FEATool Multiphysics  v1.16.4 Finite Element Analysis Toolbox
ex_axistressstrain5.m File Reference

## Description

EX_AXISTRESSSTRAIN5 Axisymmetric vibration modes of a hollow cylinder.

[ FEA, OUT ] = EX_AXISTRESSSTRAIN5( VARARGIN ) Axisymmetric vibration modes of a hollow cylinder (NAFEMS Free Vibration Benchmark 41).

Reference

[1] F. Abassian, D.J. Dawswell, and N.C. Knowles, Free Vibration Benchmarks, Volume 3, NAFEMS, Glasgow, 1987.

Accepts the following property/value pairs.

Input       Value/{Default}        Description
-----------------------------------------------------------------------------------
igrid       scalar 0/{2}           Cell type (>0=quadrilaterals, <0=triangles)
sfun        string {sflag1}        Shape function
iplot       scalar 0/{1}           Plot solution (=1)
.
Output      Value/(Size)           Description
-----------------------------------------------------------------------------------
fea         struct                 Problem definition struct
out         struct                 Output struct


# Code listing

 cOptDef = { 'igrid',    2;
'sfun',     'sflag1';
'iplot',    1;
'tol',      0.01;
'fid',      1 };
[got,opt] = parseopt(cOptDef,varargin{:});
fid       = opt.fid;

E   = 2e11;
nu  = 0.3;
rho = 8000;

% Geometry definition.
fea.sdim = {'r' 'z'};
gobj = gobj_rectangle( 1.8, 2.2, 0, 10, 'R1' );
fea.geom.objects = { gobj };

fea.grid = rectgrid( abs(opt.igrid)*2, abs(opt.igrid)*50, [ 1.8, 2.2; 0, 10 ]);
if( opt.igrid<0 )
end

% Equations and problem definition.
fea = addphys( fea, @axistressstrain );
fea.phys.css.eqn.coef{1,end} = { nu  };
fea.phys.css.eqn.coef{2,end} = { E   };
fea.phys.css.eqn.coef{3,end} = { rho };
fea.phys.css.sfun            = { opt.sfun, opt.sfun };

% Solve problem.
fea = parsephys( fea );
fea = parseprob( fea );

[fea.sol.u,fea.sol.l] = solveeig( fea, 'fid', fid );

% Postprocessing.
if( opt.iplot>0 )
postplot( fea, 'surfexpr', 'sqrt((r*u)^2+w^2)', 'solnum', 2 )
end

out = [];
f = sqrt(max(0,fea.sol.l))/(2*pi);
f_ref = [ 0; 243.773387; 378.534723; 394.046384; 397.467494; 405.041753 ];
out.err  = norm(f_ref-f)/norm(f_ref);
out.pass = out.err < opt.tol;

if( nargout==0 )
clear fea out
end