Source code for sfepy.discrete.structural.mappings

"""
Finite element reference mappings for structural elements.
"""
import numpy as nm

from sfepy.linalg import dot_sequences as ddot
from sfepy.discrete.common.mappings import Mapping, PhysicalQPs
import sfepy.mechanics.shell10x as shell10x

[docs]class Shell10XMapping(Mapping): """ The reference mapping for the shell10x element. """ def __init__(self, region, field): self.region = region self.field = field
[docs] def get_physical_qps(self, qp_coors): """ Get physical quadrature points corresponding the given reference element quadrature points. Returns ------- qps : array The physical quadrature points ordered element by element, i.e. with shape (n_el, n_qp, dim). """ phys_qps = PhysicalQPs() bf = self.bfu.squeeze() qps_loc = nm.einsum('qi,cqij->cqj', bf, self.coors_loc_3d) qps = nm.einsum('cqi,cji->cqj', qps_loc, self.mtx_t) qps += self.e_centres[:, None, :] n_el, n_qp = qps.shape[0], qps.shape[1] phys_qps.num = n_el * n_qp phys_qps.shape = qps.shape qps.shape = (phys_qps.num, qps.shape[2]) phys_qps.values = qps return phys_qps
[docs] def get_mapping(self, qp_coors, weights): """ Get the mapping for given quadrature points and weights. """ domain = self.region.domain mesh = domain.mesh iels = self.region.get_cells() conn = nm.take(domain.get_conn(), iels.astype(nm.int32), axis=0) e_coors = mesh.coors[conn] mtx_t = shell10x.create_transformation_matrix(e_coors) e_centres = mesh.cmesh.get_centroids(2)[iels] coors_loc = ddot((e_coors - e_centres[:, None, :]), mtx_t) ebs = shell10x.create_local_bases(coors_loc) rops = shell10x.create_rotation_ops(ebs) ps = self.field.poly_space qp_coors0 = nm.array([[0.5, 0.5, 0.5]]) # Should be thickness, but not used anywhere. qp_weights0 = nm.array([0.0]) dxidx0, det0 = shell10x.get_mapping_data(ebs, rops, ps, coors_loc, qp_coors0, qp_weights0, special_dx3=True) aux = shell10x.get_mapping_data(ebs, rops, ps, coors_loc, qp_coors, weights) coors_loc_3d, bfu, bfgm, dxidx, det = aux self.coors_loc = coors_loc self.e_centres = e_centres self.mtx_t = mtx_t self.ebs = ebs self.rops = rops self.dxidx0 = dxidx0 self.det0 = det0 self.coors_loc_3d = coors_loc_3d self.bfu = bfu self.bfgm = bfgm self.dxidx = dxidx self.det = det self.volume = (det * weights).sum(1) return self