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rAKA/src/model/integration_scheme/newmark-beta_inline_impl.cc
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newmark-beta_inline_impl.cc
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/**
* @file newmark-beta_inline_impl.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/>.
*
*/
/* -------------------------------------------------------------------------- */
/*
* @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$
*/
inline void NewmarkBeta::integrationSchemePred(Real delta_t,
Array<Real> & u,
Array<Real> & u_dot,
Array<Real> & u_dot_dot,
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();
}
/* -------------------------------------------------------------------------- */
/*
* @f$ u_{n+1} = \tilde{u_{n+1}} + \alpha \beta \Delta t^2 \delta \ddot{u}_n @f$
* @f$ \dot{u}_{n+1} = \tilde{\dot{u}_{n+1}} + \beta \Delta t * \delta \ddot{u}_{n+1} @f$
* @f$ \ddot{u}_{n+1} = \tilde{\ddot{u}_{n+1}} + \delta \ddot{u}_{n+1} @f$
*/
inline void NewmarkBeta::integrationSchemeCorrAccel(Real delta_t,
Array<Real> & u,
Array<Real> & u_dot,
Array<Real> & u_dot_dot,
Array<bool> & blocked_dofs,
Array<Real> & delta
) const {
AKANTU_DEBUG_IN();
integrationSchemeCorr<_acceleration_corrector>(delta_t,
u,
u_dot,
u_dot_dot,
blocked_dofs,
delta);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
/*
* @f$ u_{n+1} = \tilde{u_{n+1}} + \alpha \Delta t \delta \dot{u}_n @f$
* @f$ \dot{u}_{n+1} = \tilde{\dot{u}_{n+1}} + \delta \dot{u}_{n+1} @f$
* @f$ \ddot{u}_{n+1} = \tilde{\ddot{u}_{n+1}} + \frac{1}{\beta \Delta t} \delta \dot{u}_{n+1} @f$
*/
inline void NewmarkBeta::integrationSchemeCorrVeloc(Real delta_t,
Array<Real> & u,
Array<Real> & u_dot,
Array<Real> & u_dot_dot,
Array<bool> & blocked_dofs,
Array<Real> & delta
) const {
AKANTU_DEBUG_IN();
integrationSchemeCorr<_velocity_corrector>(delta_t,
u,
u_dot,
u_dot_dot,
blocked_dofs,
delta);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
/*
* @f$ u_{n+1} = \tilde{u_{n+1}} + \delta u_n @f$
* @f$ \dot{u}_{n+1} = \tilde{\dot{u}_{n+1}} + \frac{1}{\alpha \Delta t} \delta u_{n+1} @f$
* @f$ \ddot{u}_{n+1} = \tilde{\ddot{u}_{n+1}} + \frac{1}{\alpha \beta \Delta t^2} \delta u_{n+1} @f$
*/
inline void NewmarkBeta::integrationSchemeCorrDispl(Real delta_t,
Array<Real> & u,
Array<Real> & u_dot,
Array<Real> & u_dot_dot,
Array<bool> & blocked_dofs,
Array<Real> & delta
) const {
AKANTU_DEBUG_IN();
integrationSchemeCorr<_displacement_corrector>(delta_t,
u,
u_dot,
u_dot_dot,
blocked_dofs,
delta);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<>
inline Real NewmarkBeta::getAccelerationCoefficient<NewmarkBeta::_acceleration_corrector>(__attribute__((unused)) Real delta_t) const {
return 1.;
}
template<>
inline Real NewmarkBeta::getAccelerationCoefficient<NewmarkBeta::_velocity_corrector>(Real delta_t) const {
return 1. / (beta * delta_t);
}
template<>
inline Real NewmarkBeta::getAccelerationCoefficient<NewmarkBeta::_displacement_corrector>(Real delta_t) const {
return 1. / (alpha * beta * delta_t * delta_t);
}
/* -------------------------------------------------------------------------- */
template<>
inline Real NewmarkBeta::getVelocityCoefficient<NewmarkBeta::_acceleration_corrector>(Real delta_t) const {
return beta * delta_t;
}
template<>
inline Real NewmarkBeta::getVelocityCoefficient<NewmarkBeta::_velocity_corrector>(__attribute__((unused)) Real delta_t) const {
return 1.;
}
template<>
inline Real NewmarkBeta::getVelocityCoefficient<NewmarkBeta::_displacement_corrector>(Real delta_t) const {
return 1. / (alpha * delta_t);
}
/* -------------------------------------------------------------------------- */
template<>
inline Real NewmarkBeta::getDisplacementCoefficient<NewmarkBeta::_acceleration_corrector>(Real delta_t) const {
return alpha * beta * delta_t * delta_t;
}
template<>
inline Real NewmarkBeta::getDisplacementCoefficient<NewmarkBeta::_velocity_corrector>(Real delta_t) const {
return alpha * delta_t;
}
template<>
inline Real NewmarkBeta::getDisplacementCoefficient<NewmarkBeta::_displacement_corrector>(__attribute__((unused)) Real delta_t) const {
return 1.;
}
/* -------------------------------------------------------------------------- */
template<NewmarkBeta::IntegrationSchemeCorrectorType type>
void NewmarkBeta::integrationSchemeCorr(Real delta_t,
Array<Real> & u,
Array<Real> & u_dot,
Array<Real> & u_dot_dot,
Array<bool> & blocked_dofs,
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();
}
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