Functions implementing the shell10x element.
Add additional strain components [Andelfinger and Ramm] (7 parameters to be condensed out).
Create the transformation matrix for locking of the drilling rotations.
Create the elastic tensor with the applied shear correction (the default) for the shell10x element.
Create local orthonormal bases in each vertex of quadrilateral cells.
Parameters: | coors : array
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Returns: | ebs : array
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Create operators associated to rotation DOFs.
Parameters: | ebs : array
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Returns: | rops : array
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Create the strain operator matrix.
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}].
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: | coors : array
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Returns: | mtx_t : array
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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.
Compute DSG strain components.
Returns: | dsg : array
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Notes
Involves w, \alpha, \beta DOFs.
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.
Lock the drilling rotations in the stiffness matrix.
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.
Transform matrix assembling contributions to global coordinate system, one node at a time.
Parameters: | out : array
mtx_t : array
blocks : array
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