GooseFEM::Element::Quad4::QuadraturePlanar Class Reference

Interpolation and quadrature. More...

#include <GooseFEM/ElementQuad4Planar.h>

Inheritance diagram for GooseFEM::Element::Quad4::QuadraturePlanar:

Public Member Functions
template<class T >
	QuadraturePlanar (const T &x, double thick=1.0)
	Constructor: use default Gauss integration.
template<class T , class X , class W >
	QuadraturePlanar (const T &x, const X &xi, const W &w, double thick=1.0)
	Constructor with custom integration.
Public Member Functions inherited from GooseFEM::Element::QuadratureBaseCartesian< QuadraturePlanar >
void	update_x (const T &x)
	Update the nodal positions.
auto	GradN () const -> const array_type::tensor< double, 4 > &
	Shape function gradients (in global coordinates).
auto	dV () const -> const array_type::tensor< double, 2 > &
	Integration volume.
auto	InterpQuad_vector (const T &elemvec) const -> array_type::tensor< double, 3 >
	Interpolate element vector and evaluate at each quadrature point.
void	interpQuad_vector (const T &elemvec, R &qvector) const
	Same as InterpQuad_vector(), but writing to preallocated return.
auto	GradN_vector (const T &elemvec) const -> array_type::tensor< double, 4 >
	Element-by-element: dyadic product of the shape function gradients and a nodal vector.
void	gradN_vector (const T &elemvec, R &qtensor) const
	Same as GradN_vector(), but writing to preallocated return.
auto	GradN_vector_T (const T &elemvec) const -> array_type::tensor< double, 4 >
	The transposed output of GradN_vector().
void	gradN_vector_T (const T &elemvec, R &qtensor) const
	Same as GradN_vector_T(), but writing to preallocated return.
auto	SymGradN_vector (const T &elemvec) const -> array_type::tensor< double, 4 >
	The symmetric output of GradN_vector().
void	symGradN_vector (const T &elemvec, R &qtensor) const
	Same as SymGradN_vector(), but writing to preallocated return.
auto	Int_N_vector_dV (const T &qvector) const -> array_type::tensor< double, 3 >
	Element-by-element: integral of a continuous vector-field.
void	int_N_vector_dV (const T &qvector, R &elemvec) const
	Same as Int_N_vector_dV(), but writing to preallocated return.
auto	Int_N_scalar_NT_dV (const T &qscalar) const -> array_type::tensor< double, 3 >
	Element-by-element: integral of the scalar product of the shape function with a scalar.
void	int_N_scalar_NT_dV (const T &qscalar, R &elemmat) const
	Same as Int_N_scalar_NT_dV(), but writing to preallocated return.
auto	Int_gradN_dot_tensor2_dV (const T &qtensor) const -> array_type::tensor< double, 3 >
	Element-by-element: integral of the dot product of the shape function gradients with a second order tensor.
void	int_gradN_dot_tensor2_dV (const T &qtensor, R &elemvec) const
	Same as Int_gradN_dot_tensor2_dV(), but writing to preallocated return.
auto	Int_gradN_dot_tensor4_dot_gradNT_dV (const T &qtensor) const -> array_type::tensor< double, 3 >
	Element-by-element: integral of the dot products of the shape function gradients with a fourth order tensor.
void	int_gradN_dot_tensor4_dot_gradNT_dV (const T &qtensor, R &elemmat) const
	Same as Int_gradN_dot_tensor4_dot_gradNT_dV(), but writing to preallocated return.
Public Member Functions inherited from GooseFEM::Element::QuadratureBase< D >
auto	nelem () const
	Number of elements.
auto	nne () const
	Number of nodes per element.
auto	ndim () const
	Number of dimensions for node vectors.
auto	tdim () const
	Number of dimensions for integration point tensors.
auto	nip () const
	Number of integration points.
template<class T , class R >
void	asTensor (const T &arg, R &ret) const
	Convert "qscalar" to "qtensor" of certain rank.
template<size_t rank, class T >
auto	AsTensor (const T &arg) const
	Convert "qscalar" to "qtensor" of certain rank.
template<class T >
auto	AsTensor (size_t rank, const T &arg) const
	Convert "qscalar" to "qtensor" of certain rank.
auto	shape_elemvec () const -> std::array< size_t, 3 >
	Get the shape of an "elemvec".
auto	shape_elemvec (size_t arg) const -> std::array< size_t, 3 >
	Get the shape of an "elemvec".
auto	shape_elemmat () const -> std::array< size_t, 3 >
	Get the shape of an "elemmat".
template<size_t rank = 0>
auto	shape_qtensor () const -> std::array< size_t, 2+rank >
	Get the shape of a "qtensor" of a certain rank (0 = scalar, 1, vector, 2 = 2nd-order tensor, etc.).
auto	shape_qtensor (size_t rank) const -> std::vector< size_t >
	Get the shape of a "qtensor" of a certain rank (0 = scalar, 1, vector, 2 = 2nd-order tensor, etc.).
template<size_t trank>
auto	shape_qtensor (size_t rank, size_t arg) const -> std::array< size_t, 2+trank >
	Get the shape of a "qtensor" of a certain rank (0 = scalar, 1, vector, 2 = 2nd-order tensor, etc.).
auto	shape_qtensor (size_t rank, size_t arg) const -> std::vector< size_t >
	Get the shape of a "qtensor" of a certain rank (0 = scalar, 1, vector, 2 = 2nd-order tensor, etc.).
auto	shape_qscalar () const -> std::array< size_t, 2 >
	Get the shape of a "qscalar" (a "qtensor" of rank 0)
auto	shape_qvector () const -> std::array< size_t, 3 >
	Get the shape of a "qvector" (a "qtensor" of rank 1)
auto	shape_qvector (size_t arg) const -> std::array< size_t, 3 >
	Get the shape of a "qvector" (a "qtensor" of rank 1)
template<class R >
auto	allocate_elemvec () const
	Get an allocated array_type::tensor to store a "elemvec".
template<class R >
auto	allocate_elemvec (R val) const
	Get an allocated and initialised xt::xarray to store a "elemvec".
template<class R >
auto	allocate_elemmat () const
	Get an allocated array_type::tensor to store a "elemmat".
template<class R >
auto	allocate_elemmat (R val) const
	Get an allocated and initialised xt::xarray to store a "elemmat".
template<size_t rank = 0, class R >
auto	allocate_qtensor () const
	Get an allocated array_type::tensor to store a "qtensor" of a certain rank (0 = scalar, 1, vector, 2 = 2nd-order tensor, etc.).
template<size_t rank = 0, class R >
auto	allocate_qtensor (R val) const
	Get an allocated and initialised array_type::tensor to store a "qtensor" of a certain rank (0 = scalar, 1, vector, 2 = 2nd-order tensor, etc.).
template<class R >
auto	allocate_qtensor (size_t rank) const
	Get an allocated xt::xarray to store a "qtensor" of a certain rank (0 = scalar, 1, vector, 2 = 2nd-order tensor, etc.).
template<class R >
auto	allocate_qtensor (size_t rank, R val) const
	Get an allocated and initialised xt::xarray to store a "qtensor" of a certain rank (0 = scalar, 1, vector, 2 = 2nd-order tensor, etc.).
template<class R >
auto	allocate_qscalar () const
	Get an allocated array_type::tensor to store a "qscalar" (a "qtensor" of rank 0).
template<class R >
auto	allocate_qscalar (R val) const
	Get an allocated and initialised xt::xarray to store a "qscalar" (a "qtensor" of rank 0).

Additional Inherited Members
Public Types inherited from GooseFEM::Element::QuadratureBaseCartesian< QuadraturePlanar >
using	derived_type
	Underlying type.
Public Types inherited from GooseFEM::Element::QuadratureBase< D >
using	derived_type = D
	Underlying type.
Protected Member Functions inherited from GooseFEM::Element::QuadratureBaseCartesian< QuadraturePlanar >
void	compute_dN ()
	Update the shape function gradients (called when the nodal positions are updated).

Detailed Description

Interpolation and quadrature.

Similar to Element::Quad4::Quadrature with the only different that quadrature point tensors are 3d ("plane strain") while the mesh is 2d.

Fixed dimensions:

• ndim = 2: number of dimensions.
• tdim = 3: number of dimensions or tensor.
• nne = 4: number of nodes per element.

Naming convention:

• elemmat: matrices stored per element, [nelem, nne * ndim, nne * ndim]
• elemvec: nodal vectors stored per element, [nelem, nne, ndim]
• qtensor: integration point tensor, [nelem, nip, tdim, tdim]
• qscalar: integration point scalar, [nelem, nip]

Definition at line 38 of file ElementQuad4Planar.h.

Constructor & Destructor Documentation

QuadraturePlanar() [1/2]

template<class T >

GooseFEM::Element::Quad4::QuadraturePlanar::QuadraturePlanar ( const T & x, double thick = 1.0 )

inline

Constructor: use default Gauss integration.

The following is pre-computed during construction:

• the shape functions,
• the shape function gradients (in local and global) coordinates,
• the integration points volumes. They can be reused without any cost. They only have to be recomputed when the nodal position changes (note that they are assumed to be constant under a small-strain assumption). In that case use update_x() to update the nodal positions and to recompute the above listed quantities.

Parameters

x	nodal coordinates (elemvec).
thick	out-of-plane thickness (incorporated in the element volume).

Definition at line 58 of file ElementQuad4Planar.h.

QuadraturePlanar() [2/2]

template<class T , class X , class W >

GooseFEM::Element::Quad4::QuadraturePlanar::QuadraturePlanar ( const T & x, const X & xi, const W & w, double thick = 1.0 )

inline

Constructor with custom integration.

The following is pre-computed during construction:

• the shape functions,
• the shape function gradients (in local and global) coordinates,
• the integration points volumes. They can be reused without any cost. They only have to be recomputed when the nodal position changes (note that they are assumed to be constant under a small-strain assumption). In that case use update_x() to update the nodal positions and to recompute the above listed quantities.

Parameters

x	nodal coordinates (elemvec).
xi	Integration point coordinates (local coordinates) [nip].
w	Integration point weights [nip].
thick	out-of-plane thickness (incorporated in the element volume).

Definition at line 81 of file ElementQuad4Planar.h.

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The documentation for this class was generated from the following file:

• GooseFEM/ElementQuad4Planar.h