Verification & Validation

It is imperative to do some checks to make sure that the numerical results are accurate. Numerical results can either be compared directly to empirical data or they may be compared to theory.

Qualitative Verification

It should be expected that the structure will experience most of its deformation in the horizontal direction. Additionally, there should be little deformation in the y direction. The results from ANSYS agree with our intuition here.

Mesh Refinement

Another, way to verify the solution of a numerical method is to examine the convergence of the solution as the mesh is refined. Generally, the numerical solution should converge to the exact solution as the mesh is refined. In order to refine the mesh, first expand the mesh tab, , in the tree outline. Next, click on "Edge Sizing", , such that it highlights blue. Now, change the number of divisions in the "Details of "Edge Sizing"" table. Remember, that each line segment of the plane frame structure will be divided in to the number of divisions that you specify. After you have changed the "Number of Divisions" to your preference, click on the solve button, , to recalculate the solution with the new mesh.

The table below displays the outputs of the ANSYS simulation for a mesh of 2 elements and a mesh of 10 elements.

As one can see from the table above the results do not change much as the mesh is refined. After 32 elements, the total deformation has converged up to the sixth decimal place. The exact solution for the deformation is cubic and for this setup ANSYS uses element BEAM 188 which in turn uses cubic interpolation. Thus, for the simple cantilever beam setup the numerical method converges very quickly.