sfepy.mechanics.shell10x module¶

Functions implementing the shell10x element.

sfepy.mechanics.shell10x.add_eas_dofs(mtx_b, qp_coors, det, det0, dxidx0)[source]¶: Add additional strain components [Andelfinger and Ramm] (7 parameters to be condensed out).

sfepy.mechanics.shell10x.create_drl_transform(ebs)[source]¶: Create the transformation matrix for locking of the drilling rotations.

sfepy.mechanics.shell10x.create_elastic_tensor(young, poisson, shear_correction=True)[source]¶: Create the elastic tensor with the applied shear correction (the default) for the shell10x element.

sfepy.mechanics.shell10x.create_local_bases(coors)[source]¶

Create local orthonormal bases in each vertex of quadrilateral cells.

Parameters:

coorsarray: The coordinates of cell vertices, shape (n_el, 4, 3).

Returns:

ebsarray: The local bases, shape (n_el, 4, 3, 3). The basis vectors are rows of the (…, 3, 3) blocks.

sfepy.mechanics.shell10x.create_rotation_ops(ebs)[source]¶

Create operators associated to rotation DOFs.

Parameters:

ebsarray: The local bases, shape (n_el, 4, 3, 3).

Returns:

ropsarray: The rotation operators, shape (n_el, 4, 3, 3).

sfepy.mechanics.shell10x.create_strain_matrix(bfgm, dxidx, dsg)[source]¶: Create the strain operator matrix.

sfepy.mechanics.shell10x.create_strain_transform(mtx_ts)[source]¶

Create strain tensor transformation matrices, given coordinate transformation matrices.

Notes

Expresses $T E T^T$ in terms of symmetrix storage as $Q e$ , with the ordering of components: $e = [e_{11}, e_{22}, e_{33}, 2 e_{12}, 2 e_{13}, 2 e_{23}]$ .

sfepy.mechanics.shell10x.create_transformation_matrix(coors)[source]¶

Create a transposed coordinate transformation matrix, that transforms 3D coordinates of quadrilateral cell vertices so that the transformed vertices of a plane cell are in the $x-y$ plane. The rotation is performed w.r.t. the centres of quadrilaterals.

Parameters:

coorsarray: The coordinates of cell vertices, shape (n_el, 4, 3).

Returns:

mtx_tarray: The transposed transformation matrix $T$ , i.e. $X_{inplane} = T^T X_{3D}$ .

Notes

$T = [t_1, t_2, n]$ , where $t_1$ , $t_2$ , are unit in-plane (column) vectors and $n$ is the unit normal vector, all mutually orthonormal.

sfepy.mechanics.shell10x.get_dsg_strain(coors_loc, qp_coors)[source]¶

Compute DSG strain components.

Returns:

dsgarray: The strain matrix components corresponding to $e_{13}$ , $e_{23}$ , shape (n_el, n_qp, 2, 24).

Notes

Involves $w$ , $\alpha$ , $\beta$ DOFs.

sfepy.mechanics.shell10x.get_mapping_data(ebs, rops, ps, coors_loc, qp_coors, qp_weights, special_dx3=False)[source]¶

Compute reference element mapping data for shell10x elements.

Notes

The code assumes that the quadrature points are w.r.t. ( $t$ = thickness of the shell) $[0, 1] \times [0, 1] \times [-t/2, t/2]$ reference cell and the quadrature weights are multiplied by $t$ .

sfepy.mechanics.shell10x.lock_drilling_rotations(mtx, ebs, coefs)[source]¶: Lock the drilling rotations in the stiffness matrix.

sfepy.mechanics.shell10x.rotate_elastic_tensor(mtx_d, bfu, ebs)[source]¶: Rotate the elastic tensor into the local coordinate system of each cell. The local coordinate system results from interpolation of ebs with the bilinear basis.

sfepy.mechanics.shell10x.transform_asm_matrices(out, mtx_t, blocks)[source]¶

Transform matrix assembling contributions to global coordinate system, one node at a time.

Parameters:

outarray: The array of matrices, transformed in-place.
mtx_tarray: The array of transposed transformation matrices $T$ , see create_transformation_matrix().
blocksarray: The DOF blocks that are