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FEATool Multiphysics
v1.17.1
Finite Element Analysis Toolbox
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FEATool Multiphysics
v1.17.1
Finite Element Analysis Toolbox
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EX_PLANESTRESS6 Plane stress analysis of a pressure vessel.
[ FEA, OUT ] = EX_PLANESTRESS6( VARARGIN ) Model example for plain stress approximation of a pressure vessel (annular cross section with symmetry).
Accepts the following property/value pairs.
Input Value/{Default} Description
-----------------------------------------------------------------------------------
E scalar {207e9} Modulus of elasticity
nu scalar {0.27} Poissons ratio
sfun string {sflag1} Shape function for displacements
iplot scalar 0/{1} Plot solution (=1)
.
Output Value/(Size) Description
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fea struct Problem definition struct
out struct Output struct
cOptDef = { ...
'E', 207e9; ...
'nu', 0.27; ...
'sfun', 'sflag1'; ...
'iplot', 1; ...
'igrid', 1; ...
'tol', 0.1; ...
'fid', 1 };
[got,opt] = parseopt( cOptDef, varargin{:} );
fid = opt.fid;
% Geometry and grid.
fea.sdim = { 'x' 'y' }; % Coordinate names.
fea.grid = ringgrid( 12, 216, 100e-3, 120e-3 );
fea.grid = delcells( fea.grid, selcells( fea.grid, '(x<=eps) | (y<=eps)') );
if( opt.igrid~=1 )
fea.grid = quad2tri( fea.grid );
end
n_bdr = max(fea.grid.b(3,:)); % Number of boundaries.
% Problem definition.
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 };
% Boundary conditions.
bctype = mat2cell( zeros(2,n_bdr), [1 1], ones(1,n_bdr) );
bctype{1,4} = 1;
bctype{2,3} = 1;
fea.phys.pss.bdr.coef{1,5} = bctype;
bccoef = mat2cell( zeros(2,n_bdr), [1 1], ones(1,n_bdr) );
bccoef{1,1} = '-nx*1e4';
bccoef{2,1} = '-ny*1e4';
fea.phys.pss.bdr.coef{1,end} = bccoef;
% Parse and solve problem.
fea = parsephys( fea );
fea = parseprob( fea ); % Check and parse problem struct.
fea.sol.u = solvestat( fea, 'fid', fid, 'icub', 1+str2num(strrep(opt.sfun,'sflag','')) ); % Call to stationary solver.
% Postprocessing.
s_disp = fea.phys.pss.eqn.vars{2,end};
if( opt.iplot>0 )
figure
postplot( fea, 'surfexpr', s_disp )
title( 'Total displacement' )
end
% Error checking.
s_sx = fea.phys.pss.eqn.vars{5,end};
s_sy = fea.phys.pss.eqn.vars{6,end};
s_sxy = fea.phys.pss.eqn.vars{7,end};
s_sp1 = fea.phys.pss.eqn.vars{8,end};
s_sp3 = fea.phys.pss.eqn.vars{10,end};
s_ez = fea.phys.pss.eqn.vars{13,end};
s_ep1 = fea.phys.pss.eqn.vars{15,end};
s_ep2 = fea.phys.pss.eqn.vars{16,end};
s_ep3 = fea.phys.pss.eqn.vars{17,end};
v_disp = evalexpr( s_disp, [100e-3 120e-3-2*sqrt(eps);0 0]+sqrt(eps), fea )';
v_dref = [2.809e-8 2.635e-8];
[v_sx(1),v_sx(2)] = minmaxsubd( s_sx, fea );
v_sxref = [-10000 55454];
[v_sy(1),v_sy(2)] = minmaxsubd( s_sy, fea );
v_syref = [-10000 55454];
[v_sxy(1),v_sxy(2)] = minmaxsubd( s_sxy, fea );
v_sxyref = [-32730 0];
[v_sp1(1),v_sp1(2)] = minmaxsubd( s_sp1, fea );
v_sp1ref = [4.5e4 55454];
[v_sp3(1),v_sp3(2)] = minmaxsubd( s_sp3, fea );
v_sp3ref = [-1e4 0];
[v_ez(1),v_ez(2)] = minmaxsubd( s_ez, fea );
v_ezref = [-5.929e-8 -5.929e-8];
[v_ep1(1),v_ep1(2)] = minmaxsubd( s_ep1, fea );
v_ep1ref = [2.196e-7 2.809e-7];
[v_ep2(1),v_ep2(2)] = minmaxsubd( s_ep2, fea );
v_ep2ref = [-5.929e-8 -5.929e-8];
[v_ep3(1),v_ep3(2)] = minmaxsubd( s_ep3, fea );
v_ep3ref = [-1.206e-7 -5.929e-8];
out.err = [ abs([v_dref-v_disp])./v_dref ;
abs([v_sxref-v_sx])./v_sxref ;
abs([v_syref-v_sy])./v_syref ;
abs([v_sxyref(1)-v_sxy(1)])./v_sxyref(1) 0 ;
abs([v_sp1ref(2)-v_sp1(2)])./v_sp1ref(2) 0 ;
abs([v_sp3ref(1)-v_sp3(1)])./v_sp3ref(1) 0 ;
abs([v_ezref(1)-v_ez(1)])./v_ezref(1) 0 ;
abs([v_ep1ref(1)-v_ep1(1)])./v_ep1ref(1) 0 ;
abs([v_ep2ref(1)-v_ep2(1)])./v_ep2ref(1) 0 ;
abs([v_ep3ref(1)-v_ep3(1)])./v_ep3ref(1) 0 ];
out.pass = all( out.err(:) <= opt.tol );
if( nargout==0 )
clear fea out
end