from pumapy.physicsmodels.mpsa_elasticity import Elasticity
from pumapy.physicsmodels.property_maps import ElasticityMap
from scipy.optimize import fsolve
import numpy as np
[docs]def compute_elasticity(workspace, elast_map, direction, side_bc='p', prescribed_bc=None, tolerance=1e-4,
maxiter=100000, solver_type='gmres', display_iter=True, print_matrices=(0, 0, 0, 0, 0)):
""" Compute the effective elasticity coefficient
(N.B. 0 material ID in workspace refers to air unless otherwise specified)
:param workspace: domain
:type workspace: pumapy.Workspace
:param elast_map: local elasticity of the constituents
:type elast_map: pumapy.ElasticityMap
:param direction: direction for solve ('x','y', 'z', 'yz', 'xz', 'xy')
:type direction: string
:param side_bc: side boundary conditions can be symmetric ('s'), periodic ('p'), dirichlet ('d') or free ('f')
:type side_bc: string
:param prescribed_bc: 3D array holding dirichlet BC
:type prescribed_bc: pumapy.ElasticityBC or None
:param tolerance: tolerance for iterative solver
:type: tolerance: float
:param maxiter: maximum Iterations for solver
:type maxiter: int
:param solver_type: solver type, options: 'bicgstab', 'cg', 'gmres' (default), 'direct'
:type solver_type: string
:param display_iter: display iterations and residual
:type display_iter: bool
:param print_matrices: corresponding to b, E, A, u, s decimal places. If 0, they are not printed
:type print_matrices: (int, int, int, int, int)
:return: elasticity, displacement field, direct stresses (sigma xx, yy, zz), shear stresses (tau yz, xz, xy)
:rtype: ((float, float, float, float, float, float), numpy.ndarray, numpy.ndarray, numpy.ndarray)
:Example:
>>> import pumapy as puma
>>> ws = puma.Workspace.from_shape_value((20, 20, 20), 1)
>>> ws[int(ws.matrix.shape[0] / 2):] = 2
>>> elast_map = puma.ElasticityMap()
>>> elast_map.add_isotropic_material((1, 1), 200, 0.3)
>>> elast_map.add_isotropic_material((2, 2), 400, 0.1)
>>> C, u, s, t = puma.compute_elasticity(ws, elast_map, direction='x', side_bc='f', solver_type="direct")
>>> print(C)
"""
if isinstance(elast_map, ElasticityMap):
solver = Elasticity(workspace, elast_map, direction, side_bc, prescribed_bc, tolerance, maxiter,
solver_type, display_iter, print_matrices)
else:
raise Exception("elast_map has to be an ElasticityMap")
solver.error_check()
solver.log_input()
solver.compute()
solver.log_output()
return solver.Ceff, solver.u, solver.s, solver.t
[docs]def compute_stress_analysis(workspace, elast_map, prescribed_bc, side_bc='p', tolerance=1e-4,
maxiter=100000, solver_type='gmres', display_iter=True, print_matrices=(0, 0, 0, 0, 0)):
""" Compute stress analysis
(N.B. 0 material ID in workspace refers to air unless otherwise specified)
:param workspace: domain
:type workspace: pumapy.Workspace
:param elast_map: local elasticity of the constituents
:type elast_map: pumapy.ElasticityMap
:param prescribed_bc: 3D array holding dirichlet BC
:type prescribed_bc: pumapy.ElasticityBC
:param side_bc: side boundary conditions can be symmetric ('s'), periodic ('p'), dirichlet ('d') or free ('f')
:type side_bc: string
:param tolerance: tolerance for iterative solver
:type tolerance: float
:param maxiter: maximum Iterations for solver
:type maxiter: int
:param solver_type: solver type, options: 'bicgstab', 'cg', 'gmres' (default), 'direct'
:type solver_type: string
:param display_iter: display iterations and residual
:type display_iter: bool
:param print_matrices: corresponding to b, E, A, u, s decimal places. If 0, they are not printed
:type print_matrices: (int, int, int, int, int)
:return: displacement field, direct stresses (sigma xx, yy, zz), shear stresses (tau yz, xz, xy)
:rtype: (numpy.ndarray, numpy.ndarray, numpy.ndarray)
:Example:
>>> import pumapy as puma
>>> ws = puma.Workspace.from_shape_value((20, 20, 20), 1)
>>> ws[ws.matrix.shape[0]//2:] = 2
>>> elast_map = puma.ElasticityMap()
>>> elast_map.add_isotropic_material((1, 1), 200, 0.3)
>>> elast_map.add_isotropic_material((2, 2), 400, 0.1)
>>> bc = puma.ElasticityBC(ws)
>>> bc.dirichlet[0] = 0 # hold x -ve face
>>> bc.dirichlet[-1, :, :, 0] = 1 # displace x +ve face by 1 in x direction
>>> bc.dirichlet[-1, :, :, 1:] = 0 # hold x +ve face in y and z directions
>>> u, s, t = puma.compute_stress_analysis(ws, elast_map, bc, side_bc='f', solver_type="direct")
>>> puma.render_volume(u[:, :, :, 1], cmap='jet') # displacement magnitude in y direction
"""
if isinstance(elast_map, ElasticityMap):
solver = Elasticity(workspace, elast_map, None, side_bc, prescribed_bc, tolerance, maxiter,
solver_type, display_iter, print_matrices)
else:
raise Exception("elast_map has to be an ElasticityMap")
solver.error_check()
solver.log_input()
solver.compute()
solver.log_output()
return solver.u, solver.s, solver.t
[docs]def get_E_nu_from_elasticity(C11, C12, C13, C22, C23, C33):
""" Compute Young's moduli E1, E2, E3 and Poisson's ratios nu12, nu23, nu31 from symmetric elastic stiffness tensor
:param C11: elasticity tensor component
:type C11: float
:param C12: elasticity tensor component
:type C12: float
:param C13: elasticity tensor component
:type C13: float
:param C22: elasticity tensor component
:type C22: float
:param C23: elasticity tensor component
:type C23: float
:param C33: elasticity tensor component
:type C33: float
:return: Young's moduli E1, E2, E3 and Poisson's ratios nu12, nu23, nu31
:rtype: (float, float, float, float, float, float)
"""
def eqs(unknowns, *cs):
E1, E2, E3, nu12, nu23, nu31 = unknowns
c11, c12, c31, c22, c23, c33 = cs
nu21 = nu12 * E2 / E1
nu32 = nu23 * E3 / E2
nu13 = nu31 * E1 / E3
c0 = (1 - nu12 * nu21 - nu23 * nu32 - nu13 * nu31 - 2 * nu21 * nu32 * nu13) / (E1 * E2 * E3)
return (c11 - (1 - nu23 * nu32) / (c0 * E2 * E3),
c22 - (1 - nu13 * nu31) / (c0 * E1 * E3),
c33 - (1 - nu21 * nu12) / (c0 * E2 * E1),
c12 - (nu12 + nu32 * nu13) / (c0 * E1 * E3),
c23 - (nu23 + nu21 * nu13) / (c0 * E1 * E2),
c31 - (nu31 + nu21 * nu32) / (c0 * E2 * E3))
s = fsolve(eqs, np.full(6, 0.1), args=(C11, C12, C13, C22, C23, C33))
[print(i, j) for i, j in zip(["E1", "E2", "E3", "nu12", "nu23", "nu31"], s)]
return s