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

Abstract

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.

On understanding of design problem formulation for compliant mechanisms through topology optimization

“…the case , a so-called spring model have been developed (Ananthasuresh, 1994;Saxena and Ananthasuresh, 2000;Deepak et al, 2009). In the model, the work-piece was modeled as a spring of constant stiffness, i.e.…”

“…By considering formulations for mechanical functional requirements in the design of CMs, instead of getting the same results with those for flexibility-stiffness purpose, optimal topologies, whose performances are consistent with the mechanical functional requirements, can be obtained. However, there are nonlinear constraints in all the formulations for MA and GA, which brings difficulty in algorithm convergence and the results suffer from point flexure problem (Deepak et al, 2009;Wang, 2009b). Canfield and Frecker (2000) designed compliant displacement amplifier for stack actuators by maximizing ME (F14), which was the product of GA and MA.…”

“…to restrain the motion; however, they did not change the tendency of lumped compliance. In addition, Deepak et al (2009) also found that when the mechanical specification was not set properly, e.g. the desired GA was too large, point flexures still appeared in the optimum.…”

“…In the literature, flexibility, stiffness, mechanical efficiency (ME), mechanical advantage (MA), geometrical advantage (GA), weight, strength and so on, have been defined as objective functions or constraints (Howell, 2001;Saxena and Ananthasuresh, 2001;Deepak et al, 2009). Ananthasuresh (1994) pioneered the TO of CM design with a multi-criteria model and a spring model.…”

“…displacement or force, need to be considered as the first priority. Deepak et al (2009) had a comparative study of five formulations, i.e. stiffness-flexibility, MA, work ratio, characteristic stiffness and artificial springs.…”