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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 {
// ================================ GooseFEM::Element::Quad4::Gauss ================================
namespace Gauss {
inline size_t nip(); // number of integration points
inline ArrD coordinates(); // integration point coordinates (local coordinates)
inline ArrD weights(); // integration point weights
}
// ================================ GooseFEM::Element::Quad4::Nodal ================================
namespace Nodal {
inline size_t nip(); // number of integration points
inline ArrD coordinates(); // integration point coordinates (local coordinates)
inline ArrD weights(); // integration point weights
}
// =================================================================================================
// ------------------------------------------ quadrature -------------------------------------------
class Quadrature
{
private:
// dimensions
size_t m_nelem; // number of elements
size_t m_nip; // number of integration points
static const size_t m_nne=4; // number of nodes per element
static const size_t m_ndim=2; // number of dimensions
// data arrays
ArrD m_x; // nodal positions stored per element [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_N; // shape functions [nip, nne]
ArrD m_dNxi; // shape function gradients w.r.t. local coordinate [nip, nne, ndim]
ArrD m_dNx; // shape function gradients w.r.t. 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:
// notation:
// "elemmat" - matrices stored per element - ArrD - [nelem, nne*ndim, nne*ndim]
// "elemvec" - nodal vectors stored per element - ArrD - [nelem, nne, ndim]
// "qtensor" - integration point tensor - ArrD - [nelem, nip, #tensor-components]
// "qscalar" - integration point scalar - ArrD - [nelem, nip]
//
// alias:
// T2 = cppmat::cartesian2d::tensor2<double> - #tensor-components = 4
// T2s = cppmat::cartesian2d::tensor2s<double> - #tensor-components = 3
// vT2 = cppmat::view::cartesian2d::tensor2<double> - #tensor-components = 4
// vT2s = cppmat::view::cartesian2d::tensor2s<double> - #tensor-components = 3
// constructor: integration point coordinates and weights are optional (default: Gauss)
Quadrature(const ArrD &x, const ArrD &xi=ArrD(), const ArrD &w=ArrD());
// update the nodal positions (shape of "x" should match the earlier definition)
void update_x(const ArrD &x);
// return dimensions
size_t nelem() const; // number of elements
size_t nne() const; // number of nodes per element
size_t ndim() const; // number of dimension
size_t nip() const; // number of integration points
// return integration volume (per tensor-component)
ArrD dV() const;
ArrD dV(size_t ncomp) const;
// dyadic product "qtensor(i,j) += dNdx(m,i) * elemvec(m,j)", its transpose and its symmetric part
// - allow template (e.g. vT2)
template<class T> ArrD gradN_vector (const ArrD &elemvec) const;
template<class T> ArrD gradN_vector_T (const ArrD &elemvec) const;
template<class T> ArrD symGradN_vector(const ArrD &elemvec) const;
// - default template with:
ArrD gradN_vector (const ArrD &elemvec) const; // vT2
ArrD gradN_vector_T (const ArrD &elemvec) const; // vT2
ArrD symGradN_vector(const ArrD &elemvec) const; // vT2s
// integral of the scalar product "elemmat(m*ndim+i,n*ndim+i) += N(m) * qscalar * N(n) * dV"
ArrD int_N_scalar_NT_dV(const ArrD &qscalar) const;
// integral of the dot product "elemvec(m,j) += dNdx(m,i) * qtensor(i,j) * dV"
// - allow template (e.g. vT2)
template<class T> ArrD int_gradN_dot_tensor2_dV(const ArrD &qtensor) const;
// - default template with:
ArrD int_gradN_dot_tensor2_dV (const ArrD &qtensor) const; // vT2 / vT2s (automatic selection)
ArrD int_gradN_dot_tensor2s_dV(const ArrD &qtensor) const; // vT2s
};
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#endif

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