FEATool Multiphysics
v1.17.0
Finite Element Analysis Toolbox
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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
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).index = [0;2]; fea.pnt(1).type = 'constr'; fea.pnt(1).dvar = 'u'; fea.pnt(1).expr = 0'; fea.pnt(2).index = [0;2]; fea.pnt(2).type = 'constr'; 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); 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