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ElementQuad4Axisymmetric.h
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ElementQuad4Axisymmetric.h
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/**
Quadrature for 4-noded quadrilateral element in 2d (GooseFEM::Mesh::ElementType::Quad4),
in an axisymmetric coordinated system.
\file ElementQuad4Axisymmetric.h
\copyright Copyright 2017. Tom de Geus. All rights reserved.
\license This project is released under the GNU Public License (GPLv3).
*/
#ifndef GOOSEFEM_ELEMENTQUAD4AXISYMMETRIC_H
#define GOOSEFEM_ELEMENTQUAD4AXISYMMETRIC_H
#include "config.h"
namespace GooseFEM {
namespace Element {
namespace Quad4 {
/**
Interpolation and quadrature.
Fixed dimensions:
- ``ndim = 2``: number of dimensions.
- ``tdim = 3``: number of dimensions or tensor.
- ``nne = 4``: 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, #tdim, #tdim]
- ``qscalar``: integration point scalar, [#nelem, #nip]
*/
class QuadratureAxisymmetric : public GooseFEM::Element::QuadratureBaseCartesian<4, 2, 3> {
public:
QuadratureAxisymmetric() = default;
/**
Constructor: use default Gauss integration.
During construction the values of the shape functions and the shape function gradients
(in local and global) coordinates are computed. They can be reused without any cost.
They only have to be recomputed when the nodal position changes.
In that case use update_x() to update the nodal positions and to recompute the
shape functions and their gradients.
\param x nodal coordinates (``elemvec``).
*/
QuadratureAxisymmetric(const xt::xtensor<double, 3>& x);
/**
Constructor with custom integration.
During construction the values of the shape functions and the shape function gradients
(in local and global) coordinates are computed. They can be reused without any cost.
They only have to be recomputed when the nodal position changes.
In that case use update_x() to update the nodal positions and to recompute the
shape functions and their gradients.
\param x nodal coordinates (``elemvec``).
\param xi Integration point coordinates (local coordinates) [#nip].
\param w Integration point weights [#nip].
*/
QuadratureAxisymmetric(
const xt::xtensor<double, 3>& x,
const xt::xtensor<double, 2>& xi,
const xt::xtensor<double, 1>& w);
/**
Get the B-matrix (shape function gradients) (in global coordinates).
Note that the functions and their gradients are precomputed upon construction,
or updated when calling update_x().
\return ``B`` matrix stored per element, per integration point [#nelem, #nne, #tdim, #tdim, #tdim]
*/
xt::xtensor<double, 6> B() const;
// qtensor(e, q, i, j) += B(e, q, m, i, j, k) * elemvec(e, q, m, k)
void gradN_vector(
const xt::xtensor<double, 3>& elemvec, xt::xtensor<double, 4>& qtensor) const override;
void gradN_vector_T(
const xt::xtensor<double, 3>& elemvec, xt::xtensor<double, 4>& qtensor) const override;
void symGradN_vector(
const xt::xtensor<double, 3>& elemvec, xt::xtensor<double, 4>& qtensor) const override;
// elemmat(e, q, m * ndim + i, n * ndim + i) +=
// N(e, q, m) * qscalar(e, q) * N(e, q, n) * dV(e, q)
void int_N_scalar_NT_dV(
const xt::xtensor<double, 2>& qscalar, xt::xtensor<double, 3>& elemmat) const override;
// fm = ( Bm^T : qtensor ) dV
void int_gradN_dot_tensor2_dV(
const xt::xtensor<double, 4>& qtensor, xt::xtensor<double, 3>& elemvec) const override;
// Kmn = ( Bm^T : qtensor : Bn ) dV
void int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double, 6>& qtensor, xt::xtensor<double, 3>& elemmat) const override;
protected:
void compute_dN() override;
private:
xt::xtensor<double, 4> GradN() const override;
private:
xt::xtensor<double, 6> m_B; ///< B-matrix [#nelem, #nne, #tdim, #tdim, #tdim]
};
} // namespace Quad4
} // namespace Element
} // namespace GooseFEM
#include "ElementQuad4Axisymmetric.hpp"
#endif

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