Geometrically non-linear analysis of thin-film compliant MEMS via shell and solid elements

This paper presents a performance-based comparison of quadratic shell elements with shear deformation and 3-D quadratic solid elements for modeling geometrically non-linear coupled in-plane and out-of-plane deflection of thin-film compliant microelectromechanical systems. A mesh density study of a single out-of-plane torsional compliant element indicates that a relatively coarse shell element mesh can produce force, displacement, and stress results very similar to those predicted by a much larger and computationally costly 3-D solid element model for out-of-plane loading. Shell and 3-D solid element models of a macro-scale prototype of a MEMS compliant lamina emergent constant-force mechanism are shown to agree very well with experientially acquired force displacement data, and to agree well in their estimates of Von Mises stresses. Close agreement of shell element and 3-D solid element models is also demonstrated for models of a thin-film MEMS constant-force mechanism and a thin-film MEMS cellular lance mechanism. Both of these mechanisms exhibit highly non-linear mechanism stiffness, and large, coupled in and out-of-plane displacements. Together, these results strongly suggest that quadratic shell elements with shear deformation can be used to model the coupled in-plane and out-of-plane motion of thin-film compliant mechanisms.