Create mapping from transformed (in x-y plane) element faces to reference element faces.
Parameters: | coors : array
gel : GeometryElement instance
order : int
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Returns: | mapping : VolumeMapping instance
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Create a transposed coordinate transformation matrix, that transforms 3D coordinates of element face nodes so that the transformed nodes are in the x-y plane. The rotation is performed w.r.t. the first node of each face.
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.
Describe deformation of a thin incompressible 2D membrane in 3D space, composed of flat finite element faces.
The coordinate system of each element (face), i.e. the membrane mid-surface, should coincide with the x, y axes of the x-y plane.
Parameters: | el_disps : array
bfg : array
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Returns: | mtx_c ; array :
c33 : array
mtx_b : array
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Describe membrane geometry in a given region.
Parameters: | field : Field instance
region : Region instance
integral : Integral instance
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Returns: | mtx_t : array
membrane_geo : CMapping instance
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Get the 3D Green strain tensor in symmetric storage.
Parameters: | mtx_c ; array :
c33 : array
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Returns: | mtx_e : array
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Get the first and second invariants of the right Cauchy-Green deformation tensor describing deformation of an incompressible membrane.
Parameters: | mtx_c ; array :
c33 : array
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Returns: | i1 : array
i2 : array
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Get the tangent stress matrix of a thin incompressible 2D membrane in 3D space, given a stress.
Parameters: | stress : array
bfg : array
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Returns: | mtx : array
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Transform matrix assembling contributions to global coordinate system, one node at a time.
Parameters: | out : array
mtx_t : array
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Transform vector assembling contributions to global coordinate system, one node at a time.
Parameters: | out : array
mtx_t : array
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