Topological layout design of electro-fluid-thermal-compliant actuator

Abstract

While the sequential solution procedure (the sequence of solutions) for a steady-state electro-thermal-compliant (ETC) actuator device has been considered in previous studies, very few researches have concurrently considered the mutual couplings between fluid and thermal domains and between fluid and structural domains. Such an analysis allows a straightforward and accurate finite element (FE) simulation of various flow boundary conditions and different flow types, but makes the involved differential equations highly nonlinear. Thus, the goal of this research is to develop a new and rigorous monolithic analysis and optimization framework for an electro-fluid-thermal-compliant (EFTC) microactuator. To accommodate the coupling effect of the fluid and thermal domains, a modified incompressible Navier–Stokes equation with Darcy’s force and a heat transfer equation coupled with fluid motion are additionally formulated in the present research. In addition, a new nonlinear monolithic FE modeling method that involves the use of the deformation tensor is employed in order to consider the mutual coupling between fluid and structural domains. Using the solid isotropic material with penalization (SIMP) approach to interpolate seven material properties (Young’s modulus, electrical conductivity, heat conductivity, heat capacity, mass density, heat capacity, and Darcy’s force coefficient) with respect to a density design variable, it is possible to achieve topology optimization (TO) upon consideration of the strong nonlinear couplings of the EFTC actuator. To efficiently solve four sets of nonlinearly coupled equations, a sequence of iterative solutions to the equations is proposed and a nonlinear sensitivity analysis without consideration of the iterative solution sequence is derived based on the adjoint sensitivity analysis method. Several three-dimensional examples are also examined in order to demonstrate the validity and potential of the present formulations for analysis and TO.