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element_class_bernoulli_beam_inline_impl.hh
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rAKA akantu
element_class_bernoulli_beam_inline_impl.hh
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/**
* @file element_class_bernoulli_beam_inline_impl.hh
*
* @author Fabian Barras <fabian.barras@epfl.ch>
* @author Lucas Frerot <lucas.frerot@epfl.ch>
*
* @date creation: Fri Jul 15 2011
* @date last modification: Mon Feb 19 2018
*
* @brief Specialization of the element_class class for the type
* _bernoulli_beam_2
*
*
* Copyright (©) 2010-2018 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/>.
*
*
* @verbatim
--x-----q1----|----q2-----x---> x
-1 0 1
@endverbatim
*
*/
/* -------------------------------------------------------------------------- */
#include "aka_static_if.hh"
#include "element_class_structural.hh"
//#include "aka_element_classes_info.hh"
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_HH__
#define __AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_HH__
namespace akantu {
/* -------------------------------------------------------------------------- */
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, _ek_structural, 2,
_git_segment, 3);
AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY(_bernoulli_beam_3,
_gt_segment_2,
_itp_bernoulli_beam_3,
_segment_2, _ek_structural, 3,
_git_segment, 3);
/* -------------------------------------------------------------------------- */
template <>
inline void
InterpolationElement<_itp_bernoulli_beam_2, _itk_structural>::computeShapes(
const Vector<Real> & natural_coords, const Matrix<Real> & real_coord,
Matrix<Real> & N) {
Vector<Real> L(2);
InterpolationElement<_itp_lagrange_segment_2, _itk_lagrangian>::computeShapes(
natural_coords, L);
Matrix<Real> H(2, 4);
InterpolationElement<_itp_hermite_2, _itk_structural>::computeShapes(
natural_coords, real_coord, H);
// clang-format off
// u1 v1 t1 u2 v2 t2
N = {{L(0), 0 , 0 , L(1), 0 , 0 }, // u
{0 , H(0, 0), H(0, 1), 0 , H(0, 2), H(0, 3)}, // v
{0 , H(1, 0), H(1, 1), 0 , H(1, 2), H(1, 3)}}; // theta
// clang-format on
}
template <>
inline void
InterpolationElement<_itp_bernoulli_beam_3, _itk_structural>::computeShapes(
const Vector<Real> & natural_coords, const Matrix<Real> & real_coord,
Matrix<Real> & N) {
Vector<Real> L(2);
InterpolationElement<_itp_lagrange_segment_2, _itk_lagrangian>::computeShapes(
natural_coords, L);
Matrix<Real> H(2, 4);
InterpolationElement<_itp_hermite_2, _itk_structural>::computeShapes(
natural_coords, real_coord, H);
// clang-format off
// u1 v1 w1 x1 y1 z1 u2 v2 w2 x2 y2 z2
N = {{L(0), 0 , 0 , 0 , 0 , 0 , L(1), 0 , 0 , 0 , 0 , 0 }, // u
{0 , H(0, 0), 0 , 0 , H(0, 1), 0 , 0 , H(0, 2), 0 , 0 , H(0, 3), 0 }, // v
{0 , 0 , H(0, 0), 0 , 0 , H(0, 1), 0 , 0 , H(0, 2), 0 , 0 , H(0, 3)}, // w
{0 , 0 , 0 , L(0), 0 , 0 , 0 , 0 , 0 , L(1), 0 , 0 }, // thetax
{0 , H(1, 0), 0 , 0 , H(1, 1), 0 , 0 , H(1, 2), 0 , 0 , H(1, 3), 0 }, // thetay
{0 , 0 , H(1, 0), 0 , 0 , H(1, 1), 0 , 0 , H(1, 2), 0 , 0 , H(1, 3)}}; // thetaz
// clang-format on
}
/* -------------------------------------------------------------------------- */
template <>
inline void
InterpolationElement<_itp_bernoulli_beam_2, _itk_structural>::computeDNDS(
const Vector<Real> & natural_coords, const Matrix<Real> & real_coord,
Matrix<Real> & dnds) {
Matrix<Real> L(1, 2);
InterpolationElement<_itp_lagrange_segment_2, _itk_lagrangian>::computeDNDS(
natural_coords, L);
Matrix<Real> H(1, 4);
InterpolationElement<_itp_hermite_2, _itk_structural>::computeDNDS(
natural_coords, real_coord, H);
// Storing the derivatives in dnds
dnds.block(L, 0, 0);
dnds.block(H, 0, 2);
}
/* -------------------------------------------------------------------------- */
template <>
inline void
InterpolationElement<_itp_bernoulli_beam_2, _itk_structural>::arrangeInVoigt(
const Matrix<Real> & dnds, Matrix<Real> & B) {
auto L = dnds.block(0, 0, 1, 2); // Lagrange shape derivatives
auto H = dnds.block(0, 2, 1, 4); // Hermite shape derivatives
// clang-format off
// u1 v1 t1 u2 v2 t2
B = {{L(0, 0), 0, 0, L(0, 1), 0, 0 },
{0, H(0, 0), H(0, 1), 0, H(0, 2), H(0, 3)}};
// clang-format on
}
/* -------------------------------------------------------------------------- */
template <>
inline void
InterpolationElement<_itp_bernoulli_beam_3, _itk_structural>::computeDNDS(
const Vector<Real> & natural_coords, const Matrix<Real> & real_coord,
Matrix<Real> & dnds) {
InterpolationElement<_itp_bernoulli_beam_2, _itk_structural>::computeDNDS(
natural_coords, real_coord, dnds);
}
/* -------------------------------------------------------------------------- */
template <>
inline void
InterpolationElement<_itp_bernoulli_beam_3, _itk_structural>::arrangeInVoigt(
const Matrix<Real> & dnds, Matrix<Real> & B) {
auto L = dnds.block(0, 0, 1, 2); // Lagrange shape derivatives
auto H = dnds.block(0, 2, 1, 4); // Hermite shape derivatives
// clang-format off
// u1 v1 w1 x1 y1 z1 u2 v2 w2 x2 y2 z2
B = {{L(0, 0), 0 , 0 , 0 , 0 , 0 , L(0, 1), 0 , 0 , 0 , 0 , 0 }, // eps
{0 , H(0, 0), 0 , 0 , 0 , H(0, 1), 0 , H(0, 2), 0 , 0 , 0 , H(0, 3)}, // chi strong axis
{0 , 0 ,-H(0, 0), 0 , H(0, 1), 0 , 0 , 0 ,-H(0, 2), 0 , H(0, 3), 0 }, // chi weak axis
{0 , 0 , 0 , L(0, 0), 0 , 0 , 0 , 0 , 0 , L(0, 1), 0 , 0 }}; // chi torsion
// clang-format on
}
/* -------------------------------------------------------------------------- */
template <>
inline void ElementClass<_bernoulli_beam_2>::computeRotationMatrix(
Matrix<Real> & R, const Matrix<Real> & X, const Vector<Real> &) {
Vector<Real> x2 = X(1); // X2
Vector<Real> x1 = X(0); // X1
auto cs = (x2 - x1);
cs.normalize();
auto c = cs(0);
auto s = cs(1);
// clang-format off
/// Definition of the rotation matrix
R = {{ c, s, 0.},
{-s, c, 0.},
{ 0., 0., 1.}};
// clang-format on
}
/* -------------------------------------------------------------------------- */
template <>
inline void ElementClass<_bernoulli_beam_3>::computeRotationMatrix(
Matrix<Real> & R, const Matrix<Real> & X, const Vector<Real> & n) {
Vector<Real> x2 = X(1); // X2
Vector<Real> x1 = X(0); // X1
auto dim = X.rows();
auto x = (x2 - x1);
x.normalize();
auto x_n = x.crossProduct(n);
Matrix<Real> Pe = {{1., 0., 0.}, {0., -1., 0.}, {0., 0., 1.}};
Matrix<Real> Pg(dim, dim);
Pg(0) = x;
Pg(1) = x_n;
Pg(2) = n;
Pe *= Pg.inverse();
R.clear();
/// Definition of the rotation matrix
for (UInt i = 0; i < dim; ++i)
for (UInt j = 0; j < dim; ++j)
R(i + dim, j + dim) = R(i, j) = Pe(i, j);
}
} // namespace akantu
#endif /* __AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_HH__ */
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