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rGOOSEFEM/include/GooseFEM/ElementHex8.h
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ElementHex8.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_ELEMENTHEX8_H
#define GOOSEFEM_ELEMENTHEX8_H
// -------------------------------------------------------------------------------------------------
#include "config.h"
// =================================================================================================
namespace GooseFEM {
namespace Element {
namespace Hex8 {
// -------------------------------------------------------------------------------------------------
inline double inv(
const xt::xtensor_fixed<double, xt::xshape<3,3>>& A,
xt::xtensor_fixed<double, xt::xshape<3,3>>& Ainv);
// -------------------------------------------------------------------------------------------------
namespace Gauss {
inline size_t nip(); // number of integration points
inline xt::xtensor<double,2> xi(); // integration point coordinates (local coordinates)
inline xt::xtensor<double,1> w(); // integration point weights
}
// -------------------------------------------------------------------------------------------------
namespace Nodal {
inline size_t nip(); // number of integration points
inline xt::xtensor<double,2> xi(); // integration point coordinates (local coordinates)
inline xt::xtensor<double,1> w(); // integration point weights
}
// -------------------------------------------------------------------------------------------------
class Quadrature
{
public:
// Fixed dimensions:
// ndim = 3 - number of dimensions
// nne = 8 - 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, ndim, ndim]
// "qscalar" - integration point scalar - [nelem, nip]
// Constructor: integration point coordinates and weights are optional (default: Gauss)
Quadrature() = default;
Quadrature(
const xt::xtensor<double,3>& x);
Quadrature(
const xt::xtensor<double,3>& x,
const xt::xtensor<double,2>& xi,
const xt::xtensor<double,1>& w);
// Update the nodal positions (shape of "x" should match the earlier definition)
void update_x(const xt::xtensor<double,3>& 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 shape function gradients
xt::xtensor<double,4> gradN() const;
// Return integration volume
void dV(xt::xtensor<double,2>& qscalar) const;
void dV(xt::xtensor<double,4>& qtensor) const; // same volume for all tensor components
void dV(xt::xarray<double>& qtensor) const; // same volume for all tensor components
// 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; // overwritten
void gradN_vector_T(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const; // overwritten
void symGradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const; // overwritten
// 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; // overwritten
// 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; // overwritten
// 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; // overwritten
// Auto-allocation of the functions above
xt::xtensor<double,2> DV() const;
xt::xarray<double> DV(
size_t rank) const;
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:
// Dimensions (flexible)
size_t m_nelem; // number of elements
size_t m_nip; // number of integration points
// Dimensions (fixed for this element type)
static const size_t m_nne=8; // number of nodes per element
static const size_t m_ndim=3; // number of dimensions
const size_t m_nd=3; // number of dimensions (non-static, sometimes useful)
// Data arrays
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. w.r.t. local coor. [nip, nne, ndim]
xt::xtensor<double,4> m_dNx; // shape function grad. w.r.t. global coor. [nelem, nip, nne, ndim]
xt::xtensor<double,2> m_vol; // integration point volume [nelem, nip]
};
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#include "ElementHex8.hpp"
// =================================================================================================
#endif
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