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solid_mechanics_model_element.hh
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			/**
			* @file solid_mechanics_model_element.hh
			*
			* @author Alejandro M. Aragón <alejandro.aragon@epfl.ch>
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			*
			* @date creation: Tue May 07 2013
			* @date last modification: Tue May 13 2014
			*
			* @brief elements for solid mechanics models
			*
			* @section LICENSE
			*
			* Copyright (©) 2014 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/>.
			*
			*/

			/* -------------------------------------------------------------------------- */


			#ifndef AKANTU_SOLID_MECHANICS_MODEL_ELEMENT_HH
			#define AKANTU_SOLID_MECHANICS_MODEL_ELEMENT_HH

			#include <array/expr.hpp>

			#include "mesh.hh"
			#include "aka_error.hh"
			#include "solid_mechanics_model.hh"
			#include "aka_bounding_box.hh"


			__BEGIN_AKANTU__


			typedef array::vector_type<Real> vector_type;
			typedef array::matrix_type<Real> matrix_type;




			template <>
			class ModelElement<SolidMechanicsModel> : public Element {

			public:


			typedef Element element_base;

			SolidMechanicsModel *model_; //!< Reference to model
			UInt *connectivity_; //!< Ponter to connectivity array


			typedef SolidMechanicsModel model_type;

			ModelElement() : element_base(), model_(nullptr), connectivity_() {}

			ModelElement(SolidMechanicsModel& m, Element &el)
			: element_base(el), model_(&m) {
			connectivity_ = &m.getMesh().getConnectivity(this->type, this->ghost_type)(this->element);
			}

			ModelElement(SolidMechanicsModel& m, ElementType type, UInt id, GhostType gt = _not_ghost)
			: element_base(type, id, gt), model_(&m) {
			connectivity_ = &m.getMesh().getConnectivity(type, gt)(id);
			}

			ModelElement(const ModelElement& p) : element_base(static_cast<element_base>(p)), model_(p.model_), connectivity_(p.connectivity_) {}


			model_type& model() { return *model_; }

			UInt numNodes() const
			{ return Mesh::getNbNodesPerElement(type); }

			template <class element_type>
			bool shareNodes(element_type& el) {

			for (UInt i=0; i<Mesh::getNbNodesPerElement(type); ++i)
			for (UInt j=0; j<Mesh::getNbNodesPerElement(el.type); ++j)
			if (connectivity_[i] == el.connectivity_[j])
			return true;
			return false;
			}

			template <class element_type>
			UInt shareNode(element_type& el) {

			for (UInt i=0; i<Mesh::getNbNodesPerElement(type); ++i)
			for (UInt j=0; j<Mesh::getNbNodesPerElement(el.type); ++j)
			if (connectivity_[i] == el.connectivity_[j])
			return connectivity_[i];
			return -1;
			}


			UInt& node(UInt n) {
			AKANTU_DEBUG_ASSERT(n < Mesh::getNbNodesPerElement(type),
			"Node "<<n<<" is larger than element number of nodes: "<<Mesh::getNbNodesPerElement(type));
			return connectivity_[n];
			}

			UInt node(UInt n) const {
			AKANTU_DEBUG_ASSERT(n < Mesh::getNbNodesPerElement(type),
			"Node "<<n<<" is larger than element number of nodes: "<<Mesh::getNbNodesPerElement(type));
			return connectivity_[n];
			}


			// vector of pointers to nodes' first coordinates
			std::vector<const Real*> coordinates() {

			UInt nb_nodes = Mesh::getNbNodesPerElement(this->type);
			const Array<Real> &position = model_->getCurrentPosition();
			std::vector<const Real*> coord(nb_nodes);
			for (size_t i=0; i<nb_nodes; ++i)
			coord[i] = &position(connectivity_[i]);
			return coord;
			}

			// barycenter
			vector_type barycenter() const {

			typedef typename vector_type::value_type value_type;

			UInt nb_nodes = Mesh::getNbNodesPerElement(this->type);
			const Array<Real> &position = model_->getCurrentPosition();
			vector_type sum(model_->getSpatialDimension());
			for (size_t i=0; i<nb_nodes; ++i) {
			Real * p = const_cast<Real*>(&position(connectivity_[i]));
			sum += vector_type(model_->getSpatialDimension(), p);
			}

			return (1./static_cast<value_type>(nb_nodes)) * sum;
			}

			//! Returns the closest point to an element and the element normal
			vector_type normal() {

			vector_type n;
			auto coord = coordinates();

			switch (type) {
			case _segment_2:
			{
			// create points from segment
			Point<2> x(coord[0]);
			Point<2> y(coord[1]);
			Point<2> t = y-x;
			n = vector_type(2);
			// normal2 normalizes the normal so that its magnitude is 1
			Math::normal2(&t[0], &n[0]);

			break;
			}
			case _triangle_3:
			{
			Point<3> x(coord[0]);
			Point<3> y(coord[1]);
			Point<3> z(coord[2]);
			Point<3> t1 = y-x;
			Point<3> t2 = z-x;
			n = vector_type(3);
			Math::vectorProduct3(&t1[0], &t2[0], &n[0]);
			Math::normalize3(&n[0]);

			break;
			}
			default:
			AKANTU_DEBUG_ERROR("No element type found");
			}
			return n;
			}



			template <int dim>
			BoundingBox<dim> boundingBox() {

			typedef typename BoundingBox<dim>::point_type point_type;

			assert(dim == model_->getSpatialDimension());
			BoundingBox<dim> bb;
			UInt nb_nodes = Mesh::getNbNodesPerElement(this->type);
			const Array<Real> &position = model_->getCurrentPosition();
			for (size_t i=0; i<nb_nodes; ++i) {
			point_type p(&position(connectivity_[i]));
			bb += p;
			}
			return bb;
			}

			template <int dim>
			Point<dim> point(UInt nid) {

			AKANTU_DEBUG_ASSERT(dim == model_->getSpatialDimension(),
			"Point and model dimensions do not match");
			UInt n = node(nid);
			const Array<Real> &position = model_->getCurrentPosition();
			Real * p = const_cast<Real*>(&position(n));
			return Point<dim>(p);
			}


			// mass
			vector_type getMass(UInt nid) {
			UInt n = node(nid);
			Array<Real> &mass = model_->getMass();
			return vector_type(model_->getSpatialDimension(), &mass(n));
			}

			// mass for const objects
			const vector_type getMass(UInt nid) const {
			UInt n = node(nid);
			Array<Real> &mass = model_->getMass();
			return vector_type(model_->getSpatialDimension(), &mass(n));
			}

			// initial coordinates
			vector_type getInitialCoordinates(UInt nid) {
			UInt n = node(nid);
			Array<Real> &coord = model_->getMesh().getNodes();
			return vector_type(model_->getSpatialDimension(), &coord(n));
			}

			const vector_type getInitialCoordinates(UInt nid) const {
			UInt n = node(nid);
			Array<Real> &coord = model_->getMesh().getNodes();
			return vector_type(model_->getSpatialDimension(), &coord(n));
			}


			// displacement
			vector_type getDisplacement(UInt nid) {
			UInt n = node(nid);
			Array<Real> &displacement = model_->getDisplacement();
			return vector_type(model_->getSpatialDimension(), &displacement(n));
			}

			// displacement for const objects
			const vector_type getDisplacement(UInt nid) const {
			UInt n = node(nid);
			Array<Real> &displacement = model_->getDisplacement();
			return vector_type(model_->getSpatialDimension(), &displacement(n));
			}

			// velocity
			vector_type getVelocity(UInt nid) {
			UInt n = node(nid);
			Array<Real> &velocity = model_->getVelocity();
			return vector_type(model_->getSpatialDimension(), &velocity(n));
			}

			// velocity for const objects
			const vector_type getVelocity(UInt nid) const {
			UInt n = node(nid);
			Array<Real> &velocity = model_->getVelocity();
			return vector_type(model_->getSpatialDimension(), &velocity(n));
			}

			// acceleration
			vector_type getAcceleration(UInt nid) {
			UInt n = node(nid);
			Array<Real> &acceleration = model_->getAcceleration();
			return vector_type(model_->getSpatialDimension(), &acceleration(n));
			}

			// acceleration for const objects
			const vector_type getAcceleration(UInt nid) const {
			UInt n = node(nid);
			Array<Real> &acceleration = model_->getAcceleration();
			return vector_type(model_->getSpatialDimension(), &acceleration(n));
			}

			// position (location + displacement)
			vector_type getCurrentPosition(UInt nid) {
			UInt n = node(nid);
			const Array<Real> &position = model_->getCurrentPosition();
			Real * p = const_cast<Real*>(&position(n));
			return vector_type(model_->getSpatialDimension(), p);
			}

			// position (location + displacement) for const objects
			const vector_type getCurrentPosition(UInt nid) const {
			UInt n = node(nid);
			const Array<Real> &position = model_->getCurrentPosition();
			Real * p = const_cast<Real*>(&position(n));
			return vector_type(model_->getSpatialDimension(), p);
			}

			// residual
			vector_type getResidual(UInt nid) {
			UInt n = node(nid);
			const Array<Real> & residual = model_->getResidual();
			Real * p = const_cast<Real*>(&residual(n));
			return vector_type(model_->getSpatialDimension(), p);
			}

			// residual for const objects
			const vector_type getResidual(UInt nid) const {
			UInt n = node(nid);
			const Array<Real> & residual = model_->getResidual();
			Real * p = const_cast<Real*>(&residual(n));
			return vector_type(model_->getSpatialDimension(), p);
			}

			// momentum
			vector_type getMomentum(UInt nid) {
			UInt n = node(nid);
			Array<Real> &velocity = model_->getVelocity();
			Array<Real> &mass = model_->getMass();
			vector_type p(model_->getSpatialDimension());
			for (size_t i=0; i<p.size(); ++i)
			p[i] = mass(n,i)*velocity(n,i);
			return p;
			}

			// momentum for const objects
			const vector_type getMomentum(UInt nid) const {
			return const_cast<ModelElement&>(*this).getMomentum(nid);
			}

			};


			//! Returns the closest point to an element and the element normal
			template <class point_type, class element_type>
			std::pair<point_type, vector_type> closest_point_to_element(const point_type& p, element_type& el) {

			point_type r;
			vector_type n;

			switch (el.type) {
			case _segment_2:
			{
			// create points from segment
			auto coord = el.coordinates();
			assert (coord.size() == 2);
			point_type x(coord[0]);
			point_type y(coord[1]);

			r = closest_point_to_segment(p, x, y);

			point_type t = y-x;
			n = vector_type(2);
			Math::normal2(&t[0], &n[0]);

			break;
			}

			default:
			AKANTU_DEBUG_ERROR("No element type found");
			}

			return std::make_pair(r, n);
			}





			template <class point_type, class pair_type>
			bool balance(Real Dt, int id, const pair_type& r, ModelElement<SolidMechanicsModel>& sel, ModelElement<SolidMechanicsModel>& mel) {


			// constexpr int dim = point_type::dim();

			// treat first element as slave
			auto coord = sel.coordinates();

			// create point
			point_type p(coord[id]);

			// else find closest distance from p to contacting element c2
			// std::pair<point_type, vector_type> r = closest_point_to_element(p, mel);
			const point_type& q = r.first;
			const vector_type& n = r.second;

			// get distance from current position
			Real delta = sqrt((q-p).sq_norm());

			auto mass = sel.getMass(id)[0];

			// compute force at slave node
			vector_type N = 2 * delta * mass / pow(Dt,2.) * n;

			// update residual and velocity for slave
			vector_type sr = sel.getResidual(id);
			vector_type m = sel.getMass(id);
			vector_type v = sel.getVelocity(id);
			vector_type a = sel.getAcceleration(id);
			for (size_t i=0; i<N.size(); ++i) {
			// sr[i] = N[i];
			v[i] += N[i]/m[i] * Dt;
			// a[i] -= N[i]/m[i];
			}

			// set location of slave node
			auto xs = sel.getDisplacement(id);
			auto oc = sel.getInitialCoordinates(id);
			for (size_t i=0; i<xs.size(); ++i)
			xs[i] = q[i] - oc[i];

			// balance with slave forces
			switch (mel.type) {
			case _segment_2:
			{
			// create points from segment
			auto coord = mel.coordinates();
			assert (coord.size() == 2);
			point_type X1(coord[0]);
			point_type X2(coord[1]);

			// get weights for distribution of loads
			Real alpha = (q - X1).sq_norm() / (X2 - X1).sq_norm();

			//get vectors
			vector_type R1 = mel.getResidual(0);
			vector_type R2 = mel.getResidual(1);
			vector_type V1 = mel.getVelocity(0);
			vector_type V2 = mel.getVelocity(1);
			// vector_type A1 = mel.getAcceleration(0);
			// vector_type A2 = mel.getAcceleration(1);
			vector_type M1 = mel.getMass(0);
			vector_type M2 = mel.getMass(1);

			for (size_t i=0; i<N.size(); ++i) {
			Real r1 = (alpha - 1)*N[i];
			Real r2 = -alpha * N[i];
			// R1[i] = r1;
			// R2[i] = r2;
			V1[i] += r1/M1[i] * Dt;
			V2[i] += r2/M2[i] * Dt;
			// A1[i] -= R1[i]/M1[i];
			// A2[i] -= R2[i]/M2[i];
			}

			break;
			}

			default:
			AKANTU_DEBUG_ERROR("No element type found");
			}


			return true;

			}



			template <class point_type, class element_container>
			std::pair<point_type, vector_type> commonPonit(const element_container& els) {

			typedef std::pair<point_type, vector_type> pair_type;

			// balance with slave forces
			switch (els.size()) {
			case 2:
			{

			auto it = els.begin();
			auto el1 = *it++;
			auto el2 = *it;

			// get normals
			auto n1 = el1.normal();
			auto n2 = el2.normal();

			// average normal
			vector_type n = n1 + n2;
			n *= (1/n.norm());

			// get common point
			assert(el1.shareNodes(el2));

			UInt c = el1.shareNode(el2);

			assert(el1.shareNode(el2) == el2.shareNode(el1));

			// set location of slave node
			Array<Real> &displacement = el1.model().getDisplacement();
			Array<Real> &coord = el1.model().getMesh().getNodes();

			point_type p;
			for (int i=0; i<point_type::dim(); ++i)
			p[i] = coord(c,i) + displacement(c,i);

			return std::make_pair(p,n);

			break;
			}

			default:
			AKANTU_DEBUG_ERROR("Invalid size");
			}


			return pair_type();
			}



			template <class point_type, class element_type>
			bool penetrates(point_type& r, element_type& el) {

			// balance with slave forces
			switch (el.type) {
			case _segment_2:
			{

			// create points from master
			auto coord = el.coordinates();
			assert (coord.size() == 2);
			point_type p(coord[0]);
			point_type q(coord[1]);

			return left_turn(p,q,r) > 0 && has_projection(r, p, q);
			break;
			}

			default:
			AKANTU_DEBUG_ERROR("No element type found");
			}

			// should never get here
			assert(false);
			return false;
			}

			__END_AKANTU__


			#endif /* AKANTU_SOLID_MECHANICS_MODEL_ELEMENT_HH */

rAKA/src/model/solid_mechanics/solid_mechanics_model_element.hh74a41d6f0ef2features/friction_examp…

solid_mechanics_model_element.hhView Options

rAKA/src/model/solid_mechanics/solid_mechanics_model_element.hh
74a41d6f0ef2features/friction_examp…

solid_mechanics_model_element.hh
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