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structural_mechanics_model_inline_impl.cc
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			/**
			* @file structural_mechanics_model_inline_impl.cc
			*
			* @author Fabian Barras <fabian.barras@epfl.ch>
			* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			* @author Damien Spielmann <damien.spielmann@epfl.ch>
			*
			* @date creation: Fri Jul 15 2011
			* @date last modification: Thu Oct 15 2015
			*
			* @brief Implementation of inline functions of StructuralMechanicsModel
			*
			* @section LICENSE
			*
			* Copyright (©) 2010-2012, 2014, 2015 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 "structural_mechanics_model.hh"
			/* -------------------------------------------------------------------------- */

			#ifndef __AKANTU_STRUCTURAL_MECHANICS_MODEL_INLINE_IMPL_CC__
			#define __AKANTU_STRUCTURAL_MECHANICS_MODEL_INLINE_IMPL_CC__

			namespace akantu {
			/* -------------------------------------------------------------------------- */
			template <ElementType type>
			void StructuralMechanicsModel::computeTangentModuli(
			Array<Real> & tangent_moduli) {
			AKANTU_DEBUG_TO_IMPLEMENT();
			}
			} // namespace akantu

			#include "structural_element_bernoulli_beam_2.hh"
			#include "structural_element_bernoulli_beam_3.hh"
			#include "structural_element_kirchhoff_shell.hh"

			namespace akantu {

			/* -------------------------------------------------------------------------- */
			template <ElementType type>
			void StructuralMechanicsModel::assembleStiffnessMatrix() {
			AKANTU_DEBUG_IN();

			auto nb_element = getFEEngine().getMesh().getNbElement(type);
			auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			auto nb_quadrature_points = getFEEngine().getNbIntegrationPoints(type);
			auto tangent_size = ElementClass<type>::getVoigtSize();

			auto tangent_moduli = std::make_unique<Array<Real>>(
			nb_element * nb_quadrature_points, tangent_size * tangent_size,
			"tangent_stiffness_matrix");
			computeTangentModuli<type>(*tangent_moduli);

			/// compute @f$\mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			UInt bt_d_b_size = nb_degree_of_freedom * nb_nodes_per_element;

			auto bt_d_b = std::make_unique<Array<Real>>(
			nb_element * nb_quadrature_points, bt_d_b_size * bt_d_b_size, "B^tDB");

			const auto & b = getFEEngine().getShapesDerivatives(type);

			Matrix<Real> Bt_D(bt_d_b_size, tangent_size);

			auto B = b.begin(tangent_size, bt_d_b_size);
			auto D = tangent_moduli->begin(tangent_size, tangent_size);
			auto Bt_D_B = bt_d_b->begin(bt_d_b_size, bt_d_b_size);
			auto T = rotation_matrix(type).begin(bt_d_b_size, bt_d_b_size);

			for (UInt e = 0; e < nb_element; ++e, ++T) {
			for (UInt q = 0; q < nb_quadrature_points; ++q, ++B, ++D, ++Bt_D_B) {
			auto BT = B *T;
			Bt_D.mul<true, false>(BT, *D);
			Bt_D_B->mul<false, false>(Bt_D, BT);
			}
			}

			/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
			auto int_bt_d_b = std::make_unique<Array<Real>>(
			nb_element, bt_d_b_size * bt_d_b_size, "int_B^tDB");

			getFEEngine().integrate(bt_d_b, int_bt_d_b, bt_d_b_size * bt_d_b_size,
			type);

			getDOFManager().assembleElementalMatricesToMatrix(
			"K", "displacement", *int_bt_d_b, type, _not_ghost, _symmetric);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <ElementType type>
			void StructuralMechanicsModel::computeStressOnQuad() {
			AKANTU_DEBUG_IN();

			Array<Real> & sigma = stress(type, _not_ghost);

			auto nb_element = mesh.getNbElement(type);
			auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
			auto nb_quadrature_points = getFEEngine().getNbIntegrationPoints(type);
			auto tangent_size = ElementClass<type>::getVoigtSize();

			auto tangent_moduli = std::make_unique<Array<Real>>(
			nb_element * nb_quadrature_points, tangent_size * tangent_size,
			"tangent_stiffness_matrix");

			computeTangentModuli<type>(*tangent_moduli);

			/// compute DB
			auto d_b_size = nb_degree_of_freedom * nb_nodes_per_element;

			auto d_b = std::make_unique<Array<Real>>(nb_element * nb_quadrature_points,
			d_b_size * tangent_size, "D*B");

			const auto & b = getFEEngine().getShapesDerivatives(type);

			auto B = b.begin(tangent_size, d_b_size);
			auto D = tangent_moduli->begin(tangent_size, tangent_size);
			auto D_B = d_b->begin(tangent_size, d_b_size);

			for (UInt e = 0; e < nb_element; ++e) {
			for (UInt q = 0; q < nb_quadrature_points; ++q, ++B, ++D, ++D_B) {
			D_B->mul<false, false>(D, B);
			}
			}

			/// compute DBu
			D_B = d_b->begin(tangent_size, d_b_size);
			auto DBu = sigma.begin(tangent_size);
			Vector<Real> ul(d_b_size);

			Array<Real> u_el(0, d_b_size);
			FEEngine::extractNodalToElementField(mesh, *displacement_rotation, u_el,
			type);

			auto ug = u_el.begin(d_b_size);
			auto T = rotation_matrix(type).begin(d_b_size, d_b_size);

			for (UInt e = 0; e < nb_element; ++e, ++T, ++ug) {
			ul.mul<false>(T, ug);
			for (UInt q = 0; q < nb_quadrature_points; ++q, ++D_B, ++DBu) {
			DBu->mul<false>(*D_B, ul);
			}
			}

			delete d_b;

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <ElementType type>
			void StructuralMechanicsModel::computeForcesByLocalTractionArray(
			const Array<Real> & tractions) {
			AKANTU_DEBUG_IN();

			UInt nb_element = getFEEngine().getMesh().getNbElement(type);
			UInt nb_nodes_per_element =
			getFEEngine().getMesh().getNbNodesPerElement(type);
			UInt nb_quad = getFEEngine().getNbIntegrationPoints(type);

			// check dimension match
			AKANTU_DEBUG_ASSERT(
			Mesh::getSpatialDimension(type) == getFEEngine().getElementDimension(),
			"element type dimension does not match the dimension of boundaries : "
			<< getFEEngine().getElementDimension()
			<< " != " << Mesh::getSpatialDimension(type));

			// check size of the vector
			AKANTU_DEBUG_ASSERT(
			tractions.size() == nb_quad * nb_element,
			"the size of the vector should be the total number of quadrature points");

			// check number of components
			AKANTU_DEBUG_ASSERT(tractions.getNbComponent() == nb_degree_of_freedom,
			"the number of components should be the spatial "
			"dimension of the problem");

			Array<Real> Nvoigt(nb_element * nb_quad, nb_degree_of_freedom *
			nb_degree_of_freedom *
			nb_nodes_per_element);
			transferNMatrixToSymVoigtNMatrix<type>(Nvoigt);

			Array<Real>::const_matrix_iterator N_it = Nvoigt.begin(
			nb_degree_of_freedom, nb_degree_of_freedom * nb_nodes_per_element);
			Array<Real>::const_matrix_iterator T_it =
			rotation_matrix(type).begin(nb_degree_of_freedom * nb_nodes_per_element,
			nb_degree_of_freedom * nb_nodes_per_element);
			Array<Real>::const_vector_iterator te_it =
			tractions.begin(nb_degree_of_freedom);

			Array<Real> funct(nb_element * nb_quad,
			nb_degree_of_freedom * nb_nodes_per_element, 0.);
			Array<Real>::iterator<Vector<Real>> Fe_it =
			funct.begin(nb_degree_of_freedom * nb_nodes_per_element);

			Vector<Real> fe(nb_degree_of_freedom * nb_nodes_per_element);
			for (UInt e = 0; e < nb_element; ++e, ++T_it) {
			const Matrix<Real> & T = *T_it;
			for (UInt q = 0; q < nb_quad; ++q, ++N_it, ++te_it, ++Fe_it) {
			const Matrix<Real> & N = *N_it;
			const Vector<Real> & te = *te_it;
			Vector<Real> & Fe = *Fe_it;

			// compute N^t tl
			fe.mul<true>(N, te);
			// turn N^t tl back in the global referential
			Fe.mul<true>(T, fe);
			}
			}

			// allocate the vector that will contain the integrated values
			std::stringstream name;
			name << id << type << ":integral_boundary";
			Array<Real> int_funct(nb_element, nb_degree_of_freedom * nb_nodes_per_element,
			name.str());

			// do the integration
			getFEEngine().integrate(funct, int_funct,
			nb_degree_of_freedom * nb_nodes_per_element, type);

			// assemble the result into force vector
			getFEEngine().assembleArray(int_funct, *force_momentum,
			dof_synchronizer->getLocalDOFEquationNumbers(),
			nb_degree_of_freedom, type);
			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			template <ElementType type>
			void StructuralMechanicsModel::computeForcesByGlobalTractionArray(
			const Array<Real> & traction_global) {
			AKANTU_DEBUG_IN();
			UInt nb_element = mesh.getNbElement(type);
			UInt nb_quad = getFEEngine().getNbIntegrationPoints(type);
			UInt nb_nodes_per_element =
			getFEEngine().getMesh().getNbNodesPerElement(type);

			std::stringstream name;
			name << id << ":structuralmechanics:imposed_linear_load";
			Array<Real> traction_local(nb_element * nb_quad, nb_degree_of_freedom,
			name.str());

			Array<Real>::const_matrix_iterator T_it =
			rotation_matrix(type).begin(nb_degree_of_freedom * nb_nodes_per_element,
			nb_degree_of_freedom * nb_nodes_per_element);

			Array<Real>::const_iterator<Vector<Real>> Te_it =
			traction_global.begin(nb_degree_of_freedom);
			Array<Real>::iterator<Vector<Real>> te_it =
			traction_local.begin(nb_degree_of_freedom);

			Matrix<Real> R(nb_degree_of_freedom, nb_degree_of_freedom);
			for (UInt e = 0; e < nb_element; ++e, ++T_it) {
			const Matrix<Real> & T = *T_it;
			for (UInt i = 0; i < nb_degree_of_freedom; ++i)
			for (UInt j = 0; j < nb_degree_of_freedom; ++j)
			R(i, j) = T(i, j);

			for (UInt q = 0; q < nb_quad; ++q, ++Te_it, ++te_it) {
			const Vector<Real> & Te = *Te_it;
			Vector<Real> & te = *te_it;
			// turn the traction in the local referential
			te.mul<false>(R, Te);
			}
			}

			computeForcesByLocalTractionArray<type>(traction_local);

			AKANTU_DEBUG_OUT();
			}

			/* -------------------------------------------------------------------------- */
			/**
			* @param myf pointer to a function that fills a vector/tensor with respect to
			* passed coordinates
			*/
			template <ElementType type>
			inline void StructuralMechanicsModel::computeForcesFromFunction(
			BoundaryFunction myf, BoundaryFunctionType function_type) {
			/** function type is
			** _bft_forces : linear load is given
			** _bft_stress : stress function is given -> Not already done for this kind
			*of model
			*/

			std::stringstream name;
			name << id << ":structuralmechanics:imposed_linear_load";
			Array<Real> lin_load(0, nb_degree_of_freedom, name.str());
			name.clear();

			UInt offset = nb_degree_of_freedom;

			// prepare the loop over element types
			UInt nb_quad = getFEEngine().getNbIntegrationPoints(type);
			UInt nb_element = getFEEngine().getMesh().getNbElement(type);

			name.clear();
			name << id << ":structuralmechanics:quad_coords";
			Array<Real> quad_coords(nb_element * nb_quad, spatial_dimension,
			"quad_coords");

			getFEEngineClass<MyFEEngineType>()
			.getShapeFunctions()
			.interpolateOnIntegrationPoints<type>(getFEEngine().getMesh().getNodes(),
			quad_coords, spatial_dimension);
			getFEEngineClass<MyFEEngineType>()
			.getShapeFunctions()
			.interpolateOnIntegrationPoints<type>(
			getFEEngine().getMesh().getNodes(), quad_coords, spatial_dimension,
			_not_ghost, empty_filter, true, 0, 1, 1);
			if (spatial_dimension == 3)
			getFEEngineClass<MyFEEngineType>()
			.getShapeFunctions()
			.interpolateOnIntegrationPoints<type>(
			getFEEngine().getMesh().getNodes(), quad_coords, spatial_dimension,
			_not_ghost, empty_filter, true, 0, 2, 2);
			lin_load.resize(nb_element * nb_quad);
			Real * imposed_val = lin_load.storage();

			/// sigma/load on each quadrature points
			Real * qcoord = quad_coords.storage();
			for (UInt el = 0; el < nb_element; ++el) {
			for (UInt q = 0; q < nb_quad; ++q) {
			myf(qcoord, imposed_val, NULL, 0);
			imposed_val += offset;
			qcoord += spatial_dimension;
			}
			}

			switch (function_type) {
			case _bft_traction_local:
			computeForcesByLocalTractionArray<type>(lin_load);
			break;
			case _bft_traction:
			computeForcesByGlobalTractionArray<type>(lin_load);
			break;
			default:
			break;
			}
			}

			} // namespace akantu

			#endif /* __AKANTU_STRUCTURAL_MECHANICS_MODEL_INLINE_IMPL_CC__ */

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structural_mechanics_model_inline_impl.ccView Options

rAKA/src/model/structural_mechanics/structural_mechanics_model_inline_impl.cc
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structural_mechanics_model_inline_impl.cc
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