"""
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(tdim=self.region.tdim),
iels.astype(nm.int32), axis=0)
e_coors = mesh.coors[conn]
mtx_t = shell10x.create_transformation_matrix(e_coors)
e_centres = self.region.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