Page Menu
Home
c4science
Search
Configure Global Search
Log In
Files
F102274417
ElementHex8.h
No One
Temporary
Actions
Download File
Edit File
Delete File
View Transforms
Subscribe
Mute Notifications
Award Token
Subscribers
None
File Metadata
Details
File Info
Storage
Attached
Created
Wed, Feb 19, 00:09
Size
5 KB
Mime Type
text/x-c++
Expires
Fri, Feb 21, 00:09 (2 d)
Engine
blob
Format
Raw Data
Handle
24319967
Attached To
rGOOSEFEM GooseFEM
ElementHex8.h
View Options
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef XGOOSEFEM_ELEMENTHEX8_H
#define XGOOSEFEM_ELEMENTHEX8_H
// -------------------------------------------------------------------------------------------------
#include "GooseFEM.h"
// ==================================== GooseFEM::Element::Hex8 ====================================
namespace xGooseFEM {
namespace Element {
namespace Hex8 {
// ======================================== tensor algebra =========================================
using T2 = xt::xtensor_fixed<double, xt::xshape<3,3>>;
inline double inv(const T2 &A, T2 &Ainv);
// ================================ GooseFEM::Element::Hex8::Gauss =================================
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
}
// ================================ GooseFEM::Element::Hex8::Nodal =================================
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
}
// =================================================================================================
// ------------------------------------------ quadrature -------------------------------------------
class Quadrature
{
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
// 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 gradients w.r.t. local coordinate [nip, nne, ndim]
xt::xtensor<double,4> m_dNx; // shape function gradients w.r.t. global coordinate [nelem, nip, nne, ndim]
xt::xtensor<double,2> m_vol; // integration point volume [nelem, nip]
private:
// compute "vol" and "dNdx" based on current "x"
void compute_dN();
public:
// 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 integration volume
// - in-place
void dV(xt::xtensor<double,2> &qscalar) const;
void dV(xt::xtensor<double,4> &qtensor) const;
// - return qscalar/qtensor
xt::xtensor<double,2> dV() const;
xt::xtensor<double,4> dVtensor() const;
// dyadic product "qtensor(i,j) += dNdx(m,i) * elemvec(m,j)", its transpose and its symmetric part
// - in-place
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;
// - return qtensor
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;
// integral of the scalar product "elemmat(m*ndim+i,n*ndim+i) += N(m) * qscalar * N(n) * dV"
// - in-place
void int_N_scalar_NT_dV(const xt::xtensor<double,2> &qscalar, xt::xtensor<double,3> &elemmat) const;
// - return elemmat
xt::xtensor<double,3> int_N_scalar_NT_dV(const xt::xtensor<double,2> &qscalar) const;
// integral of the dot product "elemvec(m,j) += dNdx(m,i) * qtensor(i,j) * dV"
// - in-place
void int_gradN_dot_tensor2_dV(const xt::xtensor<double,4> &qtensor, xt::xtensor<double,3> &elemvec) const;
// - return elemvec
xt::xtensor<double,3> int_gradN_dot_tensor2_dV(const xt::xtensor<double,4> &qtensor) const;
};
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#endif
Event Timeline
Log In to Comment