How can I improve accuracy using PDE Toolbox

Hello,

I have a cantilever with a constant force. I'm computing the reaction on the clamped edge with the PDE Toolbox.

However the difference between numerical and exact solution is too high.

Is there a way too reduce the difference, other then reducing maximum element size Hmax?

yModulus = 200e3; % young's modulus
ny = 0.2;         % Poissons ratio
Hmax = 0.01;      % max element size
l = 1;            % length of cantilever
b = 0.2;          % height of cantilever
q = 10;           % constant force

f_press = @(region,state) [q*ones(size(region.y)),zeros(size(region.y))];

structModel = createpde('structural','static-planestress');

gd = [3;4;0;b;b;0;0;0;l;l];
g = decsg(gd,'R',char('R'));

geometryFromEdges(structModel,g);
generateMesh(structModel,'Hmax',Hmax);

structuralProperties(structModel,...
        'YoungsModulus',yModulus,...
        'PoissonsRatio',ny);

structuralBC(structModel,'Edge',1,'Constraint','fixed');
structuralBoundaryLoad(structModel,'Edge',4,'SurfaceTraction',f_press);

res = solve(structModel);

% Fx should equal 10
reaction = evaluateReaction(res,'Edge',1);

Answer 1

[Alan Weiss]

If your toolbox version were R2017a or earlier, the default mesh for 2-D geometry has linear elements. You can get improved accuracy by using quadratic elements:

generateMesh(model,'GeometricOrder','quadratic')

However, since your toolbox version is R2017b or later (that's when structural analysis was introduced), then I don't know of a way to get more accuracy other than taking a finer mesh.

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[Svetlana Pease]

For this particular example, using a finer mesh seems to be the only way to get a more accurate result. In general, you can also try different solver options - for example, you can tighten the tolerances:

https://www.mathworks.com/help/pde/ug/pde.pdesolveroptions-properties.html

Svetlana Pease

MathWorks Documentation Group