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newmark-beta.cc
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/**
* @file newmark-beta.cc
*
* @author David Simon Kammer <david.kammer@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Tue Oct 05 2010
* @date last modification: Thu Jun 05 2014
*
* @brief implementation of the newmark-@f$\beta@f$ integration scheme. This
* implementation is taken from Méthodes numériques en mécanique des solides by
* Alain Curnier \note{ISBN: 2-88074-247-1}
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 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/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "newmark-beta.hh"
#include "dof_manager.hh"
#include "sparse_matrix.hh"
/* -------------------------------------------------------------------------- */
__BEGIN_AKANTU__
/*
* @f$ \tilde{u_{n+1}} = u_{n} + \Delta t \dot{u}_n + \frac{\Delta t^2}{2}
* \ddot{u}_n @f$
* @f$ \tilde{\dot{u}_{n+1}} = \dot{u}_{n} + \Delta t \ddot{u}_{n} @f$
* @f$ \tilde{\ddot{u}_{n}} = \ddot{u}_{n} @f$
*/
void NewmarkBeta::predictor(Real delta_t, Array<Real> & u, Array<Real> & u_dot,
Array<Real> & u_dot_dot,
const Array<bool> & blocked_dofs) const {
AKANTU_DEBUG_IN();
UInt nb_nodes = u.getSize();
UInt nb_degree_of_freedom = u.getNbComponent() * nb_nodes;
Real * u_val = u.storage();
Real * u_dot_val = u_dot.storage();
Real * u_dot_dot_val = u_dot_dot.storage();
bool * blocked_dofs_val = blocked_dofs.storage();
for (UInt d = 0; d < nb_degree_of_freedom; d++) {
if (!(*blocked_dofs_val)) {
Real dt_a_n = delta_t * *u_dot_dot_val;
*u_val += (1 - k * alpha) * delta_t * *u_dot_val +
(.5 - h * alpha * beta) * delta_t * dt_a_n;
*u_dot_val = (1 - k) * *u_dot_val + (1 - h * beta) * dt_a_n;
*u_dot_dot_val = (1 - h) * *u_dot_dot_val;
}
u_val++;
u_dot_val++;
u_dot_dot_val++;
blocked_dofs_val++;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void NewmarkBeta::corrector(const SolutionType & type, Real delta_t,
Array<Real> & u, Array<Real> & u_dot,
Array<Real> & u_dot_dot,
const Array<bool> & blocked_dofs,
const Array<Real> & delta) const {
AKANTU_DEBUG_IN();
switch (type) {
case _acceleration: {
this->allCorrector<_acceleration>(delta_t, u, u_dot, u_dot_dot,
blocked_dofs, delta);
break;
}
case _velocity: {
this->allCorrector<_velocity>(delta_t, u, u_dot, u_dot_dot, blocked_dofs,
delta);
break;
}
case _displacement: {
this->allCorrector<_displacement>(delta_t, u, u_dot, u_dot_dot,
blocked_dofs, delta);
break;
}
default:
AKANTU_EXCEPTION("The corrector type : "
<< type
<< " is not supported by this type of integration scheme");
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
Real NewmarkBeta::getAccelerationCoefficient(const SolutionType & type,
Real delta_t) const {
switch (type) {
case _acceleration:
return 1.;
case _velocity:
return 1. / (beta * delta_t);
case _displacement:
return 1. / (alpha * beta * delta_t * delta_t);
default:
AKANTU_EXCEPTION("The corrector type : "
<< type
<< " is not supported by this type of integration scheme");
}
}
/* -------------------------------------------------------------------------- */
Real NewmarkBeta::getVelocityCoefficient(const SolutionType & type,
Real delta_t) const {
switch (type) {
case _acceleration:
return beta * delta_t;
case _velocity:
return 1.;
case _displacement:
return 1. / (alpha * delta_t);
default:
AKANTU_EXCEPTION("The corrector type : "
<< type
<< " is not supported by this type of integration scheme");
}
}
/* -------------------------------------------------------------------------- */
Real NewmarkBeta::getDisplacementCoefficient(const SolutionType & type,
Real delta_t) const {
switch (type) {
case _acceleration:
return alpha * beta * delta_t * delta_t;
case _velocity:
return alpha * delta_t;
case _displacement:
return 1.;
default:
AKANTU_EXCEPTION("The corrector type : "
<< type
<< " is not supported by this type of integration scheme");
}
}
/* -------------------------------------------------------------------------- */
template <IntegrationScheme::SolutionType type>
void NewmarkBeta::allCorrector(Real delta_t, Array<Real> & u,
Array<Real> & u_dot, Array<Real> & u_dot_dot,
const Array<bool> & blocked_dofs,
const Array<Real> & delta) const {
AKANTU_DEBUG_IN();
UInt nb_nodes = u.getSize();
UInt nb_degree_of_freedom = u.getNbComponent() * nb_nodes;
Real c = getAccelerationCoefficient(type, delta_t);
Real d = getVelocityCoefficient(type, delta_t);
Real e = getDisplacementCoefficient(type, delta_t);
Real * u_val = u.storage();
Real * u_dot_val = u_dot.storage();
Real * u_dot_dot_val = u_dot_dot.storage();
Real * delta_val = delta.storage();
bool * blocked_dofs_val = blocked_dofs.storage();
for (UInt dof = 0; dof < nb_degree_of_freedom; dof++) {
if (!(*blocked_dofs_val)) {
*u_val += e * *delta_val;
*u_dot_val += d * *delta_val;
*u_dot_dot_val += c * *delta_val;
}
u_val++;
u_dot_val++;
u_dot_dot_val++;
delta_val++;
blocked_dofs_val++;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void NewmarkBeta::assembleJacobian(const SolutionType & type,
Real delta_t) {
AKANTU_DEBUG_IN();
SparseMatrix & J = this->dof_manager.getMatrix("J");
const SparseMatrix & M = this->dof_manager.getMatrix("M");
const SparseMatrix & K = this->dof_manager.getMatrix("K");
Real c = this->getAccelerationCoefficient(type, delta_t);
Real e = this->getDisplacementCoefficient(type, delta_t);
J.add(K, e);
J.add(M, c);
try {
Real d = this->getVelocityCoefficient(type, delta_t);
const SparseMatrix & C = this->dof_manager.getMatrix("C");
J.add(C, d);
} catch (debug::Exception &) {
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
__END_AKANTU__

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