Description

EX_PLANESTRESS3 NAFEMS benchmarks IC1-4 linear static stress analysis of a tapered membrane.

[ FEA, OUT ] = EX_PLANESTRESS3( VARARGIN ) NAFEMS benchmarks IC1-4 for linear static plane stress analysis of a tapered membrane. Four test cases are modeled, the first with a horizonal load on the left edge, second with horizonal volume force, third with a vertical shear load on the left edge, and fourth with a vertical volume (gravity) force.

Reference: Linear Statics Benchmarks Vol. 1, NAFEMS Ltd., 1987.

Accepts the following property/value pairs.

   Input       Value/{Default}        Description
   -----------------------------------------------------------------------------------
   icase       scalar 1-4/{1}
   hmax        scalar {0.3}           Max grid cell size
   sfun        string {sflag2}        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 = { 'E',     210e9;
             'nu',    0.3;
             'thick', 0.1;
             'icase', 1;
             'hmax',  0.3;
             'sfun',  'sflag2';
             'solver',   '';
             'iplot', 1;
             'tol',   0.01;
             'fid',   1 };
 [got,opt] = parseopt(cOptDef,varargin{:});
 fid       = opt.fid;


% Geometry definition.
 gobj = gobj_polygon( [0 4 4 0 0 0;0 1 3 4 2 0]', 'P1' );
 fea.geom.objects = { gobj };
 fea.sdim = { 'x' 'y' };


% Grid generation.
 fea.grid = gridgen( fea, 'hmax', opt.hmax, 'fid', fid );


% Add plane stress physics mode.
 fea = addphys(fea,@planestress);
 fea.phys.pss.eqn.coef{1,end} = { opt.nu };
 fea.phys.pss.eqn.coef{2,end} = { opt.E  };
 fea.phys.pss.sfun            = { opt.sfun opt.sfun };
 if( opt.icase == 2 )
   fea.phys.pss.eqn.coef{4,end} = { 9.81*7000 };
 elseif( opt.icase == 4 )
   fea.phys.pss.eqn.coef{5,end} = { -9.81*7000 };
 end


% Set boundary conditions.
 dtol = 0.1;
 lbdr = findbdr( fea, ['x<',num2str(dtol)] );     % Left boundary number.
 rbdr = findbdr( fea, ['x>',num2str(1-dtol)] );   % Right boundary number.
 n_bdr  = max(fea.grid.b(3,:));        % Number of boundaries.
 bctype = mat2cell( zeros(2,n_bdr), [1 1], ones(1,n_bdr) );
 bccoef = mat2cell( zeros(2,n_bdr), [1 1], ones(1,n_bdr) );
 switch( opt.icase )
   case {1,2}
     [bctype{1,lbdr}] = deal(1);
     if( opt.icase == 1 )
       bccoef{1,rbdr} = 1e7/opt.thick;
     end
     fea.pnt(1).type  = 'constr';
     fea.pnt(1).index = [0;2];
     fea.pnt(1).dvar  = 'u';
     fea.pnt(1).expr  = 0';

     fea.pnt(2).type  = 'constr';
     fea.pnt(2).index = [0;2];
     fea.pnt(2).dvar  = 'v';
     fea.pnt(2).expr  = 0';
   case 3
     [bctype{:,lbdr}] = deal(1);
     bccoef{2,rbdr} = 1e7/opt.thick;
   case 4
     [bctype{:,lbdr}] = deal(1);
 end
 fea.phys.pss.bdr.coef{1,end} = bccoef;
 fea.phys.pss.bdr.coef{1,5}   = bctype;


% Parse and solve problem.
 fea       = parsephys(fea);             % Check and parse physics modes.
 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.
 if( opt.icase <= 2 )
   s_title = fea.phys.pss.eqn.vars{5,1};
   s_expr  = fea.phys.pss.eqn.vars{5,2};
 else
   s_title = fea.phys.pss.eqn.vars{7,1};
   s_expr  = fea.phys.pss.eqn.vars{7,2};
 end
 if ( opt.iplot>0 )
   figure
   postplot( fea, 'surfexpr', s_expr, 'isoexpr', s_expr )
   title( s_title )
 end


% Error checking.
 s_02 = evalexpr( s_expr, [0;2], fea );
 s_ref = [61.3, 0.247, 26.9, -0.2]*1e6;
 out.stress = s_02;
 out.err    = abs(s_02 - s_ref(opt.icase))/s_ref(opt.icase);
 out.pass   = out.err < opt.tol;


 if ( nargout==0 )
   clear fea out
 end