NewmarkBetaIntegrator.h

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/* ---------------------------------------------------------------------
 *                                       _
 *  _ __ ___   __ _ _ __ _ __ ___   ___ | |_
 * | '_ ` _ \ / _` | '__| '_ ` _ \ / _ \| __|
 * | | | | | | (_| | |  | | | | | | (_) | |_
 * |_| |_| |_|\__,_|_|  |_| |_| |_|\___/ \__|
 *
 * Unit of Strength of Materials and Structural Analysis
 * University of Innsbruck,
 * 2020 - today
 *
 * festigkeitslehre@uibk.ac.at
 *
 * Matthias Neuner matthias.neuner@uibk.ac.at
 *
 * This file is part of the MAteRialMOdellingToolbox (marmot).
 *
 * This library 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 2.1 of the License, or (at your option) any later version.
 *
 * The full text of the license can be found in the file LICENSE.md at
 * the top level directory of marmot.
 * ---------------------------------------------------------------------
 */
 
#pragma once
 
#include <algorithm>
namespace Marmot::TimeIntegration {
 
  template < int nDim >
  void newmarkBetaIntegration( const double* du,
                               double*       v,
                               double*       a,
                               double        dT,
                               double        newmarkBeta,
                               double        newmarkGamma,
                               double*       da_ddu )
  {
    for ( int i = 0; i < nDim; i++ ) {
      dT                    = std::max( dT, 1e-16 );
      const double du_tilde = dT * v[i] + 0.5 * dT * dT * ( ( 1 - 2 * newmarkBeta ) * a[i] );
      const double v_tilde  = v[i] + dT * ( 1 - newmarkGamma ) * a[i];
 
      a[i]                 = newmarkBeta != 0 ? ( du[i] - du_tilde ) / ( newmarkBeta * dT * dT ) : 0;
      da_ddu[i + i * nDim] = newmarkBeta != 0 ? 1. / ( newmarkBeta * dT * dT ) : 0.0;
      v[i]                 = v_tilde + newmarkGamma * dT * a[i];
    }
  }
 
} // namespace Marmot::TimeIntegration