A Comparative Study of the Formulations and Benchmark Problems for the Topology Optimization of Compliant Mechanisms

The topology optimization problem for the synthesis of compliant mechanisms has been formulated in many different ways in the past $15years$⁠, but there is not yet a definitive formulation that is universally accepted. Furthermore, there are two unresolved issues in this problem. In this paper, we present a comparative study of five distinctly different formulations that are reported in the literature. Three benchmark examples are solved with these formulations using the same input and output specifications and the same numerical optimization algorithm. A total of 35 different synthesis examples are implemented. The examples are limited to desired instantaneous output direction for prescribed input force direction. Hence, this study is limited to linear elastic modeling with small deformations. Two design parametrizations, namely, the frame element-based ground structure and the density approach using continuum elements, are used. The obtained designs are evaluated with all other objective functions and are compared with each other. The checkerboard patterns, point flexures, and the ability to converge from an unbiased uniform initial guess are analyzed. Some observations and recommendations are noted based on the extensive implementation done in this study. Complete details of the benchmark problems and the results are included. The computer codes related to this study are made available on the internet for ready access.