A Fully Coupled Finite Element Formlation for Multi-Physics Micro Domains

In the analysis and modeling of MEMS devices, a general modeling approach is necessary to solve a multi-disciplinary domain of the device with large number of nodes and elements. In this paper, we present a step by step finite element formulation for automated modeling of multi-disciplinary domains. The electro-thermo-mechanical domain is explained and an algorithmic approach for sequential analysis of an arbitrary ground structure with multi-disciplinary boundaries is developed and implemented in Matlab with a graphical user interface. The results of the finite element approach is compared and verified with exact solutions and test results from literature. The agreement of results verifies the application of proposed finite element formulation to the analysis of elector-thermo-mechanical domains. This formulation provides a fast and reliable tool to analyze electro-thermo-elastic devices which allows large flexibility in the selection of mechanical, thermal and electrical boundary conditions.