Demo problem: Small-amplitude non-axisymmetric oscillations of a thin-walled elastic ring

Detailed documentation to be written. Here's the already fairly well documented driver code...

//LIC// ====================================================================
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//LIC// multi-physics finite-element library, available 
//LIC// at http://www.oomph-lib.org.
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//LIC// Copyright (C) 2006-2023 Matthias Heil and Andrew Hazel
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//LIC// License as published by the Free Software Foundation; either
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//LIC//====================================================================
//Driver for small amplitude ring oscillations
 
//OOMPH-LIB includes
#include "generic.h"
#include "beam.h"
#include "meshes/one_d_lagrangian_mesh.h"
 
using namespace std;
 
using namespace oomph;
 
/// /////////////////////////////////////////////////////////////////////
/// /////////////////////////////////////////////////////////////////////
/// /////////////////////////////////////////////////////////////////////
 
 
//====start_of_namespace============================
/// Namespace for physical parameters
//==================================================
namespace Global_Physical_Variables
{
 
 /// Flag for long/short run: Default =  perform long run
 unsigned Long_run_flag=1;
 
 /// Flag for fixed timestep: Default = fixed timestep
 unsigned Fixed_timestep_flag=1;
 
 /// Boolean flag to decide if to set IC for Newmark
 /// directly or consistently : No Default
 bool Consistent_newmark_ic;
 
} // end of namespace
 
/// //////////////////////////////////////////////////////////////////
/// //////////////////////////////////////////////////////////////////
/// //////////////////////////////////////////////////////////////////
 
 
 
//==start_of_problem_class==============================================
/// Oscillating ring problem: Compare small-amplitude oscillations
/// against analytical solution of the linearised equations.
//======================================================================
template<class ELEMENT, class TIMESTEPPER>
class ElasticRingProblem : public Problem
{
 
public:
 
 /// Constructor: Number of elements, length of domain, flag for
 /// setting Newmark IC directly or consistently
 ElasticRingProblem(const unsigned &N, const double &L);
                    
 /// Access function for the mesh
 OneDLagrangianMesh<ELEMENT>* mesh_pt() 
  {
   return dynamic_cast<OneDLagrangianMesh<ELEMENT>*>(Problem::mesh_pt());
  }
 
 /// Update function is empty 
 void actions_after_newton_solve() {}
 
 /// Update function is empty 
 void actions_before_newton_solve() {}
 
 /// Doc solution
 void doc_solution(DocInfo& doc_info);
 
 /// Do unsteady run
 void unsteady_run();
 
private:
 
 /// Length of domain (in terms of the Lagrangian coordinates)
 double Length;
 
 /// In which element are we applying displacement control?
 /// (here only used for doc of radius)
 ELEMENT* Displ_control_elem_pt;
 
 /// At what local coordinate are we applying displacement control?
 Vector<double> S_displ_control;
 
 /// Pointer to geometric object that represents the undeformed shape
 GeomObject* Undef_geom_pt;
 
 /// Pointer to object that specifies the initial condition
 SolidInitialCondition* IC_pt;
 
 /// Trace file for recording control data
 ofstream Trace_file;
}; // end of problem class
 
 
 
 
//===start_of_constructor===============================================
/// Constructor for elastic ring problem
//======================================================================
template<class ELEMENT,class TIMESTEPPER>
ElasticRingProblem<ELEMENT,TIMESTEPPER>::ElasticRingProblem
(const unsigned& N, const double& L) 
 : Length(L)
{
 
 //Allocate the timestepper -- This constructs the time object as well
 add_time_stepper_pt(new TIMESTEPPER());
 
 // Undeformed beam is an elliptical ring 
 Undef_geom_pt=new Ellipse(1.0,1.0); 
 
 //Now create the (Lagrangian!) mesh
 Problem::mesh_pt() = new OneDLagrangianMesh<ELEMENT>(
  N,L,Undef_geom_pt,Problem::time_stepper_pt()); 
 
 // Boundary condition: 
 
 // Bottom: 
 unsigned ibound=0;
 // No vertical displacement
 mesh_pt()->boundary_node_pt(ibound,0)->pin_position(1); 
 // Zero slope: Pin type 1 dof for displacement direction 0 
 mesh_pt()->boundary_node_pt(ibound,0)->pin_position(1,0);
 
 // Top: 
 ibound=1;
 // No horizontal displacement
 mesh_pt()->boundary_node_pt(ibound,0)->pin_position(0); 
 // Zero slope: Pin type 1 dof for displacement direction 1
 mesh_pt()->boundary_node_pt(ibound,0)->pin_position(1,1); 
 
 
 // Resize vector of local coordinates for control displacement
 // (here only used to identify the point whose displacement we're
 // tracing)
 S_displ_control.resize(1);
 
 // Complete build of all elements so they are fully functional
 // -----------------------------------------------------------
 
 // Find number of elements in mesh
 unsigned Nelement = mesh_pt()->nelement();
 
 // Loop over the elements to set pointer to undeformed wall shape
 for(unsigned i=0;i<Nelement;i++)
  {
   // Cast to proper element type
   ELEMENT *elem_pt = dynamic_cast<ELEMENT*>(mesh_pt()->element_pt(i));
 
   // Assign the undeformed surface
   elem_pt->undeformed_beam_pt() = Undef_geom_pt;
  }
 
 // Establish control displacment: (even though no displacement 
 // control is applied we still want to doc the displacement at the same point)
 
 // Choose element: (This is the last one)
 Displ_control_elem_pt=dynamic_cast<ELEMENT*>(
  mesh_pt()->element_pt(Nelement-1));
 
 // Fix/doc the displacement in the vertical (1) direction at right end of
 // the control element
 S_displ_control[0]=1.0;
 
 // Do equation numbering
 cout << "# of dofs " << assign_eqn_numbers() << std::endl;
 
 // Geometric object that specifies the initial conditions
 double eps_buckl=1.0e-2;
 double HoR=dynamic_cast<ELEMENT*>(mesh_pt()->element_pt(0))->h();
 unsigned n_buckl=2;
 unsigned imode=2;
 GeomObject* ic_geom_object_pt=
  new PseudoBucklingRing(eps_buckl,HoR,n_buckl,imode,
                         Problem::time_stepper_pt()); 
 
 // Setup object that specifies the initial conditions:
 IC_pt = new SolidInitialCondition(ic_geom_object_pt);
 
} // end of constructor
 
 
//===start_of_doc_solution================================================
/// Document solution
//========================================================================
template<class ELEMENT, class TIMESTEPPER>
void ElasticRingProblem<ELEMENT, TIMESTEPPER>::doc_solution(
 DocInfo& doc_info)
{ 
 
 cout << "Doc-ing step " <<  doc_info.number()
      << " for time " << time_stepper_pt()->time_pt()->time() << std::endl;
  
  
 // Loop over all elements to get global kinetic and potential energy
 unsigned Nelem=mesh_pt()->nelement();
 double global_kin=0;
 double global_pot=0;
 double pot,kin;
 for (unsigned ielem=0;ielem<Nelem;ielem++)
  {
   dynamic_cast<ELEMENT*>(mesh_pt()->element_pt(ielem))->get_energy(pot,kin);
   global_kin+=kin;
   global_pot+=pot;
  }
  
 
 // Control displacement for initial condition object
 Vector<double> xi_ctrl(1);
 Vector<double> posn_ctrl(2);
  
 // Lagrangian coordinate of control point
 xi_ctrl[0]=Displ_control_elem_pt->interpolated_xi(S_displ_control,0);
  
 // Get position
 IC_pt->geom_object_pt()->position(xi_ctrl,posn_ctrl);
 
 // Write trace file: Time, control position, energies
 Trace_file << time_pt()->time()  << " " 
            << Displ_control_elem_pt->interpolated_x(S_displ_control,1) 
            << " " << global_pot  << " " << global_kin
            << " " << global_pot + global_kin 
            << " " << posn_ctrl[1]
            << std::endl; 
  
  
 ofstream some_file;
 char filename[100];
  
 // Number of plot points
 unsigned npts=5;
 
 // Output solution 
 sprintf(filename,"%s/ring%i.dat",doc_info.directory().c_str(),
         doc_info.number());
 some_file.open(filename);
 mesh_pt()->output(some_file,npts);
 some_file.close();
 
 // Loop over all elements do dump out previous solutions
 unsigned nsteps=time_stepper_pt()->nprev_values();
 for (unsigned t=0;t<=nsteps;t++)
  {     
   sprintf(filename,"%s/ring%i-%i.dat",doc_info.directory().c_str(),
           doc_info.number(),t);
   some_file.open(filename);
   unsigned Nelem=mesh_pt()->nelement();
   for (unsigned ielem=0;ielem<Nelem;ielem++)
    {
     dynamic_cast<ELEMENT*>(mesh_pt()->element_pt(ielem))->
      output(t,some_file,npts);
    }
   some_file.close();
  }
  
 // Output for initial condition object
 sprintf(filename,"%s/ic_ring%i.dat",doc_info.directory().c_str(),
         doc_info.number());
 some_file.open(filename);
  
 unsigned nplot=1+(npts-1)*mesh_pt()->nelement();
 Vector<double> xi(1);
 Vector<double> posn(2);
 Vector<double> veloc(2);
 Vector<double> accel(2);
  
 for (unsigned iplot=0;iplot<nplot;iplot++)
  {
   xi[0]=Length/double(nplot-1)*double(iplot);
    
   IC_pt->geom_object_pt()->position(xi,posn);
   IC_pt->geom_object_pt()->dposition_dt(xi,1,veloc);
   IC_pt->geom_object_pt()->dposition_dt(xi,2,accel);
    
   some_file << posn[0] << " " << posn[1] << " "
             << xi[0] << " "
             << veloc[0] << " " << veloc[1] << " "
             << accel[0] << " " << accel[1] << " "
             << sqrt(pow(posn[0],2)+pow(posn[1],2)) << " "
             << sqrt(pow(veloc[0],2)+pow(veloc[1],2)) << " "
             << sqrt(pow(accel[0],2)+pow(accel[1],2)) << " "
             << std::endl;
  }
  
 some_file.close();
} // end of doc solution
 
 
 
//===start_of_unsteady_run=================================================
/// Solver loop to perform unsteady run
//=========================================================================
template<class ELEMENT,class TIMESTEPPER>
void ElasticRingProblem<ELEMENT,TIMESTEPPER>::unsteady_run()
{
 
 /// Label for output
 DocInfo doc_info;
 
 // Output directory
 doc_info.set_directory("RESLT");
 
 // Step number
 doc_info.number()=0;
 
 // Set up trace file
 char filename[100];
 sprintf(filename,"%s/trace_ring.dat",doc_info.directory().c_str());
 Trace_file.open(filename);
 
 Trace_file <<  "VARIABLES=\"time\",\"R<sub>ctrl</sub>\",\"E<sub>pot</sub>\"";
 Trace_file << ",\"E<sub>kin</sub>\",\"E<sub>kin</sub>+E<sub>pot</sub>\"";
 Trace_file << ",\"<sub>exact</sub>R<sub>ctrl</sub>\"" 
            << std::endl;
 
 // Number of steps
 unsigned nstep=600; 
 if (Global_Physical_Variables::Long_run_flag==0) {nstep=10;}
 
 // Initial timestep
 double dt=1.0;
 
 // Ratio for timestep reduction
 double timestep_ratio=1.0;
 if (Global_Physical_Variables::Fixed_timestep_flag==0) {timestep_ratio=0.995;}
 
 // Number of previous timesteps stored
 unsigned ndt=time_stepper_pt()->time_pt()->ndt();
 
 // Setup vector of "previous" timesteps
 Vector<double> dt_prev(ndt);
 dt_prev[0]=dt; 
 for (unsigned i=1;i<ndt;i++)
  {
   dt_prev[i]=dt_prev[i-1]/timestep_ratio;
  }
 
 // Initialise the history of previous timesteps
 time_pt()->initialise_dt(dt_prev);
 
 // Initialise time
 double time0=10.0;
 time_pt()->time()=time0;
 
 // Setup analytical initial condition?
 if (Global_Physical_Variables::Consistent_newmark_ic)
  {
   // Note: Time has been scaled on intrinsic timescale so
   // we don't need to specify a multiplier for the inertia
   // terms (the default assignment of 1.0 is OK)
   SolidMesh::Solid_IC_problem.
    set_newmark_initial_condition_consistently(
     this,mesh_pt(),static_cast<TIMESTEPPER*>(time_stepper_pt()),IC_pt,dt);
  }
 else
  {
   SolidMesh::Solid_IC_problem.
    set_newmark_initial_condition_directly(
     this,mesh_pt(),static_cast<TIMESTEPPER*>(time_stepper_pt()),IC_pt,dt);
  }
 
 //Output initial data
 doc_solution(doc_info);
 
 // Time integration loop
 for(unsigned i=1;i<=nstep;i++)
  {
   // Solve
   unsteady_newton_solve(dt); 
   
   // Doc solution
   doc_info.number()++;
   doc_solution(doc_info);
   
   // Reduce timestep
   if (time_pt()->time()<100.0) {dt=timestep_ratio*dt;}
  }
 
} // end of unsteady run
 
 
 
//===start_of_main=====================================================
/// Driver for ring that performs small-amplitude oscillations
//=====================================================================
int main(int argc, char* argv[])
{
 
 // Store command line arguments
 CommandLineArgs::setup(argc,argv);
 
 /// Convert command line arguments (if any) into flags:
 if (argc==2)
  {
   // Nontrivial command line input: Setup Newmark IC directly
   // (rather than consistently with PVD)
   if (atoi(argv[1])==1) 
    {
     Global_Physical_Variables::Consistent_newmark_ic=true;
     cout << "Setting Newmark IC consistently" << std::endl;
    }
   else
    {
     Global_Physical_Variables::Consistent_newmark_ic=false;
     cout << "Setting Newmark IC directly" << std::endl;
    }
   
   cout << "Not enough command line arguments specified -- using defaults." 
        << std::endl;
  } // end of 1 argument
 else if (argc==4)
  {
   cout << "Three command line arguments specified:" << std::endl;
   // Nontrivial command line input: Setup Newmark IC directly
   // (rather than consistently with PVD)
   if (atoi(argv[1])==1) 
    {
     Global_Physical_Variables::Consistent_newmark_ic=true;
     cout << "Setting Newmark IC consistently" << std::endl;
    }
   else
    {
     Global_Physical_Variables::Consistent_newmark_ic=false;
     cout << "Setting Newmark IC directly" << std::endl;
    }
   // Flag for long run
   Global_Physical_Variables::Long_run_flag=atoi(argv[2]);
   // Flag for fixed timestep
   Global_Physical_Variables::Fixed_timestep_flag=atoi(argv[3]);
  } // end of 3 arguments
 else
  {
   std::string error_message =
    "Wrong number of command line arguments. Specify one or three.\n";
   error_message += "Arg1: Long_run_flag [0/1]\n";
   error_message += "Arg2: Impulsive_start_flag [0/1]\n";
   error_message += "Arg3: Restart_flag [restart_file] (optional)\n";
 
   throw OomphLibError(error_message,
                       OOMPH_CURRENT_FUNCTION,
                       OOMPH_EXCEPTION_LOCATION);
  } // too many arguments
 cout << "Setting Newmark IC consistently: "
      <<  Global_Physical_Variables::Consistent_newmark_ic << std::endl;
 cout << "Long run flag: " 
      <<  Global_Physical_Variables::Long_run_flag << std::endl;
 cout << "Fixed timestep flag: " 
      <<  Global_Physical_Variables::Fixed_timestep_flag << std::endl;
 
 //Length of domain
 double L = MathematicalConstants::Pi/2.0;
  
 // Number of elements
 unsigned nelem = 13;
 
 //Set up the problem
 ElasticRingProblem<HermiteBeamElement,Newmark<3> > 
  problem(nelem,L);
 
 // Do unsteady run
 problem.unsteady_run();
 
} // end of main
 
 
 
 
 
 
 
 

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