Adaptive error control in multi-physical thin-structure MEMS FE-simulation

Simulating the physical behavior of thin multi-layered structures accurately is central to micro-electro-mechanical systems (MEMS) CAD. We have produced an automatic method with which to simulate the structural response of multi-layer plate and beam micro-structures accurately and reliably. The method also covers thermo-mechanical and piezoelectric effects. We use a Kirchhoff–Love thin structure model implemented as a conforming Argyris finite element suited for the calculation of thermo-mechanical membrane and bending behavior and which is extended to simulate piezoelectric effects in thin structures. For the first time a posteriori estimation is presented for such multi-layered multi-physically active thin structures. Different sources of errors are identified and specified for several usecases. The error analysis covers locally prestressed regions, plate composition inhomogeneities, geometrical singularities, and singularities conditional upon the presence of source functions of various types. Together with a refinement strategy and a geometrical split pattern the efficiency of the method is demonstrated. Local mesh refinement guarantees the computation of the most accurate solution at a minimum of computational costs.