Reliability-Based Topology Optimization of Compliant Mechanisms with Geometrically Nonlinearity

Abstract

A new reliability-based topology optimization method for compliant mechanisms with geometrical nonlinearity is presented. The aim of this paper is to integrate reliability and geometrical nonlinear analysis into the topology optimization problems. Firstly, geometrical nonlinear response analysis method of the compliant mechanisms is developed based on the Total-Lagrange finite element formulation, the incremental scheme and the Newton-Raphson iteration method. Secondly, a multi-objective topology optimal model of compliant mechanisms considering the uncertainties of the applied loads and the geometry descriptions is established. The objective function is defined by minimum the compliance and maximum the geometric advantage to meet both the stiffness and the flexibility requirements, and the reliabilities of the compliant mechanisms are evaluated by using the first order reliability method. Thirdly, the computation of the sensitivities is developed with the adjoint method and the optimization problem is solved by using the Method of Moving Asymptotes. Finally, through numerical calculations, reliability-based topology designs with geometric nonlinearity of a typical compliant micro-gripper and a multi-input and multi-output compliant sage are obtained. The importance of considering uncertainties and geometric nonlinearity is then demonstrated by comparing the results obtained by the proposed method with deterministic optimal designs, which shows that the reliability-based topology optimization yields mechanisms that are more reliable than those produced by deterministic topology optimization.