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This paper presents a wet etching simulation method for sacrifice layer of MEMS (micro electro mechanical system) that considers physical phenomenon including flow, diffusion and chemical reaction. In this method, a partial differential equation with implicit parameterization of etching properties was studied that was solvable by any commercial CFD code. Two parameters for flow and reaction were determined by fitting the numerical result to experimental one obtained using a test device. For automatic calibration of parameters, an error function was proposed considering the position of etching front, averaged etching rate and shape of etching front. The distribution of the error (response surface) was predicted by second order Lagrange interpolation. The iteration algorithm for this automatic calibration contributed to reduce the computational cost. Once the parameters were determined, the etching simulation of real MEMS device could be practically carried out.

This paper proposes a systematic scheme of removing void elements to achieve fast and efficient level set based topology optimization. When performing optimization, unless special treatment is applied to the stiffness matrix, the density of these void elements are usually represented numerically by a small positive value. In level set based topology optimization, since the amount of computational resources required for FEM dwarfs those required for level set evolution, the removal of these elements from the global stiffness matrix can drastically reduce total computation time. The proposed scheme removes the void elements, determined by their nodes' level set values, from the optimization process by use of mapping procedures. The results presented here show time reductions of at least 70%. An additional advantage of the presented scheme is that it can be easily used with any black box FEM routine.

With smooth objective functions and constraint conditions, gradient-based methods can be used to solve multi-objective optimization problems efficiently. However, when applied to structural sizing optimization problems, using the Finite Element Method (FEM) and a finite difference scheme to calculate sensitivities can be computationally expensive. The adjoint variable method can be used to reduce computational cost. In order to solve multi-objective structural sizing and shape optimization problems efficiently, this paper proposes using the adjoint variable method. The adjoint variable method efficiently calculates multiple sensitivities for objectives that involve structural responses and cuts down computational cost by reducing the number of sensitivity calculations required per design variable.