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element_class_bernoulli_beam_inline_impl.hh
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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>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jul 15 2011
* @date last modification: Fri Feb 05 2021
*
* @brief Specialization of the element_class class for the type
* _bernoulli_beam_2
*
*
* @section LICENSE
*
* Copyright (©) 2010-2021 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/>.
*
*/
/**
* @verbatim
--x-----q1----|----q2-----x---> x
-1 0 1
@endverbatim
*
*/
/* -------------------------------------------------------------------------- */
//#include "element_class_structural.hh"
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_HH_
#define AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_HH_
namespace akantu {
/* -------------------------------------------------------------------------- */
template <>
template <typename D1, typename D2, typename D3>
inline void
InterpolationElement<_itp_bernoulli_beam_2, _itk_structural>::computeShapes(
const Eigen::MatrixBase<D1> & natural_coords,
const Eigen::MatrixBase<D2> & real_coord, Eigen::MatrixBase<D3> & N) {
Eigen::Matrix<Real, 2, 1> L;
InterpolationElement<_itp_lagrange_segment_2, _itk_lagrangian>::computeShapes(
natural_coords, L);
Eigen::Matrix<Real, 2, 4> H;
InterpolationElement<_itp_hermite_2, _itk_structural>::computeShapes(
natural_coords, real_coord, H);
// clang-format off
// u1 v1 t1 u2 v2 t2
N= Matrix<Real, 3, 6>{{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 <>
template <typename D1, typename D2, typename D3>
inline void
InterpolationElement<_itp_bernoulli_beam_3, _itk_structural>::computeShapes(
const Eigen::MatrixBase<D1> & natural_coords,
const Eigen::MatrixBase<D2> & real_coord, Eigen::MatrixBase<D3> & N) {
Eigen::Matrix<Real, 2, 1> L;
InterpolationElement<_itp_lagrange_segment_2, _itk_lagrangian>::computeShapes(
natural_coords, L);
Eigen::Matrix<Real, 2, 4> H;
InterpolationElement<_itp_hermite_2, _itk_structural>::computeShapes(
natural_coords, real_coord, H);
// clang-format off
// u1 v1 w1 tx1 ty1 tz1 u2 v2 w2 tx2 ty2 tz2
N = Matrix<Real, 6, 12>{{L(0), 0 , 0 , 0 , 0 , 0 , L(1), 0 , 0 , 0 , 0 , 0 }, // u
{0 , H(0, 0), 0 , 0 , 0 , H(0, 1), 0 , H(0, 2), 0 , 0 , 0 , H(0, 3)}, // v
{0 , 0 , H(0, 0), 0 , -H(0, 1), 0 , 0 , 0 , H(0, 2), 0 , -H(0, 3), 0 }, // w
{0 , 0 , 0 , L(0), 0 , 0 , 0 , 0 , 0 , L(1), 0 , 0 }, // thetax
{0 , 0 , H(1, 0), 0 , -H(1, 1), 0 , 0 , 0 , H(1, 2), 0 , -H(1, 3), 0 }, // thetay
{0 , H(1, 0), 0 , 0 , 0 , H(1, 1), 0 , H(1, 2), 0 , 0 , 0 , H(1, 3)}}; // thetaz
// clang-format on
}
/* -------------------------------------------------------------------------- */
#if 0
template <>
inline void
InterpolationElement<_itp_bernoulli_beam_3, _itk_structural>::computeShapesDisplacements(
const Vector<Real> & natural_coords, const Matrix<Real> & real_coord,
Matrix<Real> & N) {
}
#endif
/* -------------------------------------------------------------------------- */
template <>
template <class D1, class D2, class D3>
inline void
InterpolationElement<_itp_bernoulli_beam_2, _itk_structural>::computeDNDS(
const Eigen::MatrixBase<D1> & Xs, const Eigen::MatrixBase<D2> & xs,
Eigen::MatrixBase<D3> & dnds) {
Eigen::Matrix<Real, 1, 2> L;
InterpolationElement<_itp_lagrange_segment_2, _itk_lagrangian>::computeDNDS(
Xs, L);
Eigen::Matrix<Real, 1, 4> H;
InterpolationElement<_itp_hermite_2, _itk_structural>::computeDNDS(Xs, xs, H);
// Storing the derivatives in dnds
dnds.template block<1, 2>(0, 0) = L;
dnds.template block<1, 4>(0, 2) = H;
}
/* -------------------------------------------------------------------------- */
template <>
template <class D1, class D2>
inline void
InterpolationElement<_itp_bernoulli_beam_2, _itk_structural>::arrangeInVoigt(
const Eigen::MatrixBase<D1> & dnds, Eigen::MatrixBase<D2> & B) {
auto L = dnds.template block<1, 2>(0, 0); // Lagrange shape derivatives
auto H = dnds.template block<1, 4>(0, 2); // Hermite shape derivatives
// clang-format off
// u1 v1 t1 u2 v2 t2
B = Matrix<Real, 2, 6>{{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 <>
template <class D1, class D2, class D3>
inline void
InterpolationElement<_itp_bernoulli_beam_3, _itk_structural>::computeDNDS(
const Eigen::MatrixBase<D1> & natural_coords,
const Eigen::MatrixBase<D2> & real_coord, Eigen::MatrixBase<D3> & dnds) {
InterpolationElement<_itp_bernoulli_beam_2, _itk_structural>::computeDNDS(
natural_coords, real_coord, dnds);
}
/* -------------------------------------------------------------------------- */
template <>
template <class D1, class D2>
inline void
InterpolationElement<_itp_bernoulli_beam_3, _itk_structural>::arrangeInVoigt(
const Eigen::MatrixBase<D1> & dnds, Eigen::MatrixBase<D2> & B) {
auto L = dnds.template block<1, 2>(0, 0); // Lagrange shape derivatives
auto H = dnds.template block<1, 4>(0, 2); // Hermite shape derivatives
// clang-format off
// u1 v1 w1 x1 y1 z1 u2 v2 w2 x2 y2 z2
B = Matrix<Real, 4, 12>{{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 <>
template <class D1, class D2, class D3>
inline void ElementClass<_bernoulli_beam_2>::computeRotationMatrix(
Eigen::MatrixBase<D1> & R, const Eigen::MatrixBase<D2> & X,
const Eigen::MatrixBase<D3> &) {
auto && x2 = X(1); // X2
auto && x1 = X(0); // X1
auto cs = (x2 - x1) / (x2 - x1).norm();
auto c = cs(0);
auto s = cs(1);
// clang-format off
/// Definition of the rotation matrix
R= Matrix<Real, 3, 3>{{ c, s, 0.},
{-s, c, 0.},
{0., 0., 1.}};
// clang-format on
}
/* -------------------------------------------------------------------------- */
template <>
template <class D1, class D2, class D3>
inline void ElementClass<_bernoulli_beam_3>::computeRotationMatrix(
Eigen::MatrixBase<D1> & R, const Eigen::MatrixBase<D2> & X,
const Eigen::MatrixBase<D3> & n) {
auto dim = X.rows();
Eigen::Matrix<Real, 1, 3> x = (X(1) - X(0));
Eigen::Matrix<Real, 1, 3> nv = n;
x.normalize();
auto x_n = x.cross(nv);
Matrix<Real> Pe(dim, dim);
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.zero();
/// Definition of the rotation matrix
for (Int i = 0; i < dim; ++i) {
for (Int 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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