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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 */

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