Description

EX_PLANESTRESS7 Thermally induced displacements on a rectangle.

[ FEA, OUT ] = EX_PLANESTRESS7( VARARGIN ) Thermally induced displacements on a rectangle

Accepts the following property/value pairs.

Input       Value/{Default}        Description
-----------------------------------------------------------------------------------
pss         logical {true}         Use plane stress (or plane strain)
hmax        scalar {1/20}          Max grid cell size
igrid       scalar 0/{1}           Cell type (0=quadrilaterals, ~0=triangles)
sfun        string {sflag1}        Shape function for displacements
solver      string {}              Solver selection default, fenics
iplot       scalar 0/{1}           Plot solution (=1)
                                                                                  .
Output      Value/(Size)           Description
-----------------------------------------------------------------------------------
fea         struct                 Problem definition struct
out         struct                 Output struct

Code listing

 cOptDef = { 'pss',    true;
             'hmax',   1/20;
             'igrid',  1;
             'sfun',   'sflag1';
             'solver', '';
             'iplot',  1;
             'tol',    1e-4;
             'fid',    1 };
 [got,opt] = parseopt( cOptDef, varargin{:} );
 fid       = opt.fid;


% Geometry and grid.
 fea.sdim = { 'x' 'y' };   % Coordinate names.
 fea.grid = rectgrid(1/opt.hmax, 1/opt.hmax, [0 0.01; 0 0.01]);
 if( opt.igrid~=0 || strcmpi(opt.solver,'fenics') )
   fea.grid = quad2tri( fea.grid );
 end
 n_bdr = max(fea.grid.b(3,:));   % Number of boundaries.


% Problem definition.
 if( opt.pss )
   fea = addphys( fea, @planestress );
   mode = 'pss';
 else
   fea = addphys( fea, @planestrain );
   mode = 'psn';
 end
 fea.phys.(mode).eqn.coef{1,end} = { 0.3 };
 fea.phys.(mode).eqn.coef{2,end} = { 100e9 };
 fea.phys.(mode).eqn.coef{6,end} = { 1e-3 };
 fea.phys.(mode).eqn.coef{7,end} = { 1 };
 fea.phys.(mode).sfun            = { opt.sfun opt.sfun };


% Boundary conditions.
 dtol = 1e-6;
 lbdr = findbdr( fea, ['x<',num2str(dtol)] );
 bbdr = findbdr( fea, ['y<',num2str(dtol)] );
 n_bdr  = max(fea.grid.b(3,:));
 bctype = mat2cell( zeros(2,n_bdr), [1 1], ones(1,n_bdr) );
 bccoef = mat2cell( zeros(2,n_bdr), [1 1], ones(1,n_bdr) );
 [bctype{1,lbdr}] = deal(1);
 [bctype{2,bbdr}] = deal(1);
 fea.phys.(mode).bdr.coef{1,end} = bccoef;
 fea.phys.(mode).bdr.coef{1,5}   = bctype;


% Parse and solve problem.
 fea       = parsephys( fea );
 fea       = parseprob( fea );                          % Check and parse problem struct.
 if( strcmp(opt.solver,'fenics') )
   fea = fenics(fea,'fid',fid, 'nproc', 1);
 else
   fea.sol.u = solvestat(fea,'fid',fid);   % Call to stationary solver.
 end


% Postprocessing.
 s_disp = fea.phys.(mode).eqn.vars{2,end};
 if( opt.iplot>0 )
   figure
   postplot( fea, 'surfexpr', s_disp )
   title( 'Total displacement' )
 end


% Error checking.
 if( opt.pss )
   u_max_ref = 0;
   u_mag_max_ref = 1.41421e-5;
 else
   u_max_ref = 1.3e-5;
   u_mag_max_ref = 1.83848e-5;
 end
 [u_min,u_max] = minmaxsubd('u',fea);
 [v_min,v_max] = minmaxsubd('v',fea);
 [u_mag_min,u_mag_max] = minmaxsubd('sqrt(u^2+v^2)',fea);
 out.err = [ abs(u_min), ...
             abs(u_max-u_max_ref), ...
             abs(v_min), ...
             abs(v_max-u_max_ref), ...
             abs(u_mag_min), ...
             abs(u_mag_max-u_mag_max_ref)/u_mag_max_ref ];
 out.pass = all( out.err(:) <= opt.tol );


 if( nargout==0 )
   clear fea out
 end