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element_class_structural.hh
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/**
* @file element_class_structural.hh
*
* @author Fabian Barras <fabian.barras@epfl.ch>
* @author Lucas Frerot <lucas.frerot@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Damien Spielmann <damien.spielmann@epfl.ch>
*
* @date creation: Thu Feb 21 2013
* @date last modification: Mon Feb 01 2021
*
* @brief Specialization of the element classes for structural elements
*
*
* @section LICENSE
*
* Copyright (©) 2014-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "aka_iterators.hh"
#include "element_class.hh"
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_ELEMENT_CLASS_STRUCTURAL_HH_
#define AKANTU_ELEMENT_CLASS_STRUCTURAL_HH_
namespace akantu {
/// Macro to generate the InterpolationProperty structures for different
/// interpolation types
#define AKANTU_DEFINE_STRUCTURAL_INTERPOLATION_TYPE_PROPERTY( \
itp_type, itp_geom_type, ndof, nb_stress, nb_dnds_cols) \
template <> struct InterpolationProperty<itp_type> { \
static constexpr InterpolationKind kind{_itk_structural}; \
static constexpr Int nb_nodes_per_element{ \
InterpolationProperty<itp_geom_type>::nb_nodes_per_element}; \
static constexpr InterpolationType itp_geometry_type{itp_geom_type}; \
static constexpr Int natural_space_dimension{ \
InterpolationProperty<itp_geom_type>::natural_space_dimension}; \
static constexpr Int nb_degree_of_freedom{ndof}; \
static constexpr Int nb_stress_components{nb_stress}; \
static constexpr Int dnds_columns{nb_dnds_cols}; \
} // namespace akantu
/// Macro to generate the element class structures for different structural
/// element types
/* -------------------------------------------------------------------------- */
#define AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY( \
elem_type, geom_type, interp_type, parent_el_type, sp, gauss_int_type, \
min_int_order) \
template <> struct ElementClassProperty<elem_type> { \
static constexpr GeometricalType geometrical_type{geom_type}; \
static constexpr InterpolationType interpolation_type{interp_type}; \
static constexpr ElementType parent_element_type{parent_el_type}; \
static constexpr ElementKind element_kind{_ek_structural}; \
static constexpr Int spatial_dimension{sp}; \
static constexpr GaussIntegrationType gauss_integration_type{ \
gauss_int_type}; \
static constexpr Int polynomial_degree{min_int_order}; \
}
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_STRUCTURAL_INTERPOLATION_TYPE_PROPERTY(_itp_bernoulli_beam_2,
_itp_lagrange_segment_2, 3,
2, 6);
AKANTU_DEFINE_STRUCTURAL_INTERPOLATION_TYPE_PROPERTY(_itp_bernoulli_beam_3,
_itp_lagrange_segment_2, 6,
4, 6);
AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY(_bernoulli_beam_2,
_gt_segment_2,
_itp_bernoulli_beam_2,
_segment_2, 2, _git_segment, 3);
AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY(_bernoulli_beam_3,
_gt_segment_2,
_itp_bernoulli_beam_3,
_segment_2, 3, _git_segment, 3);
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_STRUCTURAL_INTERPOLATION_TYPE_PROPERTY(
_itp_discrete_kirchhoff_triangle_18, _itp_lagrange_triangle_3, 6, 6, 21);
AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY(
_discrete_kirchhoff_triangle_18, _gt_triangle_3,
_itp_discrete_kirchhoff_triangle_18, _triangle_3, 3, _git_triangle, 2);
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
template <InterpolationType interpolation_type>
class InterpolationElement<interpolation_type, _itk_structural> {
public:
using interpolation_property = InterpolationProperty<interpolation_type>;
/// compute the shape values for a given point in natural coordinates
template <class D1, class D2, class D3>
static inline void computeShapes(const Eigen::MatrixBase<D1> & natural_coord,
const Eigen::MatrixBase<D2> & real_coord,
Eigen::MatrixBase<D3> & N);
/// compute the shape values for a given set of points in natural coordinates
template <class D1, class D2, class D3>
static inline void computeShapes(const Eigen::MatrixBase<D1> & Xs,
const Eigen::MatrixBase<D2> & x,
const Eigen::MatrixBase<D3> & T,
TensorBase<Real, 3> & Ns) {
Matrix<Real> N(Ns.size(0), Ns.size(1));
for (auto && data : zip(Xs, Ns)) {
auto && X = std::get<0>(data);
auto && N_T = std::get<1>(data);
computeShapes(X, x, N);
N_T = N * T;
}
}
template <class D1, class D2, class D3>
static inline void computeShapesMass(const Eigen::MatrixBase<D1> & Xs,
const Eigen::MatrixBase<D2> & x,
const Eigen::MatrixBase<D3> & T,
TensorBase<Real, 3> & Ns) {
for (int i = 0; i < Xs.cols(); ++i) {
auto N_T = Ns(i);
Matrix<Real> N(interpolation_property::nb_degree_of_freedom, N_T.cols());
computeShapes(Xs(i), x, N);
N_T = N.block(0, 0, N_T.rows(), N_T.cols()) * T;
}
}
/// compute shape derivatives (input is dxds) for a set of points
template <class D>
static inline void computeShapeDerivatives(const TensorBase<Real, 3> & Js,
const TensorBase<Real, 3> & DNDSs,
const Eigen::MatrixBase<D> & R,
TensorBase<Real, 3> & Bs) {
for (Int i = 0; i < Js.size(2); ++i) {
auto && DNDX = Js(i).inverse() * DNDSs(i);
auto && B_R = Bs(i);
Matrix<Real> B(B_R.rows(), B_R.cols());
arrangeInVoigt(DNDX, B);
B_R = B * R;
}
}
/**
* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the variation of
* shape functions along with variation of natural coordinates on a given set
* of points in natural coordinates
*/
template <typename D1, typename D2>
static inline void computeDNDS(const Eigen::MatrixBase<D1> & Xs,
const Eigen::MatrixBase<D2> & xs,
TensorBase<Real, 3> & dnds) {
for (auto && data : zip(Xs, dnds))
computeDNDS(std::get<0>(data), xs, std::get<1>(data));
}
/**
* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the variation of
* shape functions along with
* variation of natural coordinates on a given point in natural
* coordinates
*/
template <typename D1, typename D2, typename D3>
static inline void computeDNDS(const Eigen::MatrixBase<D1> & Xs,
const Eigen::MatrixBase<D2> & xs,
Eigen::MatrixBase<D3> & dnds);
/**
* arrange B in Voigt notation from DNDS
*/
template <class D1, class D2>
static inline void arrangeInVoigt(const Eigen::MatrixBase<D1> & dnds,
Eigen::MatrixBase<D2> & B) {
// Default implementation assumes dnds is already in Voigt notation
B = dnds;
}
public:
static inline constexpr auto getNbNodesPerInterpolationElement() {
return interpolation_property::nb_nodes_per_element;
}
static inline constexpr auto getShapeSize() {
return interpolation_property::nb_nodes_per_element *
interpolation_property::nb_degree_of_freedom *
interpolation_property::nb_degree_of_freedom;
}
static inline constexpr auto getShapeIndependantSize() {
return interpolation_property::nb_nodes_per_element *
interpolation_property::nb_degree_of_freedom *
interpolation_property::nb_stress_components;
}
static inline constexpr auto getShapeDerivativesSize() {
return interpolation_property::nb_nodes_per_element *
interpolation_property::nb_degree_of_freedom *
interpolation_property::nb_stress_components;
}
static inline constexpr auto getNaturalSpaceDimension() {
return interpolation_property::natural_space_dimension;
}
static inline constexpr auto getNbDegreeOfFreedom() {
return interpolation_property::nb_degree_of_freedom;
}
static inline constexpr auto getNbStressComponents() {
return interpolation_property::nb_stress_components;
}
};
/* -------------------------------------------------------------------------- */
/* ElementClass for structural elements */
/* -------------------------------------------------------------------------- */
template <ElementType element_type>
class ElementClass<element_type, _ek_structural>
: public GeometricalElement<
ElementClassProperty<element_type>::geometrical_type>,
public InterpolationElement<
ElementClassProperty<element_type>::interpolation_type> {
protected:
using geometrical_element =
GeometricalElement<ElementClassProperty<element_type>::geometrical_type>;
using interpolation_element = InterpolationElement<
ElementClassProperty<element_type>::interpolation_type>;
using parent_element =
ElementClass<ElementClassProperty<element_type>::parent_element_type>;
public:
template <class D1, class D2, class D3>
static inline void
computeRotationMatrix(Eigen::MatrixBase<D1> & /*R*/,
const Eigen::MatrixBase<D2> & /*X*/,
const Eigen::MatrixBase<D3> & /*extra_normal*/) {
AKANTU_TO_IMPLEMENT();
}
/// compute jacobian (or integration variable change factor) for a given point
template <typename D1, typename D2, typename D3>
static inline void computeJMat(const Eigen::MatrixBase<D1> & natural_coords,
const Eigen::MatrixBase<D2> & Xs,
Eigen::MatrixBase<D3> & J) {
Matrix<Real> dnds(Xs.rows(), Xs.cols());
parent_element::computeDNDS(natural_coords, dnds);
J = dnds * Xs.transpose();
}
template <typename D1, typename D2>
static inline void computeJMat(const Eigen::MatrixBase<D1> & Xs,
const Eigen::MatrixBase<D2> & xs,
Tensor3<Real> & Js) {
for (auto && data : zip(Xs, Js)) {
computeJMat(std::get<0>(data), xs, std::get<1>(data));
}
}
template <typename D1, typename D2, typename D3,
std::enable_if_t<aka::is_vector_v<D3>> * = nullptr>
static inline void computeJacobian(const Eigen::MatrixBase<D1> & Xs,
const Eigen::MatrixBase<D2> & xs,
Eigen::MatrixBase<D3> & jacobians) {
using itp = typename interpolation_element::interpolation_property;
Tensor3<Real> Js(itp::natural_space_dimension, itp::natural_space_dimension,
Xs.cols());
computeJMat(Xs, xs, Js);
for (auto && data : zip(jacobians, Js)) {
std::get<0>(data) = std::get<1>(data).determinant();
}
}
template <typename D1, typename D2>
static inline void computeRotation(const Eigen::MatrixBase<D1> & xs,
Eigen::MatrixBase<D2> & R);
public:
static constexpr AKANTU_GET_MACRO_AUTO_NOT_CONST(Kind, _ek_structural);
static constexpr AKANTU_GET_MACRO_AUTO_NOT_CONST(P1ElementType, _not_defined);
static constexpr AKANTU_GET_MACRO_AUTO_NOT_CONST(FacetType, _not_defined);
static constexpr auto getFacetType(__attribute__((unused)) Int t = 0) {
return _not_defined;
}
static constexpr AKANTU_GET_MACRO_AUTO_NOT_CONST(
SpatialDimension, ElementClassProperty<element_type>::spatial_dimension);
static constexpr auto getFacetTypes() {
return ElementClass<_not_defined>::getFacetTypes();
}
};
} // namespace akantu
/* -------------------------------------------------------------------------- */
#include "element_class_hermite_inline_impl.hh"
/* keep order */
#include "element_class_bernoulli_beam_inline_impl.hh"
#include "element_class_kirchhoff_shell_inline_impl.hh"
/* -------------------------------------------------------------------------- */
#endif /* AKANTU_ELEMENT_CLASS_STRUCTURAL_HH_ */

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