Authors: M. Motiee, A. Khajepour and R.R. Mansour
Affilation: University of Waterloo, Canada
Pages: 69 - 72
Keywords: finite element, MEMS, micro electro-thermo-mechanic, electro-thermal actuator
MEMS actuators are typically used for either one time deployment of structures for automatic assembly or constant periodic actuation as in case of micro optic scanners. Electro-thermal actuators rely on the joule heating resulting small mechanical expansion of a conductor when a current is passed through it. In the literature, an extensive research is done on modeling of thermal actuators but the modeling is limited to developing and solving the exact equations of a particular system with limited number of elements. Developing a new finite element formulation is necessary to solve a general multi-disciplinary domain with arbitrary arrangement of boundary conditions and large number of nodes and elements. This paper, presents a new 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 using the finite element method. To solve a specified domain with defined electrical, thermal and mechanical boundary conditions, the constitutive equations of the system in all three domains are derived and discretized into finite number of nodes and elements. The equation of continuity of current is solved by modified nodal analysis method, MNA and the Galerkin’s integration is used to integrate the thermoelstic equations over the domain. Thermal effects are included in the formulation in the form of dilatational strains. Moreover, in this paper the phenomena of heat transfer in micro scale for conduction, convection and radiation are studied. Results show that the micro scale heat transfer takes place by conduction, as opposed to convection. The above automated algorithm is implemented in Matlab and its results are compared and verified with exact solutions and experimental results of the hot arm thermal actuator and Chevron actuator. The agreement of results verifies the application of proposed finite element formulation to the analysis of electro-thermo-mechanical domains. This new finite element formulation provides a fast and reliable tool to analyze electro-thermoelastic devices. It also enables topology and hot arm placement optimization in thermal actuators.
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