def ke_cbar(model: BDF, elem: CBAR, fdtype: str = 'float64'):
"""get the elemental stiffness matrix in the basic frame"""
pid_ref = elem.pid_ref
mat = pid_ref.mid_ref
#is_passed, (wa, wb, ihat, jhat, khat) = elem.get_axes(model)
#T = np.vstack([ihat, jhat, khat])
#z = np.zeros((3, 3), dtype='float64')
prop = elem.pid_ref
mat = prop.mid_ref
I1 = prop.I11()
I2 = prop.I22()
unused_I12 = prop.I12()
pa = elem.pa
pb = elem.pb
#J = prop.J()
#E = mat.E()
#G = mat.G()
z = np.zeros((3, 3), dtype='float64')
T = z
#unused_Teb = np.block([
#[T, z],
#[z, T],
#])
is_failed, (wa, wb, ihat, jhat, khat) = elem.get_axes(model)
assert is_failed is False
#print(wa, wb)
xyz1 = elem.nodes_ref[0].get_position() + wa
xyz2 = elem.nodes_ref[1].get_position() + wb
dxyz = xyz2 - xyz1
L = np.linalg.norm(dxyz)
pid_ref = elem.pid_ref
mat = pid_ref.mid_ref
T = np.vstack([ihat, jhat, khat])
z = np.zeros((3, 3), dtype=fdtype)
Teb = np.block([
[T, z, z, z],
[z, T, z, z],
[z, z, T, z],
[z, z, z, T],
])
k1 = pid_ref.k1
k2 = pid_ref.k2
Ke = _beami_stiffness(pid_ref, mat, L, I1, I2, k1=k1, k2=k2, pa=pa, pb=pb)
K = Teb.T @ Ke @ Teb
is_passed = not is_failed
return is_passed, K
def test_pbarl_1(self):
"""tests the PBARL"""
model = BDF(log=None, debug=False)
pid = 4
mid = 40
group = 'group'
Type = 'bad_type'
dim = 42
nsm = 0.5
pbarl = PBARL(pid,
mid,
Type,
dim,
group=group,
nsm=nsm,
comment='comment')
with self.assertRaises(ValueError): # Type
pbarl.validate()
pbarl.Type = 'TUBE'
with self.assertRaises(TypeError): # dim
pbarl.validate()
pbarl.dim = [20.]
with self.assertRaises(RuntimeError):
pbarl.validate()
pbarl.dim = [2., 1.]
#with self.assertRaises(ValueError):
#pbarl.validate()
#pbarl.group = 'MSCBMLO'
pbarl.validate()
str(pbarl)
pbarl.write_card(size=8, is_double=False)
pbarl.write_card(size=16, is_double=False)
pbarl.write_card(size=16, is_double=True)
model.properties[pid] = pbarl
nid1 = 52
xyz1 = [0., 0., 0.]
model.nodes[nid1] = GRID(nid1, cp=0, xyz=xyz1)
nid2 = 53
xyz2 = [1., 0., 0.]
model.nodes[nid2] = GRID(nid2, cp=0, xyz=xyz2)
E = 30.0e7
G = None
nu = 0.3
mat = MAT1(mid, E, G, nu, rho=1.0)
model.materials[mid] = mat
eid = 42
x = None
g0 = None
cbar = CBAR(eid,
pid, [nid1, nid2],
x,
g0,
offt='GGG',
pa=0,
pb=0,
wa=None,
wb=None,
comment='')
cbar.validate()
model.elements[eid] = cbar
pbarl._verify(xref=False)
model.validate()
model.cross_reference()
pbarl._verify(xref=True)
assert allclose(cbar.Mass(), 9.9247779608), cbar.Mass()
mat.rho = 0.
assert allclose(cbar.Mass(), 0.5), cbar.Mass()
def _recover_forcei_cbar(model: BDF,
xb,
dof_map,
elem: CBAR,
prop: Union[PBAR, PBARL],
fdtype: str = 'float64'):
"""get the static CBAR force"""
#words = [' F O R C E S I N B A R E L E M E N T S ( C B A R )\n',
#'0 ELEMENT BEND-MOMENT END-A BEND-MOMENT END-B - SHEAR - AXIAL\n',
#' ID. PLANE 1 PLANE 2 PLANE 1 PLANE 2 PLANE 1 PLANE 2 FORCE TORQUE\n']
nid1, nid2 = elem.nodes
prop = elem.pid_ref
mat = prop.mid_ref
i1 = dof_map[(nid1, 1)]
i2 = dof_map[(nid2, 1)]
q_all = np.hstack([
xb[i1:i1 + 6],
xb[i2:i2 + 6],
])
#q_axial = np.array([
#xb[i1], xb[i1+1], xb[i1+2],
#xb[i2], xb[i2+1], xb[i2+2]
#])
#q_torsion = np.array([
#xb[i1+3], xb[i1+4], xb[i1+5],
#xb[i2+3], xb[i2+4], xb[i2+5]
#])
#u_axial = Lambda @ q_axial
#u_torsion = Lambda @ q_torsion
nid1, nid2 = elem.nodes
is_passed, Ke = ke_cbar(model, elem, fdtype=fdtype)
assert is_passed
#pid_ref = elem.pid_ref
#mat = pid_ref.mid_ref
# ------------------
is_failed, (wa, wb, ihat, jhat, khat) = elem.get_axes(model)
assert is_failed is False
#print(wa, wb)
#xyz1 = elem.nodes_ref[0].get_position() + wa
#xyz2 = elem.nodes_ref[1].get_position() + wb
#dxyz = xyz2 - xyz1
#L = np.linalg.norm(dxyz)
#pid_ref = elem.pid_ref
#mat = pid_ref.mid_ref
T = np.vstack([ihat, jhat, khat])
z = np.zeros((3, 3), dtype=fdtype)
Teb = np.block([
[T, z, z, z],
[z, T, z, z],
[z, z, T, z],
[z, z, z, T],
]) # 12x12
q_element = Teb @ q_all
u_e = q_element.reshape(12, 1)
Fe = Ke @ q_element
# ---------------------------------
f_e = Fe
#c, d, e, f = prop.get_cdef()
#C1, C2 = c
#D1, D2 = d
#E1, E2 = e
#F1, F2 = f
C1, C2, D1, D2, E1, E2, F1, F2 = prop.get_cdef().ravel()
A = prop.A
E = mat.E()
I1 = prop.I11()
I2 = prop.I22()
#f_e = obj.k_e * u_e
force2stress = np.array([
[1 / A, 0, 0, 0, C2 / I2, -C1 / I1],
[1 / A, 0, 0, 0, D2 / I2, -D1 / I1],
[1 / A, 0, 0, 0, E2 / I2, -E1 / I1],
[1 / A, 0, 0, 0, F2 / I2, -F1 / I1],
])
#print(force2stress.shape)
#print(f_e.shape)
stress = np.hstack([
-force2stress @ f_e[:6],
force2stress @ f_e[6:],
])
#print(E, stress)
# [End A Long. Stress or Strain at Point C;
# End A Long. Stress or Strain at Point D;
# End A Long. Stress or Strain at Point E;
# End A Long. Stress or Strain at Point F;
# End B Long. Stress or Strain at Point C;
# End B Long. Stress or Strain at Point D;
# End B Long. Stress or Strain at Point E;
# End B Long. Stress or Strain at Point F]
strain = 1 / E * stress
strain_energy = 0.5 * np.diag(u_e.T @ f_e).T
#print('strain_energy =', strain_energy)
# ---------------------------------
#k1 = pid_ref.k1
#k2 = pid_ref.k2
#Ke = _beami_stiffness(pid_ref, mat, L, I1, I2, k1=k1, k2=k2, pa=pa, pb=pb)
#K = Teb.T @ Ke @ Teb
#is_passed, (wa, wb, ihat, jhat, khat) = elem.get_axes(model)
#T = np.vstack([ihat, jhat, khat])
#z = np.zeros((3, 3), dtype='float64')
#I1 = prop.I11()
#I2 = prop.I22()
#A = prop.Area()
#J = prop.J()
#unused_I12 = prop.I12()
(Fx1, Fy1, Fz1, Mx1, My1, Mz1, Fx2, Fy2, Fz2, Mx2, My2, Mz2) = Fe
axial = Fx1
torque = Mx1
shear1 = Fy1
shear2 = Fz1
bending_moment_a1 = My1
bending_moment_a2 = Mz1
bending_moment_b1 = My2
bending_moment_b2 = Mz2
out = (bending_moment_a1, bending_moment_a2, bending_moment_b1,
bending_moment_b2, shear1, shear2, axial, torque)
return out