='SSxcte', xcte1=0, xcte2=p08.a),
        dict(p1=p06, p2=p09, func='SSxcte', xcte1=0, xcte2=p09.a),
        dict(p1=p07, p2=p08, func='SSycte', ycte1=0, ycte2=p08.b),
        dict(p1=p08, p2=p09, func='SSycte', ycte1=0, ycte2=p09.b),

        # skin-base
        dict(p1=p02, p2=p10, func='SB'),
        dict(p1=p05, p2=p12, func='SB', has_defect=has_defect),  # defect
        dict(p1=p08, p2=p14, func='SB'),

        # base-base
        dict(p1=p10, p2=p12, func='SSxcte', xcte1=0, xcte2=p12.a),
        dict(p1=p12, p2=p14, func='SSxcte', xcte1=0, xcte2=p14.a),

        # base-flange
        dict(p1=p10, p2=p11, func='BFycte', ycte1=p10.b / 2., ycte2=0),
        dict(p1=p12, p2=p13, func='BFycte', ycte1=p12.b / 2., ycte2=0),
        dict(p1=p14, p2=p15, func='BFycte', ycte1=p14.b / 2., ycte2=0),

        # flange-flange
        dict(p1=p11, p2=p13, func='SSxcte', xcte1=0, xcte2=p13.a),
        dict(p1=p13, p2=p15, func='SSxcte', xcte1=0, xcte2=p15.a),
    ]

    panels = [
        p01, p02, p03, p04, p05, p06, p07, p08, p09, p10, p11, p12, p13, p14,
        p15
    ]
    skin = [p01, p02, p03, p04, p05, p06, p07, p08, p09]
    base = [p10, p12, p14]
    flange = [p11, p13, p15]

    assy = PanelAssembly(panels)

    size = assy.get_size()

    valid_conn = []
    for connecti in conn:
        if connecti.get('has_defect'):
            continue
        valid_conn.append(connecti)

    k0 = assy.calc_k0(conn=valid_conn)
    kM = assy.calc_kM()

    eigvals, eigvecs = freq(k0,
                            kM,
                            tol=0,
                            sparse_solver=True,
                            silent=True,
                            sort=True,
                            reduced_dof=False,
                            num_eigvalues=25,
                            num_eigvalues_print=5)

    return assy, eigvals, eigvecs
示例#4
0
def test_4panels_kt_kr():
    """Compare result of 4 assembled panels with single-domain results

    The panel assembly looks like::

         _________ _____
        |         |     |
        |         |     |
        |   p01   | p02 |
        |         |     |
        |_________|_____|
        |   p03   | p04 |
        |         |     |
        |         |     |
        |         |     |
        |         |     |
        |         |     |
        |_________|_____|

    """
    print('Testing validity of the default kt and kr values')

    plyt = 1.e-3 * 0.125
    laminaprop=(142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
    stack=[0, 45, -45, 90, -45, 45, 0]
    lam = laminate.read_stack(stack=stack, plyt=plyt, laminaprop=laminaprop)

    mu=1.3e3

    r = 10.
    m = 8
    n = 8

    a1 = 1.5
    a2 = 1.5
    a3 = 2.5
    a4 = 2.5
    b1 = 1.5
    b2 = 0.5
    b3 = 1.5
    b4 = 0.5

    A11 = lam.ABD[0, 0]
    A22 = lam.ABD[1, 1]
    D11 = lam.ABD[3, 3]
    D22 = lam.ABD[4, 4]

    p01 = Panel(group='panels', x0=a3, y0=b2, a=a1, b=b1, r=r, m=m, n=n, plyt=plyt, stack=stack, laminaprop=laminaprop, mu=mu)
    p02 = Panel(group='panels', x0=a3, y0=0, a=a2, b=b2, r=r, m=m, n=n, plyt=plyt, stack=stack, laminaprop=laminaprop, mu=mu)
    p03 = Panel(group='panels', x0=0, y0=b2, a=a3, b=b3, r=r, m=m, n=n, plyt=plyt, stack=stack, laminaprop=laminaprop, mu=mu)
    p04 = Panel(group='panels', x0=0, y0=0, a=a4, b=b4, r=r, m=m, n=n, plyt=plyt, stack=stack, laminaprop=laminaprop, mu=mu)

    kt13, kr13 = connections.calc_kt_kr(p01, p03, 'xcte')
    kt24, kr24 = connections.calc_kt_kr(p02, p04, 'xcte')
    kt12, kr12 = connections.calc_kt_kr(p01, p02, 'ycte')
    kt34, kr34 = connections.calc_kt_kr(p03, p04, 'ycte')

    # boundary conditions
    p01.u1tx = 1 ; p01.u1rx = 1 ; p01.u2tx = 0 ; p01.u2rx = 1
    p01.v1tx = 1 ; p01.v1rx = 1 ; p01.v2tx = 0 ; p01.v2rx = 1
    p01.w1tx = 1 ; p01.w1rx = 1 ; p01.w2tx = 0 ; p01.w2rx = 1
    p01.u1ty = 1 ; p01.u1ry = 1 ; p01.u2ty = 0 ; p01.u2ry = 1
    p01.v1ty = 1 ; p01.v1ry = 1 ; p01.v2ty = 0 ; p01.v2ry = 1
    p01.w1ty = 1 ; p01.w1ry = 1 ; p01.w2ty = 0 ; p01.w2ry = 1

    p02.u1tx = 1 ; p02.u1rx = 1 ; p02.u2tx = 0 ; p02.u2rx = 1
    p02.v1tx = 1 ; p02.v1rx = 1 ; p02.v2tx = 0 ; p02.v2rx = 1
    p02.w1tx = 1 ; p02.w1rx = 1 ; p02.w2tx = 0 ; p02.w2rx = 1
    p02.u1ty = 0 ; p02.u1ry = 1 ; p02.u2ty = 1 ; p02.u2ry = 1
    p02.v1ty = 0 ; p02.v1ry = 1 ; p02.v2ty = 1 ; p02.v2ry = 1
    p02.w1ty = 0 ; p02.w1ry = 1 ; p02.w2ty = 1 ; p02.w2ry = 1

    p03.u1tx = 0 ; p03.u1rx = 1 ; p03.u2tx = 1 ; p03.u2rx = 1
    p03.v1tx = 0 ; p03.v1rx = 1 ; p03.v2tx = 1 ; p03.v2rx = 1
    p03.w1tx = 0 ; p03.w1rx = 1 ; p03.w2tx = 1 ; p03.w2rx = 1
    p03.u1ty = 1 ; p03.u1ry = 1 ; p03.u2ty = 0 ; p03.u2ry = 1
    p03.v1ty = 1 ; p03.v1ry = 1 ; p03.v2ty = 0 ; p03.v2ry = 1
    p03.w1ty = 1 ; p03.w1ry = 1 ; p03.w2ty = 0 ; p03.w2ry = 1

    p04.u1tx = 0 ; p04.u1rx = 1 ; p04.u2tx = 1 ; p04.u2rx = 1
    p04.v1tx = 0 ; p04.v1rx = 1 ; p04.v2tx = 1 ; p04.v2rx = 1
    p04.w1tx = 0 ; p04.w1rx = 1 ; p04.w2tx = 1 ; p04.w2rx = 1
    p04.u1ty = 0 ; p04.u1ry = 1 ; p04.u2ty = 1 ; p04.u2ry = 1
    p04.v1ty = 0 ; p04.v1ry = 1 ; p04.v2ty = 1 ; p04.v2ry = 1
    p04.w1ty = 0 ; p04.w1ry = 1 ; p04.w2ty = 1 ; p04.w2ry = 1

    conndict = [
        dict(p1=p01, p2=p02, func='SSycte', ycte1=0, ycte2=p02.b, kt=kt12, kr=kr12),
        dict(p1=p01, p2=p03, func='SSxcte', xcte1=0, xcte2=p03.a, kt=kt13, kr=kr13),
        dict(p1=p02, p2=p04, func='SSxcte', xcte1=0, xcte2=p04.a, kt=kt24, kr=kr24),
        dict(p1=p03, p2=p04, func='SSycte', ycte1=0, ycte2=p04.b, kt=kt34, kr=kr34),
        ]

    panels = [p01, p02, p03, p04]

    size = sum([3*p.m*p.n for p in panels])

    k0 = 0
    kM = 0

    row0 = 0
    col0 = 0
    for p in panels:
        k0 += p.calc_k0(row0=row0, col0=col0, size=size, silent=True, finalize=False)
        kM += p.calc_kM(row0=row0, col0=col0, size=size, silent=True, finalize=False)
        p.row_start = row0
        p.col_start = col0
        row0 += 3*p.m*p.n
        col0 += 3*p.m*p.n
        p.row_end = row0
        p.col_end = col0

    for conn in conndict:
        if conn.get('has_deffect'): # connecting if there is no deffect
            continue
        p1 = conn['p1']
        p2 = conn['p2']
        if conn['func'] == 'SSycte':
            k0 += connections.kCSSycte.fkCSSycte11(
                    conn['kt'], conn['kr'], p1, conn['ycte1'],
                    size, p1.row_start, col0=p1.col_start)
            k0 += connections.kCSSycte.fkCSSycte12(
                    conn['kt'], conn['kr'], p1, p2, conn['ycte1'], conn['ycte2'],
                    size, p1.row_start, col0=p2.col_start)
            k0 += connections.kCSSycte.fkCSSycte22(
                    conn['kt'], conn['kr'], p1, p2, conn['ycte2'],
                    size, p2.row_start, col0=p2.col_start)
        elif conn['func'] == 'SSxcte':
            k0 += connections.kCSSxcte.fkCSSxcte11(
                    conn['kt'], conn['kr'], p1, conn['xcte1'],
                    size, p1.row_start, col0=p1.col_start)
            k0 += connections.kCSSxcte.fkCSSxcte12(
                    conn['kt'], conn['kr'], p1, p2, conn['xcte1'], conn['xcte2'],
                    size, p1.row_start, col0=p2.col_start)
            k0 += connections.kCSSxcte.fkCSSxcte22(
                    conn['kt'], conn['kr'], p1, p2, conn['xcte2'],
                    size, p2.row_start, col0=p2.col_start)

    assert np.any(np.isnan(k0.data)) == False
    assert np.any(np.isinf(k0.data)) == False
    k0 = csr_matrix(make_symmetric(k0))
    assert np.any(np.isnan(kM.data)) == False
    assert np.any(np.isinf(kM.data)) == False
    kM = csr_matrix(make_symmetric(kM))

    eigvals, eigvecs = freq(k0, kM, tol=0, sparse_solver=True, silent=True,
             sort=True, reduced_dof=False,
             num_eigvalues=25, num_eigvalues_print=5)

    # Results for single panel
    m = 15
    n = 15
    singlepanel = Panel(a=(a1+a3), b=(b1+b2), r=r, m=m, n=n, plyt=plyt, stack=stack, laminaprop=laminaprop, mu=mu)
    singlepanel.freq(silent=True)

    assert np.isclose(eigvals[0], singlepanel.eigvals[0], atol=0.01, rtol=0.01)
def tstiff2d_1stiff_flutter(a, b, ys, bb, bf, defect_a, mu, plyt,
        laminaprop, stack_skin, stack_base, stack_flange,
        air_speed=None, rho_air=None, Mach=None, speed_sound=None, flow='x',
        Nxx_skin=None, Nxx_base=None, Nxx_flange=None, run_static_case=True,
        r=None, m=8, n=8, mb=None, nb=None, mf=None, nf=None):
    r"""Flutter of T-Stiffened Panel with possible defect at middle

    For more details about each parameter and the aerodynamic formulation see
    Ref. [castro2016FlutterPanel]_ .


    The panel assembly looks like::

        skin
         _________ _____ _________
        |         |     |         |
        |         |     |         |
        |   p01   | p02 |   p03   |
        |         |     |         |
        |_________|_____|_________|
        |   p04   | p05 |   p06   |      /\  x
        |_________|_____|_________|       |
        |         |     |         |       |
        |         |     |         |       |
        |   p07   | p08 |   p09   |
        |         |     |         |
        |         |     |         |
        |_________|_____|_________|
               loaded edge

                  base            flange
                   _____           _____
                  |     |         |     |
                  |     |         |     |
                  | p10 |         | p11 |
                  |     |         |     |
                  |_____|         |_____|
                  | p12 |         | p13 |
                  |_____|         |_____|
                  |     |         |     |
                  |     |         |     |
                  | p14 |         | p15 |
                  |     |         |     |
                  |     |         |     |
                  |_____|         |_____|
               loaded edge     loaded edge

    Parameters
    ----------

    a : float
        Total length of the assembly (along `x`).
    b : float
        Total width of the assembly (along `y`).
    ys : float
        Position of the stiffener along `y`.
    bb : float
        Stiffener's base width.
    bf : float
        Stiffener's flange width.
    defect_a : float
        Debonding defect/assembly length ratio.
    mu : float
        Material density.
    plyt : float
        Ply thickness.
    laminaprop : list or tuple
        Orthotropic lamina properties: `E_1, E_2, \nu_{12}, G_{12}, G_{13}, G_{23}`.
    stack_skin : list or tuple
        Stacking sequence for the skin.
    stack_base : list or tuple
        Stacking sequence for the stiffener's base.
    stack_flange : list or tuple
        Stacking sequence for the stiffener's flange.
    air_speed : float
        Airflow speed.
    rho_air : float
        Air density.
    Mach : float
        Mach number.
    speed_sound : float
        Speed of sound.
    flow : "x" or "y"
        Direction of airflow.
    Nxx_skin : float
        Skin load distributed at the assembly edge at `x=0`.
    Nxx_base : float
        Stiffener's base load distributed at the assembly edge at `x=0`.
    Nxx_flange : float
        Stiffener's flange load distributed at the assembly edge at `x=0`.
    run_static_case : bool, optional
        If True a static analysis is run before the linear buckling analysis
        to compute the real membrane stress state along the domain, otherwise
        it is assumed constant values of `N_{xx}` for all components.
    r : float or None, optional
        Radius of the stiffened panel.
    m, n : int, optional
        Number of terms of the approximation function for the skin.
    mb, nb : int, optional
        Number of terms of the approximation function for the stiffener's base.
    mf, nf : int, optional
        Number of terms of the approximation function for the stiffener's
        flange.

    Examples
    --------

    The following example is one of the test cases:

    .. literalinclude:: ../../../../../compmech/panel/assembly/tests/test_tstiff2d_assembly.py
        :pyobject: test_tstiff2d_1stiff_flutter

    """
    defect = defect_a * a
    has_defect = True if defect > 0 else False
    defect = 0.33*a if defect == 0 else defect # to avoid weird domains
    aup = (a - defect)/2.
    alow = (a - defect)/2.
    bleft = b - ys - bb/2.
    bright = ys - bb/2.
    mb = m if mb is None else mb
    nb = n if nb is None else nb
    mf = m if mf is None else mf
    nf = n if nf is None else nf
    # skin panels
    p01 = Panel(group='skin', Nxx=Nxx_skin, x0=alow+defect, y0=ys+bb/2., a=aup, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
    p02 = Panel(group='skin', Nxx=Nxx_skin, x0=alow+defect, y0=ys-bb/2., a=aup, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
    p03 = Panel(group='skin', Nxx=Nxx_skin, x0=alow+defect, y0=0, a=aup, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
    # defect
    p04 = Panel(group='skin', Nxx=Nxx_skin, x0=alow, y0=ys+bb/2., a=defect, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
    p05 = Panel(group='skin', Nxx=Nxx_skin, x0=alow, y0=ys-bb/2., a=defect, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
    p06 = Panel(group='skin', Nxx=Nxx_skin, x0=alow, y0=0, a=defect, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
    #
    p07 = Panel(group='skin', Nxx=Nxx_skin, x0=0, y0=ys+bb/2., a=alow, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
    p08 = Panel(group='skin', Nxx=Nxx_skin, x0=0, y0=ys-bb/2., a=alow, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)
    p09 = Panel(group='skin', Nxx=Nxx_skin, x0=0, y0=0, a=alow, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, rho_air=rho_air, speed_sound=speed_sound, Mach=Mach, V=air_speed, flow=flow)

    # stiffeners
    p10 = Panel(group='base', Nxx=Nxx_base, x0=alow+defect, y0=ys-bb/2., a=aup, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu)
    p11 = Panel(group='flange', Nxx=Nxx_flange, x0=alow+defect, y0=0,        a=aup, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu)
    # defect
    p12 = Panel(group='base', Nxx=Nxx_base, x0=alow, y0=ys-bb/2., a=defect, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu)
    p13 = Panel(group='flange', Nxx=Nxx_flange, x0=alow, y0=0,        a=defect, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu)
    #
    p14 = Panel(group='base', Nxx=Nxx_base, x0=0, y0=ys-bb/2., a=alow, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu)
    p15 = Panel(group='flange', Nxx=Nxx_flange, x0=0, y0=0,        a=alow, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu)

    # boundary conditions
    p01.u1tx = 1 ; p01.u1rx = 1 ; p01.u2tx = 0 ; p01.u2rx = 1
    p01.v1tx = 1 ; p01.v1rx = 1 ; p01.v2tx = 0 ; p01.v2rx = 1
    p01.w1tx = 1 ; p01.w1rx = 1 ; p01.w2tx = 0 ; p01.w2rx = 1
    p01.u1ty = 1 ; p01.u1ry = 1 ; p01.u2ty = 1 ; p01.u2ry = 1
    p01.v1ty = 1 ; p01.v1ry = 1 ; p01.v2ty = 0 ; p01.v2ry = 1
    p01.w1ty = 1 ; p01.w1ry = 1 ; p01.w2ty = 0 ; p01.w2ry = 1

    p02.u1tx = 1 ; p02.u1rx = 1 ; p02.u2tx = 0 ; p02.u2rx = 1
    p02.v1tx = 1 ; p02.v1rx = 1 ; p02.v2tx = 0 ; p02.v2rx = 1
    p02.w1tx = 1 ; p02.w1rx = 1 ; p02.w2tx = 0 ; p02.w2rx = 1
    p02.u1ty = 1 ; p02.u1ry = 1 ; p02.u2ty = 1 ; p02.u2ry = 1
    p02.v1ty = 1 ; p02.v1ry = 1 ; p02.v2ty = 1 ; p02.v2ry = 1
    p02.w1ty = 1 ; p02.w1ry = 1 ; p02.w2ty = 1 ; p02.w2ry = 1

    p03.u1tx = 1 ; p03.u1rx = 1 ; p03.u2tx = 0 ; p03.u2rx = 1
    p03.v1tx = 1 ; p03.v1rx = 1 ; p03.v2tx = 0 ; p03.v2rx = 1
    p03.w1tx = 1 ; p03.w1rx = 1 ; p03.w2tx = 0 ; p03.w2rx = 1
    p03.u1ty = 1 ; p03.u1ry = 1 ; p03.u2ty = 1 ; p03.u2ry = 1
    p03.v1ty = 0 ; p03.v1ry = 1 ; p03.v2ty = 1 ; p03.v2ry = 1
    p03.w1ty = 0 ; p03.w1ry = 1 ; p03.w2ty = 1 ; p03.w2ry = 1

    p04.u1tx = 1 ; p04.u1rx = 1 ; p04.u2tx = 1 ; p04.u2rx = 1
    p04.v1tx = 1 ; p04.v1rx = 1 ; p04.v2tx = 1 ; p04.v2rx = 1
    p04.w1tx = 1 ; p04.w1rx = 1 ; p04.w2tx = 1 ; p04.w2rx = 1
    p04.u1ty = 1 ; p04.u1ry = 1 ; p04.u2ty = 1 ; p04.u2ry = 1
    p04.v1ty = 1 ; p04.v1ry = 1 ; p04.v2ty = 0 ; p04.v2ry = 1
    p04.w1ty = 1 ; p04.w1ry = 1 ; p04.w2ty = 0 ; p04.w2ry = 1

    p05.u1tx = 1 ; p05.u1rx = 1 ; p05.u2tx = 1 ; p05.u2rx = 1
    p05.v1tx = 1 ; p05.v1rx = 1 ; p05.v2tx = 1 ; p05.v2rx = 1
    p05.w1tx = 1 ; p05.w1rx = 1 ; p05.w2tx = 1 ; p05.w2rx = 1
    p05.u1ty = 1 ; p05.u1ry = 1 ; p05.u2ty = 1 ; p05.u2ry = 1
    p05.v1ty = 1 ; p05.v1ry = 1 ; p05.v2ty = 1 ; p05.v2ry = 1
    p05.w1ty = 1 ; p05.w1ry = 1 ; p05.w2ty = 1 ; p05.w2ry = 1

    p06.u1tx = 1 ; p06.u1rx = 1 ; p06.u2tx = 1 ; p06.u2rx = 1
    p06.v1tx = 1 ; p06.v1rx = 1 ; p06.v2tx = 1 ; p06.v2rx = 1
    p06.w1tx = 1 ; p06.w1rx = 1 ; p06.w2tx = 1 ; p06.w2rx = 1
    p06.u1ty = 1 ; p06.u1ry = 1 ; p06.u2ty = 1 ; p06.u2ry = 1
    p06.v1ty = 0 ; p06.v1ry = 1 ; p06.v2ty = 1 ; p06.v2ry = 1
    p06.w1ty = 0 ; p06.w1ry = 1 ; p06.w2ty = 1 ; p06.w2ry = 1

    p07.u1tx = 1 ; p07.u1rx = 1 ; p07.u2tx = 1 ; p07.u2rx = 1
    p07.v1tx = 0 ; p07.v1rx = 1 ; p07.v2tx = 1 ; p07.v2rx = 1
    p07.w1tx = 0 ; p07.w1rx = 1 ; p07.w2tx = 1 ; p07.w2rx = 1
    p07.u1ty = 1 ; p07.u1ry = 1 ; p07.u2ty = 1 ; p07.u2ry = 1
    p07.v1ty = 1 ; p07.v1ry = 1 ; p07.v2ty = 0 ; p07.v2ry = 1
    p07.w1ty = 1 ; p07.w1ry = 1 ; p07.w2ty = 0 ; p07.w2ry = 1

    p08.u1tx = 1 ; p08.u1rx = 1 ; p08.u2tx = 1 ; p08.u2rx = 1
    p08.v1tx = 0 ; p08.v1rx = 1 ; p08.v2tx = 1 ; p08.v2rx = 1
    p08.w1tx = 0 ; p08.w1rx = 1 ; p08.w2tx = 1 ; p08.w2rx = 1
    p08.u1ty = 1 ; p08.u1ry = 1 ; p08.u2ty = 1 ; p08.u2ry = 1
    p08.v1ty = 1 ; p08.v1ry = 1 ; p08.v2ty = 1 ; p08.v2ry = 1
    p08.w1ty = 1 ; p08.w1ry = 1 ; p08.w2ty = 1 ; p08.w2ry = 1

    p09.u1tx = 1 ; p09.u1rx = 1 ; p09.u2tx = 1 ; p09.u2rx = 1
    p09.v1tx = 0 ; p09.v1rx = 1 ; p09.v2tx = 1 ; p09.v2rx = 1
    p09.w1tx = 0 ; p09.w1rx = 1 ; p09.w2tx = 1 ; p09.w2rx = 1
    p09.u1ty = 1 ; p09.u1ry = 1 ; p09.u2ty = 1 ; p09.u2ry = 1
    p09.v1ty = 0 ; p09.v1ry = 1 ; p09.v2ty = 1 ; p09.v2ry = 1
    p09.w1ty = 0 ; p09.w1ry = 1 ; p09.w2ty = 1 ; p09.w2ry = 1

    # base up
    p10.u1tx = 1 ; p10.u1rx = 1 ; p10.u2tx = 1 ; p10.u2rx = 1
    p10.v1tx = 1 ; p10.v1rx = 1 ; p10.v2tx = 1 ; p10.v2rx = 1
    p10.w1tx = 1 ; p10.w1rx = 1 ; p10.w2tx = 1 ; p10.w2rx = 1
    p10.u1ty = 1 ; p10.u1ry = 1 ; p10.u2ty = 1 ; p10.u2ry = 1
    p10.v1ty = 1 ; p10.v1ry = 1 ; p10.v2ty = 1 ; p10.v2ry = 1
    p10.w1ty = 1 ; p10.w1ry = 1 ; p10.w2ty = 1 ; p10.w2ry = 1

    # flange up
    p11.u1tx = 1 ; p11.u1rx = 1 ; p11.u2tx = 0 ; p11.u2rx = 1
    p11.v1tx = 1 ; p11.v1rx = 1 ; p11.v2tx = 0 ; p11.v2rx = 1
    p11.w1tx = 1 ; p11.w1rx = 1 ; p11.w2tx = 0 ; p11.w2rx = 1
    p11.u1ty = 1 ; p11.u1ry = 1 ; p11.u2ty = 1 ; p11.u2ry = 1
    p11.v1ty = 1 ; p11.v1ry = 1 ; p11.v2ty = 1 ; p11.v2ry = 1
    p11.w1ty = 1 ; p11.w1ry = 1 ; p11.w2ty = 1 ; p11.w2ry = 1

    # base mid
    p12.u1tx = 1 ; p12.u1rx = 1 ; p12.u2tx = 1 ; p12.u2rx = 1
    p12.v1tx = 1 ; p12.v1rx = 1 ; p12.v2tx = 1 ; p12.v2rx = 1
    p12.w1tx = 1 ; p12.w1rx = 1 ; p12.w2tx = 1 ; p12.w2rx = 1
    p12.u1ty = 1 ; p12.u1ry = 1 ; p12.u2ty = 1 ; p12.u2ry = 1
    p12.v1ty = 1 ; p12.v1ry = 1 ; p12.v2ty = 1 ; p12.v2ry = 1
    p12.w1ty = 1 ; p12.w1ry = 1 ; p12.w2ty = 1 ; p12.w2ry = 1

    # flange mid
    p13.u1tx = 1 ; p13.u1rx = 1 ; p13.u2tx = 1 ; p13.u2rx = 1
    p13.v1tx = 1 ; p13.v1rx = 1 ; p13.v2tx = 1 ; p13.v2rx = 1
    p13.w1tx = 1 ; p13.w1rx = 1 ; p13.w2tx = 1 ; p13.w2rx = 1
    p13.u1ty = 1 ; p13.u1ry = 1 ; p13.u2ty = 1 ; p13.u2ry = 1
    p13.v1ty = 1 ; p13.v1ry = 1 ; p13.v2ty = 1 ; p13.v2ry = 1
    p13.w1ty = 1 ; p13.w1ry = 1 ; p13.w2ty = 1 ; p13.w2ry = 1

    # base low
    p14.u1tx = 1 ; p14.u1rx = 1 ; p14.u2tx = 1 ; p14.u2rx = 1
    p14.v1tx = 1 ; p14.v1rx = 1 ; p14.v2tx = 1 ; p14.v2rx = 1
    p14.w1tx = 1 ; p14.w1rx = 1 ; p14.w2tx = 1 ; p14.w2rx = 1
    p14.u1ty = 1 ; p14.u1ry = 1 ; p14.u2ty = 1 ; p14.u2ry = 1
    p14.v1ty = 1 ; p14.v1ry = 1 ; p14.v2ty = 1 ; p14.v2ry = 1
    p14.w1ty = 1 ; p14.w1ry = 1 ; p14.w2ty = 1 ; p14.w2ry = 1

    # flange low
    p15.u1tx = 1 ; p15.u1rx = 1 ; p15.u2tx = 1 ; p15.u2rx = 1
    p15.v1tx = 0 ; p15.v1rx = 1 ; p15.v2tx = 1 ; p15.v2rx = 1
    p15.w1tx = 0 ; p15.w1rx = 1 ; p15.w2tx = 1 ; p15.w2rx = 1
    p15.u1ty = 1 ; p15.u1ry = 1 ; p15.u2ty = 1 ; p15.u2ry = 1
    p15.v1ty = 1 ; p15.v1ry = 1 ; p15.v2ty = 1 ; p15.v2ry = 1
    p15.w1ty = 1 ; p15.w1ry = 1 ; p15.w2ty = 1 ; p15.w2ry = 1

    conn = [
        # skin-skin
        dict(p1=p01, p2=p02, func='SSycte', ycte1=0, ycte2=p02.b),
        dict(p1=p01, p2=p04, func='SSxcte', xcte1=0, xcte2=p04.a),
        dict(p1=p02, p2=p03, func='SSycte', ycte1=0, ycte2=p03.b),
        dict(p1=p02, p2=p05, func='SSxcte', xcte1=0, xcte2=p05.a),
        dict(p1=p03, p2=p06, func='SSxcte', xcte1=0, xcte2=p06.a),
        dict(p1=p04, p2=p05, func='SSycte', ycte1=0, ycte2=p05.b),
        dict(p1=p04, p2=p07, func='SSxcte', xcte1=0, xcte2=p07.a),
        dict(p1=p05, p2=p06, func='SSycte', ycte1=0, ycte2=p06.b),
        dict(p1=p05, p2=p08, func='SSxcte', xcte1=0, xcte2=p08.a),
        dict(p1=p06, p2=p09, func='SSxcte', xcte1=0, xcte2=p09.a),
        dict(p1=p07, p2=p08, func='SSycte', ycte1=0, ycte2=p08.b),
        dict(p1=p08, p2=p09, func='SSycte', ycte1=0, ycte2=p09.b),

        # skin-base
        dict(p1=p02, p2=p10, func='SB'),
        dict(p1=p05, p2=p12, func='SB', has_defect=has_defect), # defect
        dict(p1=p08, p2=p14, func='SB'),

        # base-base
        dict(p1=p10, p2=p12, func='SSxcte', xcte1=0, xcte2=p12.a),
        dict(p1=p12, p2=p14, func='SSxcte', xcte1=0, xcte2=p14.a),

        # base-flange
        dict(p1=p10, p2=p11, func='BFycte', ycte1=p10.b/2., ycte2=0),
        dict(p1=p12, p2=p13, func='BFycte', ycte1=p12.b/2., ycte2=0),
        dict(p1=p14, p2=p15, func='BFycte', ycte1=p14.b/2., ycte2=0),

        # flange-flange
        dict(p1=p11, p2=p13, func='SSxcte', xcte1=0, xcte2=p13.a),
        dict(p1=p13, p2=p15, func='SSxcte', xcte1=0, xcte2=p15.a),
        ]

    panels = [p01, p02, p03, p04, p05, p06, p07, p08, p09,
            p10, p11, p12, p13, p14, p15]
    skin = [p01, p02, p03, p04, p05, p06, p07, p08, p09]

    assy = PanelAssembly(panels)

    size = assy.get_size()

    valid_conn = []
    for connecti in conn:
        if connecti.get('has_defect'): # connecting if there is no defect
            continue
        valid_conn.append(connecti)

    k0 = assy.calc_k0(valid_conn)
    c = None
    if (run_static_case and not
            (Nxx_skin is None and Nxx_base is None and Nxx_flange is None)):
        fext = np.zeros(size)
        for p in [p07, p08, p09, p14, p15]:
            Nforces = 100
            fx = p.Nxx*p.b/(Nforces-1.)
            for i in range(Nforces):
                y = i*p.b/(Nforces-1.)
                if i == 0 or i == (Nforces - 1):
                    p.add_force(0, y, fx/2., 0, 0)
                else:
                    p.add_force(0, y, fx, 0, 0)
            fext[p.col_start: p.col_end] = p.calc_fext(silent=True)

        incs, cs = static(k0, -fext, silent=True)
        c = cs[0]

    kM = assy.calc_kM()
    kG = assy.calc_kG0(c=c)

    kA = 0
    for p in skin:
        # TODO the current approach has somewhat hiden settings
        #     check this strategy:
        #     - define module aerodynamics
        #     - function calc_kA inside a module piston_theory
        #     - pass piston_theory parameters and compute kA
        kA += p.calc_kA(size=size, row0=p.row_start, col0=p.col_start, silent=True, finalize=False)

    assert np.any(np.isnan(kA.data)) == False
    assert np.any(np.isinf(kA.data)) == False
    kA = csr_matrix(make_skew_symmetric(kA))

    eigvals, eigvecs = freq((k0 + kG + kA), kM, tol=0, sparse_solver=True, silent=True,
             sort=True, reduced_dof=False,
             num_eigvalues=25, num_eigvalues_print=5)

    if run_static_case:
        return assy, c, eigvals, eigvecs
    else:
        return assy, eigvals, eigvecs
def tstiff2d_1stiff_compression(a, b, ys, bb, bf, defect_a, mu, plyt,
        laminaprop, stack_skin, stack_base, stack_flange,
        Nxx_skin, Nxx_base, Nxx_flange, run_static_case=True,
        r=None, m=8, n=8, mb=None, nb=None, mf=None, nf=None,
        nx=None, ny=None, nxb=None, nyb=None, nxf=None, nyf=None):
    r"""Linear Buckling of T-Stiffened panel with debonding defect

    The panel assembly looks like::

        skin
         _________ _____ _________
        |         |     |         |
        |         |     |         |
        |   p01   | p02 |   p03   |
        |         |     |         |
        |_________|_____|_________|
        |   p04   | p05 |   p06   |      /\  x
        |_________|_____|_________|       |
        |         |     |         |       |
        |         |     |         |       |
        |   p07   | p08 |   p09   |
        |         |     |         |
        |         |     |         |
        |_________|_____|_________|
               loaded edge

                  base            flange
                   _____           _____
                  |     |         |     |
                  |     |         |     |
                  | p10 |         | p11 |
                  |     |         |     |
                  |_____|         |_____|
                  | p12 |         | p13 |
                  |_____|         |_____|
                  |     |         |     |
                  |     |         |     |
                  | p14 |         | p15 |
                  |     |         |     |
                  |     |         |     |
                  |_____|         |_____|
               loaded edge     loaded edge

    For more details about the theory involved, see
    [castro2017AssemblyModels]_.

    Parameters
    ----------

    a : float
        Total length of the assembly (along `x`).
    b : float
        Total width of the assembly (along `y`).
    ys : float
        Position of the stiffener along `y`.
    bb : float
        Stiffener's base width.
    bf : float
        Stiffener's flange width.
    defect_a : float
        Debonding defect/assembly length ratio.
    mu : float
        Material density.
    plyt : float
        Ply thickness.
    laminaprop : list or tuple
        Orthotropic lamina properties: `E_1, E_2, \nu_{12}, G_{12}, G_{13}, G_{23}`.
    stack_skin : list or tuple
        Stacking sequence for the skin.
    stack_base : list or tuple
        Stacking sequence for the stiffener's base.
    stack_flange : list or tuple
        Stacking sequence for the stiffener's flange.
    Nxx_skin : float
        Skin load distributed at the assembly edge at `x=0`.
    Nxx_base : float
        Stiffener's base load distributed at the assembly edge at `x=0`.
    Nxx_flange : float
        Stiffener's flange load distributed at the assembly edge at `x=0`.
    run_static_case : bool, optional
        If True a static analysis is run before the linear buckling analysis
        to compute the real membrane stress state along the domain, otherwise
        it is assumed constant values of `N_{xx}` for all components.
    r : float or None, optional
        Radius of the stiffened panel.
    m, n : int, optional
        Number of terms of the approximation function for the skin.
    mb, nb : int, optional
        Number of terms of the approximation function for the stiffener's base.
    mf, nf : int, optional
        Number of terms of the approximation function for the stiffener's
        flange.
    nx, ny, nxb, nyb, nxf, nyf : int, optional
        Define of integration points used for skin, stiffener's base or flange;
        along x and y. Keeping ``None`` will use the default (see
        :class:`.Panel`).

    Examples
    --------

    The following example is one of the test cases:

    .. literalinclude:: ../../../../../compmech/panel/assembly/tests/test_tstiff2d_assembly.py
        :pyobject: test_tstiff2d_1stiff_compression

    """
    defect = defect_a * a
    has_defect = True if defect > 0 else False
    defect = 0.33*a if defect == 0 else defect # to avoid weird domains
    aup = (a - defect)/2.
    alow = (a - defect)/2.
    bleft = b - ys - bb/2.
    bright = ys - bb/2.
    mb = m if mb is None else mb
    nb = n if nb is None else nb
    mf = m if mf is None else mf
    nf = n if nf is None else nf
    nx = m if nx is None else nx
    ny = n if ny is None else ny
    nxb = mb if nxb is None else nxb
    nyb = nb if nyb is None else nyb
    nxf = mf if nxf is None else nxf
    nyf = nf if nyf is None else nyf

    # skin panels
    p01 = Panel(group='skin', Nxx=Nxx_skin, x0=alow+defect, y0=ys+bb/2., a=aup, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, nx=nx, ny=ny)
    p02 = Panel(group='skin', Nxx=Nxx_skin, x0=alow+defect, y0=ys-bb/2., a=aup, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, nx=nx, ny=ny)
    p03 = Panel(group='skin', Nxx=Nxx_skin, x0=alow+defect, y0=0,        a=aup, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, nx=nx, ny=ny)
    # defect
    p04 = Panel(group='skin', Nxx=Nxx_skin, x0=alow, y0=ys+bb/2., a=defect, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, nx=nx, ny=ny)
    p05 = Panel(group='skin', Nxx=Nxx_skin, x0=alow, y0=ys-bb/2., a=defect, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, nx=nx, ny=ny)
    p06 = Panel(group='skin', Nxx=Nxx_skin, x0=alow, y0=0,        a=defect, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, nx=nx, ny=ny)
    #
    p07 = Panel(group='skin', Nxx=Nxx_skin, x0=0, y0=ys+bb/2., a=alow, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, nx=nx, ny=ny)
    p08 = Panel(group='skin', Nxx=Nxx_skin, x0=0, y0=ys-bb/2., a=alow, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, nx=nx, ny=ny)
    p09 = Panel(group='skin', Nxx=Nxx_skin, x0=0, y0=0,        a=alow, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu, nx=nx, ny=ny)

    # stiffeners
    p10 = Panel(group='base', Nxx=Nxx_base, x0=alow+defect, y0=ys-bb/2., a=aup, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu, nx=nxb, ny=nyb)
    p11 = Panel(group='flange', Nxx=Nxx_flange, x0=alow+defect, y0=0,        a=aup, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu, nx=nxf, ny=nyf)
    # defect
    p12 = Panel(group='base', Nxx=Nxx_base, x0=alow, y0=ys-bb/2., a=defect, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu, nx=nxb, ny=nyb)
    p13 = Panel(group='flange', Nxx=Nxx_flange, x0=alow, y0=0,        a=defect, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu, nx=nxf, ny=nyf)
    #
    p14 = Panel(group='base', Nxx=Nxx_base, x0=0, y0=ys-bb/2., a=alow, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu, nx=nxb, ny=nyb)
    p15 = Panel(group='flange', Nxx=Nxx_flange, x0=0, y0=0,        a=alow, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu, nx=nxf, ny=nyf)

    # boundary conditions
    p01.u1tx = 1 ; p01.u1rx = 1 ; p01.u2tx = 0 ; p01.u2rx = 1
    p01.v1tx = 1 ; p01.v1rx = 1 ; p01.v2tx = 0 ; p01.v2rx = 1
    p01.w1tx = 1 ; p01.w1rx = 1 ; p01.w2tx = 0 ; p01.w2rx = 1
    p01.u1ty = 1 ; p01.u1ry = 1 ; p01.u2ty = 1 ; p01.u2ry = 1
    p01.v1ty = 1 ; p01.v1ry = 1 ; p01.v2ty = 0 ; p01.v2ry = 1
    p01.w1ty = 1 ; p01.w1ry = 1 ; p01.w2ty = 0 ; p01.w2ry = 1

    p02.u1tx = 1 ; p02.u1rx = 1 ; p02.u2tx = 0 ; p02.u2rx = 1
    p02.v1tx = 1 ; p02.v1rx = 1 ; p02.v2tx = 0 ; p02.v2rx = 1
    p02.w1tx = 1 ; p02.w1rx = 1 ; p02.w2tx = 0 ; p02.w2rx = 1
    p02.u1ty = 1 ; p02.u1ry = 1 ; p02.u2ty = 1 ; p02.u2ry = 1
    p02.v1ty = 1 ; p02.v1ry = 1 ; p02.v2ty = 1 ; p02.v2ry = 1
    p02.w1ty = 1 ; p02.w1ry = 1 ; p02.w2ty = 1 ; p02.w2ry = 1

    p03.u1tx = 1 ; p03.u1rx = 1 ; p03.u2tx = 0 ; p03.u2rx = 1
    p03.v1tx = 1 ; p03.v1rx = 1 ; p03.v2tx = 0 ; p03.v2rx = 1
    p03.w1tx = 1 ; p03.w1rx = 1 ; p03.w2tx = 0 ; p03.w2rx = 1
    p03.u1ty = 1 ; p03.u1ry = 1 ; p03.u2ty = 1 ; p03.u2ry = 1
    p03.v1ty = 0 ; p03.v1ry = 1 ; p03.v2ty = 1 ; p03.v2ry = 1
    p03.w1ty = 0 ; p03.w1ry = 1 ; p03.w2ty = 1 ; p03.w2ry = 1

    p04.u1tx = 1 ; p04.u1rx = 1 ; p04.u2tx = 1 ; p04.u2rx = 1
    p04.v1tx = 1 ; p04.v1rx = 1 ; p04.v2tx = 1 ; p04.v2rx = 1
    p04.w1tx = 1 ; p04.w1rx = 1 ; p04.w2tx = 1 ; p04.w2rx = 1
    p04.u1ty = 1 ; p04.u1ry = 1 ; p04.u2ty = 1 ; p04.u2ry = 1
    p04.v1ty = 1 ; p04.v1ry = 1 ; p04.v2ty = 0 ; p04.v2ry = 1
    p04.w1ty = 1 ; p04.w1ry = 1 ; p04.w2ty = 0 ; p04.w2ry = 1

    p05.u1tx = 1 ; p05.u1rx = 1 ; p05.u2tx = 1 ; p05.u2rx = 1
    p05.v1tx = 1 ; p05.v1rx = 1 ; p05.v2tx = 1 ; p05.v2rx = 1
    p05.w1tx = 1 ; p05.w1rx = 1 ; p05.w2tx = 1 ; p05.w2rx = 1
    p05.u1ty = 1 ; p05.u1ry = 1 ; p05.u2ty = 1 ; p05.u2ry = 1
    p05.v1ty = 1 ; p05.v1ry = 1 ; p05.v2ty = 1 ; p05.v2ry = 1
    p05.w1ty = 1 ; p05.w1ry = 1 ; p05.w2ty = 1 ; p05.w2ry = 1

    p06.u1tx = 1 ; p06.u1rx = 1 ; p06.u2tx = 1 ; p06.u2rx = 1
    p06.v1tx = 1 ; p06.v1rx = 1 ; p06.v2tx = 1 ; p06.v2rx = 1
    p06.w1tx = 1 ; p06.w1rx = 1 ; p06.w2tx = 1 ; p06.w2rx = 1
    p06.u1ty = 1 ; p06.u1ry = 1 ; p06.u2ty = 1 ; p06.u2ry = 1
    p06.v1ty = 0 ; p06.v1ry = 1 ; p06.v2ty = 1 ; p06.v2ry = 1
    p06.w1ty = 0 ; p06.w1ry = 1 ; p06.w2ty = 1 ; p06.w2ry = 1

    if run_static_case:
        p07.u1tx = 1 ; p07.u1rx = 1 ; p07.u2tx = 1 ; p07.u2rx = 1
    else:
        p07.u1tx = 0 ; p07.u1rx = 1 ; p07.u2tx = 1 ; p07.u2rx = 1
    p07.v1tx = 0 ; p07.v1rx = 1 ; p07.v2tx = 1 ; p07.v2rx = 1
    p07.w1tx = 0 ; p07.w1rx = 1 ; p07.w2tx = 1 ; p07.w2rx = 1
    p07.u1ty = 1 ; p07.u1ry = 1 ; p07.u2ty = 1 ; p07.u2ry = 1
    p07.v1ty = 1 ; p07.v1ry = 1 ; p07.v2ty = 0 ; p07.v2ry = 1
    p07.w1ty = 1 ; p07.w1ry = 1 ; p07.w2ty = 0 ; p07.w2ry = 1

    if run_static_case:
        p08.u1tx = 1 ; p08.u1rx = 1 ; p08.u2tx = 1 ; p08.u2rx = 1
    else:
        p08.u1tx = 0 ; p08.u1rx = 1 ; p08.u2tx = 1 ; p08.u2rx = 1
    p08.v1tx = 0 ; p08.v1rx = 1 ; p08.v2tx = 1 ; p08.v2rx = 1
    p08.w1tx = 0 ; p08.w1rx = 1 ; p08.w2tx = 1 ; p08.w2rx = 1
    p08.u1ty = 1 ; p08.u1ry = 1 ; p08.u2ty = 1 ; p08.u2ry = 1
    p08.v1ty = 1 ; p08.v1ry = 1 ; p08.v2ty = 1 ; p08.v2ry = 1
    p08.w1ty = 1 ; p08.w1ry = 1 ; p08.w2ty = 1 ; p08.w2ry = 1

    if run_static_case:
        p09.u1tx = 1 ; p09.u1rx = 1 ; p09.u2tx = 1 ; p09.u2rx = 1
    else:
        p09.u1tx = 0 ; p09.u1rx = 1 ; p09.u2tx = 1 ; p09.u2rx = 1
    p09.v1tx = 0 ; p09.v1rx = 1 ; p09.v2tx = 1 ; p09.v2rx = 1
    p09.w1tx = 0 ; p09.w1rx = 1 ; p09.w2tx = 1 ; p09.w2rx = 1
    p09.u1ty = 1 ; p09.u1ry = 1 ; p09.u2ty = 1 ; p09.u2ry = 1
    p09.v1ty = 0 ; p09.v1ry = 1 ; p09.v2ty = 1 ; p09.v2ry = 1
    p09.w1ty = 0 ; p09.w1ry = 1 ; p09.w2ty = 1 ; p09.w2ry = 1

    # base up
    p10.u1tx = 1 ; p10.u1rx = 1 ; p10.u2tx = 1 ; p10.u2rx = 1
    p10.v1tx = 1 ; p10.v1rx = 1 ; p10.v2tx = 1 ; p10.v2rx = 1
    p10.w1tx = 1 ; p10.w1rx = 1 ; p10.w2tx = 1 ; p10.w2rx = 1
    p10.u1ty = 1 ; p10.u1ry = 1 ; p10.u2ty = 1 ; p10.u2ry = 1
    p10.v1ty = 1 ; p10.v1ry = 1 ; p10.v2ty = 1 ; p10.v2ry = 1
    p10.w1ty = 1 ; p10.w1ry = 1 ; p10.w2ty = 1 ; p10.w2ry = 1

    # flange up
    p11.u1tx = 1 ; p11.u1rx = 1 ; p11.u2tx = 0 ; p11.u2rx = 1
    p11.v1tx = 1 ; p11.v1rx = 1 ; p11.v2tx = 0 ; p11.v2rx = 1
    p11.w1tx = 1 ; p11.w1rx = 1 ; p11.w2tx = 0 ; p11.w2rx = 1
    p11.u1ty = 1 ; p11.u1ry = 1 ; p11.u2ty = 1 ; p11.u2ry = 1
    p11.v1ty = 1 ; p11.v1ry = 1 ; p11.v2ty = 1 ; p11.v2ry = 1
    p11.w1ty = 1 ; p11.w1ry = 1 ; p11.w2ty = 1 ; p11.w2ry = 1

    # base mid
    p12.u1tx = 1 ; p12.u1rx = 1 ; p12.u2tx = 1 ; p12.u2rx = 1
    p12.v1tx = 1 ; p12.v1rx = 1 ; p12.v2tx = 1 ; p12.v2rx = 1
    p12.w1tx = 1 ; p12.w1rx = 1 ; p12.w2tx = 1 ; p12.w2rx = 1
    p12.u1ty = 1 ; p12.u1ry = 1 ; p12.u2ty = 1 ; p12.u2ry = 1
    p12.v1ty = 1 ; p12.v1ry = 1 ; p12.v2ty = 1 ; p12.v2ry = 1
    p12.w1ty = 1 ; p12.w1ry = 1 ; p12.w2ty = 1 ; p12.w2ry = 1

    # flange mid
    p13.u1tx = 1 ; p13.u1rx = 1 ; p13.u2tx = 1 ; p13.u2rx = 1
    p13.v1tx = 1 ; p13.v1rx = 1 ; p13.v2tx = 1 ; p13.v2rx = 1
    p13.w1tx = 1 ; p13.w1rx = 1 ; p13.w2tx = 1 ; p13.w2rx = 1
    p13.u1ty = 1 ; p13.u1ry = 1 ; p13.u2ty = 1 ; p13.u2ry = 1
    p13.v1ty = 1 ; p13.v1ry = 1 ; p13.v2ty = 1 ; p13.v2ry = 1
    p13.w1ty = 1 ; p13.w1ry = 1 ; p13.w2ty = 1 ; p13.w2ry = 1

    # base low
    p14.u1tx = 1 ; p14.u1rx = 1 ; p14.u2tx = 1 ; p14.u2rx = 1
    p14.v1tx = 1 ; p14.v1rx = 1 ; p14.v2tx = 1 ; p14.v2rx = 1
    p14.w1tx = 1 ; p14.w1rx = 1 ; p14.w2tx = 1 ; p14.w2rx = 1
    p14.u1ty = 1 ; p14.u1ry = 1 ; p14.u2ty = 1 ; p14.u2ry = 1
    p14.v1ty = 1 ; p14.v1ry = 1 ; p14.v2ty = 1 ; p14.v2ry = 1
    p14.w1ty = 1 ; p14.w1ry = 1 ; p14.w2ty = 1 ; p14.w2ry = 1

    # flange low
    if run_static_case:
        p15.u1tx = 1 ; p15.u1rx = 1 ; p15.u2tx = 1 ; p15.u2rx = 1
    else:
        p15.u1tx = 0 ; p15.u1rx = 1 ; p15.u2tx = 1 ; p15.u2rx = 1
    p15.v1tx = 0 ; p15.v1rx = 1 ; p15.v2tx = 1 ; p15.v2rx = 1
    p15.w1tx = 0 ; p15.w1rx = 1 ; p15.w2tx = 1 ; p15.w2rx = 1
    p15.u1ty = 1 ; p15.u1ry = 1 ; p15.u2ty = 1 ; p15.u2ry = 1
    p15.v1ty = 1 ; p15.v1ry = 1 ; p15.v2ty = 1 ; p15.v2ry = 1
    p15.w1ty = 1 ; p15.w1ry = 1 ; p15.w2ty = 1 ; p15.w2ry = 1

    conn = [
        # skin-skin
        dict(p1=p01, p2=p02, func='SSycte', ycte1=0, ycte2=p02.b),
        dict(p1=p01, p2=p04, func='SSxcte', xcte1=0, xcte2=p04.a),
        dict(p1=p02, p2=p03, func='SSycte', ycte1=0, ycte2=p03.b),
        dict(p1=p02, p2=p05, func='SSxcte', xcte1=0, xcte2=p05.a),
        dict(p1=p03, p2=p06, func='SSxcte', xcte1=0, xcte2=p06.a),
        dict(p1=p04, p2=p05, func='SSycte', ycte1=0, ycte2=p05.b),
        dict(p1=p04, p2=p07, func='SSxcte', xcte1=0, xcte2=p07.a),
        dict(p1=p05, p2=p06, func='SSycte', ycte1=0, ycte2=p06.b),
        dict(p1=p05, p2=p08, func='SSxcte', xcte1=0, xcte2=p08.a),
        dict(p1=p06, p2=p09, func='SSxcte', xcte1=0, xcte2=p09.a),
        dict(p1=p07, p2=p08, func='SSycte', ycte1=0, ycte2=p08.b),
        dict(p1=p08, p2=p09, func='SSycte', ycte1=0, ycte2=p09.b),

        # skin-base
        dict(p1=p02, p2=p10, func='SB'),
        dict(p1=p05, p2=p12, func='SB', has_defect=has_defect), # defect
        dict(p1=p08, p2=p14, func='SB'),

        # base-base
        dict(p1=p10, p2=p12, func='SSxcte', xcte1=0, xcte2=p12.a),
        dict(p1=p12, p2=p14, func='SSxcte', xcte1=0, xcte2=p14.a),

        # base-flange
        dict(p1=p10, p2=p11, func='BFycte', ycte1=p10.b/2., ycte2=0),
        dict(p1=p12, p2=p13, func='BFycte', ycte1=p12.b/2., ycte2=0),
        dict(p1=p14, p2=p15, func='BFycte', ycte1=p14.b/2., ycte2=0),

        # flange-flange
        dict(p1=p11, p2=p13, func='SSxcte', xcte1=0, xcte2=p13.a),
        dict(p1=p13, p2=p15, func='SSxcte', xcte1=0, xcte2=p15.a),
        ]

    panels = [p01, p02, p03, p04, p05, p06, p07, p08, p09,
            p10, p11, p12, p13, p14, p15]

    assy = PanelAssembly(panels)

    size = sum([3*p.m*p.n for p in panels])

    valid_conn = []
    for connecti in conn:
        if connecti.get('has_defect'): # connecting if there is no defect
            continue
        valid_conn.append(connecti)

    k0 = assy.calc_k0(valid_conn)
    c = None
    if run_static_case:
        fext = np.zeros(size)
        for p in [p07, p08, p09, p14, p15]:
            Nforces = 100
            fx = p.Nxx*p.b/(Nforces-1.)
            for i in range(Nforces):
                y = i*p.b/(Nforces-1.)
                if i == 0 or i == (Nforces - 1):
                    p.add_force(0, y, fx/2., 0, 0)
                else:
                    p.add_force(0, y, fx, 0, 0)
            fext[p.col_start: p.col_end] = p.calc_fext(silent=True)

        incs, cs = static(k0, -fext, silent=True)
        c = cs[0]

    kG = assy.calc_kG0(c=c)

    eigvals = eigvecs = None
    eigvals, eigvecs = lb(k0, kG, tol=0, sparse_solver=True, silent=True,
             num_eigvalues=25, num_eigvalues_print=5)

    if run_static_case:
        return assy, c, eigvals, eigvecs
    else:
        return assy, eigvals, eigvecs
示例#7
0
def test_panel_lb():
    for model in ['plate_clt_donnell_bardell',
                  'plate_clt_donnell_bardell_w',
                  'cpanel_clt_donnell_bardell',
                  'kpanel_clt_donnell_bardell']:
        print('Linear buckling for model {0}'.format(model))
        # ssss
        p = Panel()
        p.m = 12
        p.n = 13
        p.stack = [0, 90, -45, +45]
        p.plyt = 0.125e-3
        p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
        p.model = model
        p.a = 1.
        p.b = 0.5
        p.r = 1.e8
        p.alphadeg = 0.
        p.Nxx = -1
        k0 = p.calc_k0(silent=True)
        kG0 = p.calc_kG0(silent=True)
        eigvals, eigvecs = lb(k0, kG0, silent=True)
        if '_w' in model:
            assert np.isclose(eigvals[0], 88.47696, atol=0.1, rtol=0)
        else:
            assert np.isclose(eigvals[0], 85.2912, atol=0.1, rtol=0)

        p.Nxx = 0
        p.Nyy = -1
        k0 = p.calc_k0(silent=True)
        kG0 = p.calc_kG0(silent=True)
        eigvals, eigvecs = lb(k0, kG0, silent=True)
        if '_w' in model:
            assert np.isclose(eigvals[0], 26.45882, atol=0.1, rtol=0)
        else:
            assert np.isclose(eigvals[0], 25.17562, atol=0.1, rtol=0)

        # ssfs
        p = Panel()
        p.u2ty = 1
        p.v2ty = 1
        p.w2ty = 1
        p.u2ry = 1
        p.v2ry = 1
        p.m = 12
        p.n = 13
        p.stack = [0, 90, -45, +45]
        p.plyt = 0.125e-3
        p.laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
        p.model = model
        p.a = 1.
        p.b = 0.5
        p.r = 1.e8
        p.alphadeg = 0.
        p.Nxx = -1
        k0 = p.calc_k0(silent=True)
        kG0 = p.calc_kG0(silent=True)
        eigvals, eigvecs = lb(k0, kG0, silent=True)
        if '_w' in model:
            assert np.isclose(eigvals[0], 17.14427, atol=0.1, rtol=0)
        else:
            assert np.isclose(eigvals[0], 15.842356, atol=0.1, rtol=0)

        p.u2tx = 1
        p.v2tx = 1
        p.w2tx = 1
        p.u2rx = 1
        p.v2rx = 1
        p.u2ty = 0
        p.v2ty = 0
        p.w2ty = 0
        p.u2ry = 0
        p.v2ry = 0
        p.Nxx = 0
        p.Nyy = -1
        k0 = p.calc_k0(silent=True)
        kG0 = p.calc_kG0(silent=True)
        eigvals, eigvecs = lb(k0, kG0, silent=True)
        if '_w' in model:
            assert np.isclose(eigvals[0], 15.809986, atol=0.1, rtol=0)
        else:
            assert np.isclose(eigvals[0], 13.9421988, atol=0.1, rtol=0)
示例#8
0
def test_4panels_kt_kr():
    """Compare result of 4 assembled panels with single-domain results

    The panel assembly looks like::

         _________ _____
        |         |     |
        |         |     |
        |   p01   | p02 |
        |         |     |
        |_________|_____|
        |   p03   | p04 |
        |         |     |
        |         |     |
        |         |     |
        |         |     |
        |         |     |
        |_________|_____|

    """
    print('Testing validity of the default kt and kr values')

    plyt = 1.e-3 * 0.125
    laminaprop = (142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9)
    stack = [0, 45, -45, 90, -45, 45, 0]
    lam = laminate.read_stack(stack=stack, plyt=plyt, laminaprop=laminaprop)

    mu = 1.3e3

    r = 10.
    m = 8
    n = 8

    a1 = 1.5
    a2 = 1.5
    a3 = 2.5
    a4 = 2.5
    b1 = 1.5
    b2 = 0.5
    b3 = 1.5
    b4 = 0.5

    A11 = lam.ABD[0, 0]
    A22 = lam.ABD[1, 1]
    D11 = lam.ABD[3, 3]
    D22 = lam.ABD[4, 4]

    p01 = Panel(group='panels',
                x0=a3,
                y0=b2,
                a=a1,
                b=b1,
                r=r,
                m=m,
                n=n,
                plyt=plyt,
                stack=stack,
                laminaprop=laminaprop,
                mu=mu)
    p02 = Panel(group='panels',
                x0=a3,
                y0=0,
                a=a2,
                b=b2,
                r=r,
                m=m,
                n=n,
                plyt=plyt,
                stack=stack,
                laminaprop=laminaprop,
                mu=mu)
    p03 = Panel(group='panels',
                x0=0,
                y0=b2,
                a=a3,
                b=b3,
                r=r,
                m=m,
                n=n,
                plyt=plyt,
                stack=stack,
                laminaprop=laminaprop,
                mu=mu)
    p04 = Panel(group='panels',
                x0=0,
                y0=0,
                a=a4,
                b=b4,
                r=r,
                m=m,
                n=n,
                plyt=plyt,
                stack=stack,
                laminaprop=laminaprop,
                mu=mu)

    kt13, kr13 = connections.calc_kt_kr(p01, p03, 'xcte')
    kt24, kr24 = connections.calc_kt_kr(p02, p04, 'xcte')
    kt12, kr12 = connections.calc_kt_kr(p01, p02, 'ycte')
    kt34, kr34 = connections.calc_kt_kr(p03, p04, 'ycte')

    # boundary conditions
    p01.u1tx = 1
    p01.u1rx = 1
    p01.u2tx = 0
    p01.u2rx = 1
    p01.v1tx = 1
    p01.v1rx = 1
    p01.v2tx = 0
    p01.v2rx = 1
    p01.w1tx = 1
    p01.w1rx = 1
    p01.w2tx = 0
    p01.w2rx = 1
    p01.u1ty = 1
    p01.u1ry = 1
    p01.u2ty = 0
    p01.u2ry = 1
    p01.v1ty = 1
    p01.v1ry = 1
    p01.v2ty = 0
    p01.v2ry = 1
    p01.w1ty = 1
    p01.w1ry = 1
    p01.w2ty = 0
    p01.w2ry = 1

    p02.u1tx = 1
    p02.u1rx = 1
    p02.u2tx = 0
    p02.u2rx = 1
    p02.v1tx = 1
    p02.v1rx = 1
    p02.v2tx = 0
    p02.v2rx = 1
    p02.w1tx = 1
    p02.w1rx = 1
    p02.w2tx = 0
    p02.w2rx = 1
    p02.u1ty = 0
    p02.u1ry = 1
    p02.u2ty = 1
    p02.u2ry = 1
    p02.v1ty = 0
    p02.v1ry = 1
    p02.v2ty = 1
    p02.v2ry = 1
    p02.w1ty = 0
    p02.w1ry = 1
    p02.w2ty = 1
    p02.w2ry = 1

    p03.u1tx = 0
    p03.u1rx = 1
    p03.u2tx = 1
    p03.u2rx = 1
    p03.v1tx = 0
    p03.v1rx = 1
    p03.v2tx = 1
    p03.v2rx = 1
    p03.w1tx = 0
    p03.w1rx = 1
    p03.w2tx = 1
    p03.w2rx = 1
    p03.u1ty = 1
    p03.u1ry = 1
    p03.u2ty = 0
    p03.u2ry = 1
    p03.v1ty = 1
    p03.v1ry = 1
    p03.v2ty = 0
    p03.v2ry = 1
    p03.w1ty = 1
    p03.w1ry = 1
    p03.w2ty = 0
    p03.w2ry = 1

    p04.u1tx = 0
    p04.u1rx = 1
    p04.u2tx = 1
    p04.u2rx = 1
    p04.v1tx = 0
    p04.v1rx = 1
    p04.v2tx = 1
    p04.v2rx = 1
    p04.w1tx = 0
    p04.w1rx = 1
    p04.w2tx = 1
    p04.w2rx = 1
    p04.u1ty = 0
    p04.u1ry = 1
    p04.u2ty = 1
    p04.u2ry = 1
    p04.v1ty = 0
    p04.v1ry = 1
    p04.v2ty = 1
    p04.v2ry = 1
    p04.w1ty = 0
    p04.w1ry = 1
    p04.w2ty = 1
    p04.w2ry = 1

    conndict = [
        dict(p1=p01,
             p2=p02,
             func='SSycte',
             ycte1=0,
             ycte2=p02.b,
             kt=kt12,
             kr=kr12),
        dict(p1=p01,
             p2=p03,
             func='SSxcte',
             xcte1=0,
             xcte2=p03.a,
             kt=kt13,
             kr=kr13),
        dict(p1=p02,
             p2=p04,
             func='SSxcte',
             xcte1=0,
             xcte2=p04.a,
             kt=kt24,
             kr=kr24),
        dict(p1=p03,
             p2=p04,
             func='SSycte',
             ycte1=0,
             ycte2=p04.b,
             kt=kt34,
             kr=kr34),
    ]

    panels = [p01, p02, p03, p04]

    size = sum([3 * p.m * p.n for p in panels])

    k0 = 0
    kM = 0

    row0 = 0
    col0 = 0
    for p in panels:
        k0 += p.calc_k0(row0=row0,
                        col0=col0,
                        size=size,
                        silent=True,
                        finalize=False)
        kM += p.calc_kM(row0=row0,
                        col0=col0,
                        size=size,
                        silent=True,
                        finalize=False)
        p.row_start = row0
        p.col_start = col0
        row0 += 3 * p.m * p.n
        col0 += 3 * p.m * p.n
        p.row_end = row0
        p.col_end = col0

    for conn in conndict:
        if conn.get('has_deffect'):  # connecting if there is no deffect
            continue
        p1 = conn['p1']
        p2 = conn['p2']
        if conn['func'] == 'SSycte':
            k0 += connections.kCSSycte.fkCSSycte11(conn['kt'],
                                                   conn['kr'],
                                                   p1,
                                                   conn['ycte1'],
                                                   size,
                                                   p1.row_start,
                                                   col0=p1.col_start)
            k0 += connections.kCSSycte.fkCSSycte12(conn['kt'],
                                                   conn['kr'],
                                                   p1,
                                                   p2,
                                                   conn['ycte1'],
                                                   conn['ycte2'],
                                                   size,
                                                   p1.row_start,
                                                   col0=p2.col_start)
            k0 += connections.kCSSycte.fkCSSycte22(conn['kt'],
                                                   conn['kr'],
                                                   p1,
                                                   p2,
                                                   conn['ycte2'],
                                                   size,
                                                   p2.row_start,
                                                   col0=p2.col_start)
        elif conn['func'] == 'SSxcte':
            k0 += connections.kCSSxcte.fkCSSxcte11(conn['kt'],
                                                   conn['kr'],
                                                   p1,
                                                   conn['xcte1'],
                                                   size,
                                                   p1.row_start,
                                                   col0=p1.col_start)
            k0 += connections.kCSSxcte.fkCSSxcte12(conn['kt'],
                                                   conn['kr'],
                                                   p1,
                                                   p2,
                                                   conn['xcte1'],
                                                   conn['xcte2'],
                                                   size,
                                                   p1.row_start,
                                                   col0=p2.col_start)
            k0 += connections.kCSSxcte.fkCSSxcte22(conn['kt'],
                                                   conn['kr'],
                                                   p1,
                                                   p2,
                                                   conn['xcte2'],
                                                   size,
                                                   p2.row_start,
                                                   col0=p2.col_start)

    assert np.any(np.isnan(k0.data)) == False
    assert np.any(np.isinf(k0.data)) == False
    k0 = csr_matrix(make_symmetric(k0))
    assert np.any(np.isnan(kM.data)) == False
    assert np.any(np.isinf(kM.data)) == False
    kM = csr_matrix(make_symmetric(kM))

    eigvals, eigvecs = freq(k0,
                            kM,
                            tol=0,
                            sparse_solver=True,
                            silent=True,
                            sort=True,
                            reduced_dof=False,
                            num_eigvalues=25,
                            num_eigvalues_print=5)

    # Results for single panel
    m = 15
    n = 15
    singlepanel = Panel(a=(a1 + a3),
                        b=(b1 + b2),
                        r=r,
                        m=m,
                        n=n,
                        plyt=plyt,
                        stack=stack,
                        laminaprop=laminaprop,
                        mu=mu)
    singlepanel.freq(silent=True)

    assert np.isclose(eigvals[0], singlepanel.eigvals[0], atol=0.01, rtol=0.01)
示例#9
0
def tstiff2d_1stiff_freq(a, b, ys, bb, bf, defect_a, mu, plyt, laminaprop,
        stack_skin, stack_base, stack_flange,
        r=None, m=8, n=8, mb=None, nb=None, mf=None, nf=None):
    r"""Frequency T-Stiffened Panel with possible defect at middle

    For more details about each parameter and the aerodynamic formulation see
    Ref. [castro2016FlutterPanel]_ .

    For more details about the theory involved on the assembly of panels, see
    [castro2017AssemblyModels]_.

    The panel assembly looks like::

        skin
         _________ _____ _________
        |         |     |         |
        |         |     |         |
        |   p01   | p02 |   p03   |
        |         |     |         |
        |_________|_____|_________|
        |   p04   | p05 |   p06   |
        |_________|_____|_________|
        |         |     |         |
        |         |     |         |
        |   p07   | p08 |   p09   |
        |         |     |         |
        |         |     |         |
        |_________|_____|_________|

                  base            flange
                   _____           _____
                  |     |         |     |
                  |     |         |     |
                  | p10 |         | p11 |
                  |     |         |     |
                  |_____|         |_____|
                  | p12 |         | p13 |
                  |_____|         |_____|
                  |     |         |     |
                  |     |         |     |
                  | p14 |         | p15 |
                  |     |         |     |
                  |     |         |     |
                  |_____|         |_____|

    Parameters
    ----------

    a : float
        Total length of the assembly (along `x`).
    b : float
        Total width of the assembly (along `y`).
    ys : float
        Position of the stiffener along `y`.
    bb : float
        Stiffener's base width.
    bf : float
        Stiffener's flange width.
    defect_a : float
        Debonding defect/assembly length ratio.
    mu : float
        Material density.
    plyt : float
        Ply thickness.
    laminaprop : list or tuple
        Orthotropic lamina properties: `E_1, E_2, \nu_{12}, G_{12}, G_{13}, G_{23}`.
    stack_skin : list or tuple
        Stacking sequence for the skin.
    stack_base : list or tuple
        Stacking sequence for the stiffener's base.
    stack_flange : list or tuple
        Stacking sequence for the stiffener's flange.
    r : float or None, optional
        Radius of the stiffened panel.
    m, n : int, optional
        Number of terms of the approximation function for the skin.
    mb, nb : int, optional
        Number of terms of the approximation function for the stiffener's base.
    mf, nf : int, optional
        Number of terms of the approximation function for the stiffener's
        flange.

    Examples
    --------

    The following example is one of the test cases:

    .. literalinclude:: ../../../../../compmech/panel/assembly/tests/test_tstiff2d_assembly.py
        :pyobject: test_tstiff2d_1stiff_freq


    """
    defect = defect_a * a
    has_defect = True if defect > 0 else False
    defect = 0.33*a if defect == 0 else defect # to avoid weird domains
    aup = (a - defect)/2.
    alow = (a - defect)/2.
    bleft = b - ys - bb/2.
    bright = ys - bb/2.
    mb = m if mb is None else mb
    nb = n if nb is None else nb
    mf = m if mf is None else mf
    nf = n if nf is None else nf
    # skin panels
    p01 = Panel(group='skin', x0=alow+defect, y0=ys+bb/2., a=aup, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
    p02 = Panel(group='skin', x0=alow+defect, y0=ys-bb/2., a=aup, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
    p03 = Panel(group='skin', x0=alow+defect, y0=0,        a=aup, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
    # defect
    p04 = Panel(group='skin', x0=alow, y0=ys+bb/2., a=defect, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
    p05 = Panel(group='skin', x0=alow, y0=ys-bb/2., a=defect, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
    p06 = Panel(group='skin', x0=alow, y0=0,        a=defect, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
    #
    p07 = Panel(group='skin', x0=0, y0=ys+bb/2., a=alow, b=bleft, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
    p08 = Panel(group='skin', x0=0, y0=ys-bb/2., a=alow, b=bb, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)
    p09 = Panel(group='skin', x0=0, y0=0,        a=alow, b=bright, r=r, m=m, n=n, plyt=plyt, stack=stack_skin, laminaprop=laminaprop, mu=mu)

    # stiffeners
    p10 = Panel(group='base', x0=alow+defect, y0=ys-bb/2., a=aup, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu)
    p11 = Panel(group='flange', x0=alow+defect, y0=0,        a=aup, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu)
    # defect
    p12 = Panel(group='base', x0=alow, y0=ys-bb/2., a=defect, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu)
    p13 = Panel(group='flange', x0=alow, y0=0,        a=defect, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu)
    #
    p14 = Panel(group='base', x0=0, y0=ys-bb/2., a=alow, b=bb, r=r, m=mb, n=nb, plyt=plyt, stack=stack_base, laminaprop=laminaprop, mu=mu)
    p15 = Panel(group='flange', x0=0, y0=0,        a=alow, b=bf, m=mf, n=nf, plyt=plyt, stack=stack_flange, laminaprop=laminaprop, mu=mu)

    # boundary conditions
    p01.u1tx = 1 ; p01.u1rx = 1 ; p01.u2tx = 0 ; p01.u2rx = 1
    p01.v1tx = 1 ; p01.v1rx = 1 ; p01.v2tx = 0 ; p01.v2rx = 1
    p01.w1tx = 1 ; p01.w1rx = 1 ; p01.w2tx = 0 ; p01.w2rx = 1
    p01.u1ty = 1 ; p01.u1ry = 1 ; p01.u2ty = 0 ; p01.u2ry = 1
    p01.v1ty = 1 ; p01.v1ry = 1 ; p01.v2ty = 0 ; p01.v2ry = 1
    p01.w1ty = 1 ; p01.w1ry = 1 ; p01.w2ty = 0 ; p01.w2ry = 1

    p02.u1tx = 1 ; p02.u1rx = 1 ; p02.u2tx = 0 ; p02.u2rx = 1
    p02.v1tx = 1 ; p02.v1rx = 1 ; p02.v2tx = 0 ; p02.v2rx = 1
    p02.w1tx = 1 ; p02.w1rx = 1 ; p02.w2tx = 0 ; p02.w2rx = 1
    p02.u1ty = 1 ; p02.u1ry = 1 ; p02.u2ty = 1 ; p02.u2ry = 1
    p02.v1ty = 1 ; p02.v1ry = 1 ; p02.v2ty = 1 ; p02.v2ry = 1
    p02.w1ty = 1 ; p02.w1ry = 1 ; p02.w2ty = 1 ; p02.w2ry = 1

    p03.u1tx = 1 ; p03.u1rx = 1 ; p03.u2tx = 0 ; p03.u2rx = 1
    p03.v1tx = 1 ; p03.v1rx = 1 ; p03.v2tx = 0 ; p03.v2rx = 1
    p03.w1tx = 1 ; p03.w1rx = 1 ; p03.w2tx = 0 ; p03.w2rx = 1
    p03.u1ty = 0 ; p03.u1ry = 1 ; p03.u2ty = 1 ; p03.u2ry = 1
    p03.v1ty = 0 ; p03.v1ry = 1 ; p03.v2ty = 1 ; p03.v2ry = 1
    p03.w1ty = 0 ; p03.w1ry = 1 ; p03.w2ty = 1 ; p03.w2ry = 1

    p04.u1tx = 1 ; p04.u1rx = 1 ; p04.u2tx = 1 ; p04.u2rx = 1
    p04.v1tx = 1 ; p04.v1rx = 1 ; p04.v2tx = 1 ; p04.v2rx = 1
    p04.w1tx = 1 ; p04.w1rx = 1 ; p04.w2tx = 1 ; p04.w2rx = 1
    p04.u1ty = 1 ; p04.u1ry = 1 ; p04.u2ty = 0 ; p04.u2ry = 1
    p04.v1ty = 1 ; p04.v1ry = 1 ; p04.v2ty = 0 ; p04.v2ry = 1
    p04.w1ty = 1 ; p04.w1ry = 1 ; p04.w2ty = 0 ; p04.w2ry = 1

    p05.u1tx = 1 ; p05.u1rx = 1 ; p05.u2tx = 1 ; p05.u2rx = 1
    p05.v1tx = 1 ; p05.v1rx = 1 ; p05.v2tx = 1 ; p05.v2rx = 1
    p05.w1tx = 1 ; p05.w1rx = 1 ; p05.w2tx = 1 ; p05.w2rx = 1
    p05.u1ty = 1 ; p05.u1ry = 1 ; p05.u2ty = 1 ; p05.u2ry = 1
    p05.v1ty = 1 ; p05.v1ry = 1 ; p05.v2ty = 1 ; p05.v2ry = 1
    p05.w1ty = 1 ; p05.w1ry = 1 ; p05.w2ty = 1 ; p05.w2ry = 1

    p06.u1tx = 1 ; p06.u1rx = 1 ; p06.u2tx = 1 ; p06.u2rx = 1
    p06.v1tx = 1 ; p06.v1rx = 1 ; p06.v2tx = 1 ; p06.v2rx = 1
    p06.w1tx = 1 ; p06.w1rx = 1 ; p06.w2tx = 1 ; p06.w2rx = 1
    p06.u1ty = 0 ; p06.u1ry = 1 ; p06.u2ty = 1 ; p06.u2ry = 1
    p06.v1ty = 0 ; p06.v1ry = 1 ; p06.v2ty = 1 ; p06.v2ry = 1
    p06.w1ty = 0 ; p06.w1ry = 1 ; p06.w2ty = 1 ; p06.w2ry = 1

    p07.u1tx = 0 ; p07.u1rx = 1 ; p07.u2tx = 1 ; p07.u2rx = 1
    p07.v1tx = 0 ; p07.v1rx = 1 ; p07.v2tx = 1 ; p07.v2rx = 1
    p07.w1tx = 0 ; p07.w1rx = 1 ; p07.w2tx = 1 ; p07.w2rx = 1
    p07.u1ty = 1 ; p07.u1ry = 1 ; p07.u2ty = 0 ; p07.u2ry = 1
    p07.v1ty = 1 ; p07.v1ry = 1 ; p07.v2ty = 0 ; p07.v2ry = 1
    p07.w1ty = 1 ; p07.w1ry = 1 ; p07.w2ty = 0 ; p07.w2ry = 1

    p08.u1tx = 0 ; p08.u1rx = 1 ; p08.u2tx = 1 ; p08.u2rx = 1
    p08.v1tx = 0 ; p08.v1rx = 1 ; p08.v2tx = 1 ; p08.v2rx = 1
    p08.w1tx = 0 ; p08.w1rx = 1 ; p08.w2tx = 1 ; p08.w2rx = 1
    p08.u1ty = 1 ; p08.u1ry = 1 ; p08.u2ty = 1 ; p08.u2ry = 1
    p08.v1ty = 1 ; p08.v1ry = 1 ; p08.v2ty = 1 ; p08.v2ry = 1
    p08.w1ty = 1 ; p08.w1ry = 1 ; p08.w2ty = 1 ; p08.w2ry = 1

    p09.u1tx = 0 ; p09.u1rx = 1 ; p09.u2tx = 1 ; p09.u2rx = 1
    p09.v1tx = 0 ; p09.v1rx = 1 ; p09.v2tx = 1 ; p09.v2rx = 1
    p09.w1tx = 0 ; p09.w1rx = 1 ; p09.w2tx = 1 ; p09.w2rx = 1
    p09.u1ty = 0 ; p09.u1ry = 1 ; p09.u2ty = 1 ; p09.u2ry = 1
    p09.v1ty = 0 ; p09.v1ry = 1 ; p09.v2ty = 1 ; p09.v2ry = 1
    p09.w1ty = 0 ; p09.w1ry = 1 ; p09.w2ty = 1 ; p09.w2ry = 1

    # base up
    p10.u1tx = 1 ; p10.u1rx = 1 ; p10.u2tx = 1 ; p10.u2rx = 1
    p10.v1tx = 1 ; p10.v1rx = 1 ; p10.v2tx = 1 ; p10.v2rx = 1
    p10.w1tx = 1 ; p10.w1rx = 1 ; p10.w2tx = 1 ; p10.w2rx = 1
    p10.u1ty = 1 ; p10.u1ry = 1 ; p10.u2ty = 1 ; p10.u2ry = 1
    p10.v1ty = 1 ; p10.v1ry = 1 ; p10.v2ty = 1 ; p10.v2ry = 1
    p10.w1ty = 1 ; p10.w1ry = 1 ; p10.w2ty = 1 ; p10.w2ry = 1

    # flange up
    p11.u1tx = 1 ; p11.u1rx = 1 ; p11.u2tx = 0 ; p11.u2rx = 1
    p11.v1tx = 1 ; p11.v1rx = 1 ; p11.v2tx = 0 ; p11.v2rx = 1
    p11.w1tx = 1 ; p11.w1rx = 1 ; p11.w2tx = 0 ; p11.w2rx = 1
    p11.u1ty = 1 ; p11.u1ry = 1 ; p11.u2ty = 1 ; p11.u2ry = 1
    p11.v1ty = 1 ; p11.v1ry = 1 ; p11.v2ty = 1 ; p11.v2ry = 1
    p11.w1ty = 1 ; p11.w1ry = 1 ; p11.w2ty = 1 ; p11.w2ry = 1

    # base mid
    p12.u1tx = 1 ; p12.u1rx = 1 ; p12.u2tx = 1 ; p12.u2rx = 1
    p12.v1tx = 1 ; p12.v1rx = 1 ; p12.v2tx = 1 ; p12.v2rx = 1
    p12.w1tx = 1 ; p12.w1rx = 1 ; p12.w2tx = 1 ; p12.w2rx = 1
    p12.u1ty = 1 ; p12.u1ry = 1 ; p12.u2ty = 1 ; p12.u2ry = 1
    p12.v1ty = 1 ; p12.v1ry = 1 ; p12.v2ty = 1 ; p12.v2ry = 1
    p12.w1ty = 1 ; p12.w1ry = 1 ; p12.w2ty = 1 ; p12.w2ry = 1

    # flange mid
    p13.u1tx = 1 ; p13.u1rx = 1 ; p13.u2tx = 1 ; p13.u2rx = 1
    p13.v1tx = 1 ; p13.v1rx = 1 ; p13.v2tx = 1 ; p13.v2rx = 1
    p13.w1tx = 1 ; p13.w1rx = 1 ; p13.w2tx = 1 ; p13.w2rx = 1
    p13.u1ty = 1 ; p13.u1ry = 1 ; p13.u2ty = 1 ; p13.u2ry = 1
    p13.v1ty = 1 ; p13.v1ry = 1 ; p13.v2ty = 1 ; p13.v2ry = 1
    p13.w1ty = 1 ; p13.w1ry = 1 ; p13.w2ty = 1 ; p13.w2ry = 1

    # base low
    p14.u1tx = 1 ; p14.u1rx = 1 ; p14.u2tx = 1 ; p14.u2rx = 1
    p14.v1tx = 1 ; p14.v1rx = 1 ; p14.v2tx = 1 ; p14.v2rx = 1
    p14.w1tx = 1 ; p14.w1rx = 1 ; p14.w2tx = 1 ; p14.w2rx = 1
    p14.u1ty = 1 ; p14.u1ry = 1 ; p14.u2ty = 1 ; p14.u2ry = 1
    p14.v1ty = 1 ; p14.v1ry = 1 ; p14.v2ty = 1 ; p14.v2ry = 1
    p14.w1ty = 1 ; p14.w1ry = 1 ; p14.w2ty = 1 ; p14.w2ry = 1

    # flange low
    p15.u1tx = 0 ; p15.u1rx = 1 ; p15.u2tx = 1 ; p15.u2rx = 1
    p15.v1tx = 0 ; p15.v1rx = 1 ; p15.v2tx = 1 ; p15.v2rx = 1
    p15.w1tx = 0 ; p15.w1rx = 1 ; p15.w2tx = 1 ; p15.w2rx = 1
    p15.u1ty = 1 ; p15.u1ry = 1 ; p15.u2ty = 1 ; p15.u2ry = 1
    p15.v1ty = 1 ; p15.v1ry = 1 ; p15.v2ty = 1 ; p15.v2ry = 1
    p15.w1ty = 1 ; p15.w1ry = 1 ; p15.w2ty = 1 ; p15.w2ry = 1

    conn = [
        # skin-skin
        dict(p1=p01, p2=p02, func='SSycte', ycte1=0, ycte2=p02.b),
        dict(p1=p01, p2=p04, func='SSxcte', xcte1=0, xcte2=p04.a),
        dict(p1=p02, p2=p03, func='SSycte', ycte1=0, ycte2=p03.b),
        dict(p1=p02, p2=p05, func='SSxcte', xcte1=0, xcte2=p05.a),
        dict(p1=p03, p2=p06, func='SSxcte', xcte1=0, xcte2=p06.a),
        dict(p1=p04, p2=p05, func='SSycte', ycte1=0, ycte2=p05.b),
        dict(p1=p04, p2=p07, func='SSxcte', xcte1=0, xcte2=p07.a),
        dict(p1=p05, p2=p06, func='SSycte', ycte1=0, ycte2=p06.b),
        dict(p1=p05, p2=p08, func='SSxcte', xcte1=0, xcte2=p08.a),
        dict(p1=p06, p2=p09, func='SSxcte', xcte1=0, xcte2=p09.a),
        dict(p1=p07, p2=p08, func='SSycte', ycte1=0, ycte2=p08.b),
        dict(p1=p08, p2=p09, func='SSycte', ycte1=0, ycte2=p09.b),

        # skin-base
        dict(p1=p02, p2=p10, func='SB'),
        dict(p1=p05, p2=p12, func='SB', has_defect=has_defect), # defect
        dict(p1=p08, p2=p14, func='SB'),

        # base-base
        dict(p1=p10, p2=p12, func='SSxcte', xcte1=0, xcte2=p12.a),
        dict(p1=p12, p2=p14, func='SSxcte', xcte1=0, xcte2=p14.a),

        # base-flange
        dict(p1=p10, p2=p11, func='BFycte', ycte1=p10.b/2., ycte2=0),
        dict(p1=p12, p2=p13, func='BFycte', ycte1=p12.b/2., ycte2=0),
        dict(p1=p14, p2=p15, func='BFycte', ycte1=p14.b/2., ycte2=0),

        # flange-flange
        dict(p1=p11, p2=p13, func='SSxcte', xcte1=0, xcte2=p13.a),
        dict(p1=p13, p2=p15, func='SSxcte', xcte1=0, xcte2=p15.a),
        ]

    panels = [p01, p02, p03, p04, p05, p06, p07, p08, p09,
            p10, p11, p12, p13, p14, p15]
    skin = [p01, p02, p03, p04, p05, p06, p07, p08, p09]
    base = [p10, p12, p14]
    flange = [p11, p13, p15]

    assy = PanelAssembly(panels)

    size = assy.get_size()

    valid_conn = []
    for connecti in conn:
        if connecti.get('has_defect'):
            continue
        valid_conn.append(connecti)

    k0 = assy.calc_k0(conn=valid_conn)
    kM = assy.calc_kM()

    eigvals, eigvecs = freq(k0, kM, tol=0, sparse_solver=True, silent=True,
             sort=True, reduced_dof=False,
             num_eigvalues=25, num_eigvalues_print=5)

    return assy, eigvals, eigvecs