def _recover_straini_rod(xb, dof_map, elem, prop):
"""get the static rod strain"""
nid1, nid2 = elem.nodes
# axial
i11 = dof_map[(nid1, 1)]
i12 = i11 + 1
i13 = i11 + 2
i21 = dof_map[(nid2, 1)]
i22 = i21 + 1
i23 = i21 + 2
# torsion
i14 = i11 + 3
i15 = i11 + 4
i16 = i11 + 5
i24 = i21 + 3
i25 = i21 + 4
i26 = i21 + 5
q_axial = np.array([
xb[i11],
xb[i12],
xb[i13],
xb[i21],
xb[i22],
xb[i23],
])
q_torsion = np.array([
xb[i14],
xb[i15],
xb[i16],
xb[i24],
xb[i25],
xb[i26],
])
xyz1 = elem.nodes_ref[0].get_position()
xyz2 = elem.nodes_ref[1].get_position()
dxyz12 = xyz1 - xyz2
Lambda = lambda1d(dxyz12, debug=False)
u_axial = Lambda @ q_axial
u_torsion = Lambda @ q_torsion
du_axial = u_axial[0] - u_axial[1]
du_torsion = u_torsion[0] - u_torsion[1]
#headers = ['axial', 'SMa', 'torsion', 'SMt']
C = prop.c
xyz1 = elem.nodes_ref[0].get_position()
xyz2 = elem.nodes_ref[1].get_position()
dxyz12 = xyz1 - xyz2
L = np.linalg.norm(dxyz12)
axial_strain = du_axial / L
torsional_strain = du_torsion * C / L
return axial_strain, np.nan, torsional_strain, np.nan
def _recover_forcei_rod(xb, dof_map, elem, prop): # pragma: no cover
"""get the static rod force"""
nid1, nid2 = elem.nodes
# axial
i11 = dof_map[(nid1, 1)]
i12 = dof_map[(nid1, 2)]
i13 = dof_map[(nid1, 3)]
i21 = dof_map[(nid2, 1)]
i22 = dof_map[(nid2, 2)]
i23 = dof_map[(nid2, 3)]
# torsion
i14 = dof_map[(nid1, 4)]
i15 = dof_map[(nid1, 5)]
i16 = dof_map[(nid1, 6)]
i24 = dof_map[(nid2, 4)]
i25 = dof_map[(nid2, 5)]
i26 = dof_map[(nid2, 6)]
q_axial = np.array([xb[i11], xb[i12], xb[i13], xb[i21], xb[i22], xb[i23]])
q_torsion = np.array(
[xb[i14], xb[i15], xb[i16], xb[i24], xb[i25], xb[i26]])
xyz1 = elem.nodes_ref[0].get_position()
xyz2 = elem.nodes_ref[1].get_position()
dxyz12 = xyz1 - xyz2
Lambda = lambda1d(dxyz12, debug=False)
u_axial = Lambda @ q_axial
u_torsion = Lambda @ q_torsion
du_axial = u_axial[0] - u_axial[1]
du_torsion = u_torsion[0] - u_torsion[1]
#headers = ['axial', 'SMa', 'torsion', 'SMt']
#C = prop.c
mat = prop.mid_ref
L = np.linalg.norm(dxyz12)
G = mat.G()
J = elem.J()
A = elem.Area()
E = elem.E()
axial_strain = du_axial / L
#torsional_strain = du_torsion * C / L
axial_stress = E * axial_strain
#torsional_stress = G * torsional_strain
axial_force = axial_stress * A
torsional_moment = du_torsion * G * J / L
return axial_force, torsional_moment
def _recover_straini_rod(xb, dof_map, elem, prop):
"""get the static rod strain"""
nid1, nid2 = elem.nodes
# axial
i1 = dof_map[(nid1, 1)]
i2 = dof_map[(nid2, 1)]
q_axial = np.array([
xb[i1],
xb[i1 + 1],
xb[i1 + 2],
xb[i2],
xb[i2 + 2],
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],
])
xyz1 = elem.nodes_ref[0].get_position()
xyz2 = elem.nodes_ref[1].get_position()
dxyz12 = xyz1 - xyz2
Lambda = lambda1d(dxyz12, debug=False)
u_axial = Lambda @ q_axial
u_torsion = Lambda @ q_torsion
du_axial = u_axial[0] - u_axial[1]
du_torsion = u_torsion[0] - u_torsion[1]
#headers = ['axial', 'SMa', 'torsion', 'SMt']
C = prop.c
xyz1 = elem.nodes_ref[0].get_position()
xyz2 = elem.nodes_ref[1].get_position()
dxyz12 = xyz1 - xyz2
L = np.linalg.norm(dxyz12)
axial_strain = du_axial / L
torsional_strain = du_torsion * C / L
return axial_strain, np.nan, torsional_strain, np.nan
def _recover_forcei_rod(xb, dof_map, elem, prop):
"""get the static rod force"""
nid1, nid2 = elem.nodes
i1 = dof_map[(nid1, 1)]
i2 = dof_map[(nid2, 1)]
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]
])
xyz1 = elem.nodes_ref[0].get_position()
xyz2 = elem.nodes_ref[1].get_position()
dxyz12 = xyz1 - xyz2
Lambda = lambda1d(dxyz12, debug=False)
u_axial = Lambda @ q_axial
u_torsion = Lambda @ q_torsion
du_axial = u_axial[0] - u_axial[1]
du_torsion = u_torsion[0] - u_torsion[1]
#headers = ['axial', 'SMa', 'torsion', 'SMt']
#C = prop.c
mat = prop.mid_ref
L = np.linalg.norm(dxyz12)
G = mat.G()
J = elem.J()
A = elem.Area()
E = elem.E()
axial_strain = du_axial / L
#torsional_strain = du_torsion * C / L
axial_stress = E * axial_strain
#torsional_stress = G * torsional_strain
axial_force = axial_stress * A
torsional_moment = du_torsion * G * J / L
return axial_force, torsional_moment
def _recover_stressi_ctube(xb, dof_map, elem, prop):
"""get the static ctube stress"""
nid1, nid2 = elem.nodes
# axial
i11 = dof_map[(nid1, 1)]
i12 = i11 + 1
i13 = i11 + 2
i21 = dof_map[(nid2, 1)]
i22 = i21 + 1
i23 = i21 + 2
# torsion
i14 = i11 + 3
i15 = i11 + 4
i16 = i11 + 5
i24 = i21 + 3
i25 = i21 + 4
i26 = i21 + 5
q_axial = np.array([
xb[i11],
xb[i12],
xb[i13],
xb[i21],
xb[i22],
xb[i23],
])
q_torsion = np.array([
xb[i14],
xb[i15],
xb[i16],
xb[i24],
xb[i25],
xb[i26],
])
xyz1 = elem.nodes_ref[0].get_position()
xyz2 = elem.nodes_ref[1].get_position()
dxyz12 = xyz1 - xyz2
Lambda = lambda1d(dxyz12, debug=False)
u_axial = Lambda @ q_axial
u_torsion = Lambda @ q_torsion
du_axial = u_axial[0] - u_axial[1]
du_torsion = u_torsion[0] - u_torsion[1]
#headers = ['axial', 'SMa', 'torsion', 'SMt']
mat = prop.mid_ref
L = np.linalg.norm(dxyz12)
G = mat.G()
E = elem.E()
axial_strain = du_axial / L
torsional_strain = du_torsion / L
axial_stress = E * axial_strain
torsional_stress = G * torsional_strain
return axial_stress, np.nan, torsional_stress, np.nan
def _recover_straini_cbar(model: BDF,
xb: NDArrayNfloat,
dof_map,
elem: CBAR,
prop: Union[PBAR, PBARL],
fdtype='float64'):
"""get the static bar strain"""
nid1, nid2 = elem.nodes
# axial
i1 = dof_map[(nid1, 1)]
j1 = dof_map[(nid2, 1)]
q_all = np.hstack([
xb[i1:i1 + 6],
xb[j1:j1 + 6],
])
print(len(xb[i1:i1 + 3], ))
q_axial = np.hstack([
xb[i1:i1 + 3],
xb[j1:j1 + 3],
])
print(q_axial)
q_torsion = np.hstack([
xb[i1 + 3:i1 + 6],
xb[j1 + 3:j1 + 6],
])
#{F} = [K]{u}
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_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()
A = prop.Area()
J = prop.J()
unused_I12 = prop.I12()
Fe = Ke @ q_all
(Fx1, Fy1, Fz1, Mx1, My1, Mz1, Fx2, Fy2, Fz2, Mx2, My2, Mz2) = Fe
s_axial = Fx1 / A
s_torsion = Mx1 / J
xyz1 = elem.nodes_ref[0].get_position()
xyz2 = elem.nodes_ref[1].get_position()
#dxyz12 = xyz1 - xyz2
#Lambda = lambda1d(dxyz12, debug=False)
#u_axial = Lambda @ q_axial
#u_torsion = Lambda @ q_torsion
#du_axial = u_axial[0] - u_axial[1]
#du_torsion = u_torsion[0] - u_torsion[1]
xyz1 = elem.nodes_ref[0].get_position()
xyz2 = elem.nodes_ref[1].get_position()
dxyz12 = xyz1 - xyz2
L = np.linalg.norm(dxyz12)
Lambda = lambda1d(dxyz12, debug=False)
u_axial = Lambda @ q_axial
u_torsion = Lambda @ q_torsion
du_axial = u_axial[0] - u_axial[1]
du_torsion = u_torsion[0] - u_torsion[1]
axial = du_axial / L
# cdef = prop.get_cdef()
if prop.type == 'PBARL':
# these axes are backwards...
# ^ y
# +---|---+
# | | |
# | +------> z
# | |
# +-------+
if prop.Type in ['ROD', 'TUBE']:
R = prop.dims[0]
cdef = np.array([
[R, 0.],
[0., R],
[-R, 0.],
[0., -R],
],
dtype='float64')
elif prop.Type in ['BAR', 'BOX']:
height, width = prop.dims
cdef = np.array([
[width, height],
[width, -height],
[-width, -height],
[-width, height],
],
dtype='float64') / 2.
else:
raise NotImplementedError(prop.Type)
elif prop.type == 'PBAR':
cdef = np.array([
[prop.c1, prop.c2],
[prop.d1, prop.d2],
[prop.e1, prop.e2],
[prop.f1, prop.f2],
],
dtype='float64')
else:
raise NotImplementedError(prop.get_stats())
model.log.info(f'cdef: {cdef}\n')
Iy = I1
Iz = I2
G = mat.G()
E = mat.E()
strains = []
for (T, My, Mz) in [(Mx1, My1, Mz1), (Mx2, My2, Mz2)]:
for yz in cdef:
y, z = yz
radius = np.linalg.norm(yz)
unused_torsional_stress = (T * radius) / J
unused_phi = (T * L) / (G * J)
stress = My * y / Iy + Mz * z / Iy
strain = stress / E
strains.append(strain)
s1a = strains[0]
s2a = strains[1]
s3a = strains[2]
s4a = strains[3]
s1b = strains[4]
s2b = strains[5]
s3b = strains[6]
s4b = strains[7]
smaxa = max(s1a, s2a, s3a, s4a)
smaxb = max(s1b, s2b, s3b, s4b)
smina = min(s1a, s2a, s3a, s4a)
sminb = min(s1b, s2b, s3b, s4b)
MS_tension = MS_compression = np.nan
out = (s1a, s2a, s3a, s4a, axial, smaxa, smina, MS_tension, s1b, s2b, s3b,
s4b, sminb, sminb, MS_compression) # 15
return out
