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ElementQuad4Planar.h
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Sat, May 11, 11:39

ElementQuad4Planar.h
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/**
Quadrature for 4-noded quadrilateral element in 2d (GooseFEM::Mesh::ElementType::Quad4),
in a Cartesian coordinated system.
The different with ElementQuad4.h is that here the tensors live in 3d and are assumed plane strain.
\file ElementQuad4Planar.h
\copyright Copyright 2017. Tom de Geus. All rights reserved.
\license This project is released under the GNU Public License (GPLv3).
*/
#ifndef GOOSEFEM_ELEMENTQUAD4PLANAR_H
#define GOOSEFEM_ELEMENTQUAD4PLANAR_H
#include "config.h"
namespace GooseFEM {
namespace Element {
namespace Quad4 {
class QuadraturePlanar : public GooseFEM::Element::QuadratureBase<4, 2, 3> {
public:
// Fixed dimensions:
// ndim = 2 - number of dimensions
// nne = 4 - number of nodes per element
// tdim = 3 - number of dimensions of tensors
//
// 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]
// Constructor: integration point coordinates and weights are optional (default: Gauss)
QuadraturePlanar() = default;
QuadraturePlanar(const xt::xtensor<double, 3>& x, double thick = 1.0);
QuadraturePlanar(
const xt::xtensor<double, 3>& x,
const xt::xtensor<double, 2>& xi,
const xt::xtensor<double, 1>& w,
double thick = 1.0);
// Update the nodal positions (shape of "x" should match the earlier definition)
void update_x(const xt::xtensor<double, 3>& x);
// Return shape function gradients
xt::xtensor<double, 4> GradN() const;
// Return integration volume
xt::xtensor<double, 2> dV() const;
// Dyadic product (and its transpose and symmetric part)
// qtensor(i,j) += dNdx(m,i) * elemvec(m,j)
void gradN_vector(const xt::xtensor<double, 3>& elemvec, xt::xtensor<double, 4>& qtensor) const;
void gradN_vector_T(const xt::xtensor<double, 3>& elemvec, xt::xtensor<double, 4>& qtensor) const;
void symGradN_vector(const xt::xtensor<double, 3>& elemvec, xt::xtensor<double, 4>& qtensor) const;
// Integral of the scalar product
// elemmat(m*ndim+i,n*ndim+i) += N(m) * qscalar * N(n) * dV
void int_N_scalar_NT_dV(
const xt::xtensor<double, 2>& qscalar, xt::xtensor<double, 3>& elemmat) const;
// Integral of the dot product
// elemvec(m,j) += dNdx(m,i) * qtensor(i,j) * dV
void int_gradN_dot_tensor2_dV(
const xt::xtensor<double, 4>& qtensor, xt::xtensor<double, 3>& elemvec) const;
// Integral of the dot product
// elemmat(m*2+j, n*2+k) += dNdx(m,i) * qtensor(i,j,k,l) * dNdx(n,l) * dV
void int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double, 6>& qtensor, xt::xtensor<double, 3>& elemmat) const;
// Auto-allocation of the functions above
xt::xtensor<double, 4> GradN_vector(const xt::xtensor<double, 3>& elemvec) const;
xt::xtensor<double, 4> GradN_vector_T(const xt::xtensor<double, 3>& elemvec) const;
xt::xtensor<double, 4> SymGradN_vector(const xt::xtensor<double, 3>& elemvec) const;
xt::xtensor<double, 3> Int_N_scalar_NT_dV(const xt::xtensor<double, 2>& qscalar) const;
xt::xtensor<double, 3> Int_gradN_dot_tensor2_dV(const xt::xtensor<double, 4>& qtensor) const;
xt::xtensor<double, 3> Int_gradN_dot_tensor4_dot_gradNT_dV(const xt::xtensor<double, 6>& qtensor) const;
private:
// Compute "vol" and "dNdx" based on current "x"
void compute_dN();
private:
xt::xtensor<double, 3> m_x; // nodal positions stored per element [nelem, nne, ndim]
xt::xtensor<double, 1> m_w; // weight of each integration point [nip]
xt::xtensor<double, 2> m_xi; // local coordinate of each integration point [nip, ndim]
xt::xtensor<double, 2> m_N; // shape functions [nip, nne]
xt::xtensor<double, 3> m_dNxi; // shape function grad. wrt local coor. [nip, nne, ndim]
xt::xtensor<double, 4> m_dNx; // shape function grad. wrt global coor. [nelem, nip, nne, ndim]
xt::xtensor<double, 2> m_vol; // integration point volume [nelem, nip]
// Thickness
double m_thick;
};
} // namespace Quad4
} // namespace Element
} // namespace GooseFEM
#include "ElementQuad4Planar.hpp"
#endif

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