As a general note for nonanalytic problems when doing a finite-element
convergence study, consider the following.

First, determine if your FEM is unstable.  There are two types of
instability that come to mind: mechanical & numerical.  Mechanical
instability requires a nonlinear analysis.  Examples include post-buckling,
large deformations, crash detection, and nonlinear stress-strain
relationships & hysteresis.  Try slight variants in the loading and/or
pre-stress to determine if the response is well-behaved.  If not, the
nonlinear solver's input parameters and/or the initial conditions need
adjustment, allowing the solver to "ease up" on the solution.

Numerical instability results from a solver's digital noise.  You may find
the solver requiring an exceedingly large number of iterations to converge.
If you plot nodal values temporally or spatially, you could see
oscillations.  One option is to pick a unit system where subtraction errors
are minimized.  Using MKS units for MEMS problems that have micron
dimensions and megapascals of stress is suboptimal.  CoventorWare uses a
micron-MPa based system, and tools such as SolidWorks allow you to define
your own units.  Second, consider the geometry.  Large aspect-ratio, thin
and planar MEMS structure are ill-suited for tetrahedral meshing, although
automatic meshing that comes with tet meshing is sometimes nice.  2D shell
meshes and hexahedral (brick) meshes are more ideal.  The latter may require
structured meshing that some tools cannot provide.

Expect your problems to be greatly exacerbated when you have combined
mechanical and numerical instabilities in your model.

If you do not have instability problems, there are two options to determine
if your solution is correct.  Run a mesh convergence analysis.  This is the
simplest option.  It requires a more refined mesh.  Always be careful in the
process of refinement that you do not add numerical noise as mentioned
above.  With most CAE-based solver, mesh refinement is easy to do.  The
other option is to try two different mesh types.  For MEMS, a hexahedral
mesh is well approximated by a geometry that can be represented by a 2D
shell mesh.  See if the solutions match.  It's also a good check to see if
your model is set up correctly.

Whatever you do, know the limitations of the solver, pay attention to detail
during problem set up and meshing, simplify the model to the regions of
interest, and - stating the obvious - know that garbage-in results in even
worse out.

Good luck.
Raj


--
Raj Gupta, Ph.D.
Volant Technologies
http://terahz.org