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.

Topology-optimization based design of multi-degree-of-freedom compliant mechanisms (mechanisms with multiple pseudo-mobility)

“…For mechanisms with single pseudo-mobility in the geometrically linear case, in Frecker et al (1999) the ratio of mutual potential energy to strain energy is maximized for one input DoF, where the output displacements are included into a combined mutual potential energy by so-called virtual loads, or a weighted sum of the individual mutual potential energies is used. In Li et al (2014), a multi-objective optimization minimizes the “mean compliance” which, like the strain energy, is a measure of the structural stiffness of the mechanism, while maximizing a weighted sum of the output displacements. Here, transverse loads are included with the help of one load spring applied per output DoF.…”

Topology-optimization based design of multi-degree-of-freedom compliant mechanisms (mechanisms with multiple pseudo-mobility)

“…For mechanisms with single pseudo-mobility in the geometrically linear case, in [15] the ratio of MPE to SE is maximized for one input DoF, where the output displacements are included into a combined MPE by so-called virtual loads, or a weighted sum of the individual MPEs is used. In [16], a multi-objective optimization minimizes the "mean compliance" which, like the SE, is a measure of the structural stiffness of the mechanism, while maximizing a weighted sum of the output displacements. Here, transverse loads are included with the help of one load spring applied per output DoF.…”

A novel approach of reliability-based topology optimization for continuum structures under interval uncertainties

“…Lazarov et al (2012) introduced the stochastic collocation methods in reliability evaluation of layout design for uncertain mechanical systems. Moreover, the probabilistic RBTO has been also used for accomplishing complex design of engineering systems, mainly including geometrical nonlinear systems (Li et al , 2014), thermal systems (Qian and Dede, 2016) and multidisciplinary coupled systems (Silva et al , 2010).…”