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rGOOSEFEM/src/GooseFEM/ElementQuad4.h
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ElementQuad4.h
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/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_ELEMENTQUAD4_H
#define GOOSEFEM_ELEMENTQUAD4_H
// -------------------------------------------------------------------------------------------------
#include "GooseFEM.h"
// =================================== GooseFEM::Element::Quad4 ====================================
namespace GooseFEM {
namespace Element {
namespace Quad4 {
// --------------------------------------- Gauss integration ---------------------------------------
class Gauss
{
private:
// dimensions
size_t m_nelem; // number of elements
static const size_t m_nne=4; // number of nodes per element
static const size_t m_ndim=2; // number of dimensions
static const size_t m_nip=4; // number of integration positions
// data arrays
ArrD m_x; // element vector with nodal positions [nelem, nne, ndim]
ArrD m_w; // weight of each integration point [nip]
ArrD m_xi; // local coordinate of each integration point [nip, ndim]
ArrD m_dNxi; // shape function gradients wrt local coordinate [nip, nne, ndim]
ArrD m_dNx; // shape function gradients wrt global coordinate [nelem, nip, nne, ndim]
ArrD m_vol; // integration point volume [nelem, nip]
private:
// compute "vol" and "dNdx" based on current "x"
void compute_dN();
public:
// constructor
Gauss(const ArrD &x);
// update the element vectors with nodal positions
// (the shape of "x" should match the earlier definition)
void update_x(const ArrD &x);
// return dimensions
size_t nelem();
size_t nne();
size_t ndim();
size_t nip();
// dyadic product "out(i,j) = dNdx(m,i) * inp(m,j)"
// - allow template (allows modification of tensor storage)
template<class T>
ArrD gradN_vector(const ArrD &vector);
// - default template: "cppmat::cartesian2d::tensor2<double>"
ArrD gradN_vector(const ArrD &vector);
// dyadic product "out(j,i) = dNdx(m,i) * inp(m,j)"
// - allow template (allows modification of tensor storage)
template<class T>
ArrD vector_GradN(const ArrD &vector);
// - default template: "cppmat::cartesian2d::tensor2<double>"
ArrD vector_GradN(const ArrD &vector);
// symmetric dyadic product "out(i,j) = dNdx(m,i) * inp(m,j)"
// (the output is symmetrized)
// - allow template (allows modification of tensor storage)
template<class T>
ArrD symGradN_vector(const ArrD &vector);
// - default template: "cppmat::cartesian2d::tensor2s<double>"
ArrD symGradN_vector(const ArrD &vector);
// dot product "out(m,j) = dNdx(m,i) * inp(i,j)"
// - allow template (allows modification of tensor storage)
template<class T>
ArrD gradN_dot_tensor2(const ArrD &tensor);
// - infer template from input, may be:
// "cppmat::cartesian2d::tensor2<double>" or "cppmat::cartesian2d::tensor2s<double>"
ArrD gradN_dot_tensor2 (const ArrD &tensor);
// - default template: "cppmat::cartesian2d::tensor2s<double>"
ArrD gradN_dot_tensor2s(const ArrD &tensor);
// dot product "out(m,j) = dNdx(m,i) * inp(i,j) * dV"
// - allow template (allows modification of tensor storage)
template<class T>
ArrD gradN_dot_tensor2_dV(const ArrD &tensor);
// - infer template from input, may be:
// "cppmat::cartesian2d::tensor2<double>" or "cppmat::cartesian2d::tensor2s<double>"
ArrD gradN_dot_tensor2_dV(const ArrD &tensor);
// compute volume averaged tensor of an element
// (has to be templated with the proper cppmat-tensor)
template<class T>
T average_tensor2(const ArrD &inp, size_t e);
cppmat::cartesian2d::tensor2 <double> average_tensor2 (const ArrD &inp, size_t e);
cppmat::cartesian2d::tensor2s<double> average_tensor2s(const ArrD &inp, size_t e);
// compute volume averaged tensor of all elements
// (has to be templated with the proper cppmat-tensor)
template<class T>
T average_tensor2(const ArrD &inp);
cppmat::cartesian2d::tensor2 <double> average_tensor2 (const ArrD &inp);
cppmat::cartesian2d::tensor2s<double> average_tensor2s(const ArrD &inp);
};
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#endif
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