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.

Multiple degree-of-freedom compliant mechanisms are widely used in the fields of micro-positioning and micro-manipulation. This paper deals with multiobjective topology optimization of multi-input and multi-output compliant mechanisms undergoing large deformation. The objective function is defined by the minimum compliance and maximum geometric advantage to meet both stiffness and flexibility requirements. The suppression strategy of input and output coupling terms is studied and the expression of the output coupling terms is further developed. The weighted sum of the conflicting objectives resulting from the norm method is used to generate the optimal compromise solutions, and the decision function is set to select the preferred solution. Geometrically nonlinear mechanism response is calculated using the Total-Lagrange finite element formulation and the equilibrium is found using an incremental scheme combined with Newton-Raphson iterations. The solid isotropic material with penalization approach is used in design of compliant mechanisms. The sensitivities of the objective functions are found with the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. Numerical examples of multiple inputs and outputs are presented to show the validity of the new method. Simulation results show that the compliant mechanisms can be deformed in the desirable manner and the coupling output displacements are suppressed significantly by using the presented method.

Homogenization or material distribution method based topology optimization will create final topologies in grey level image and saw tooth jump discontinuity boundaries that are not suitable for direct engineering practice, so it is necessary to extract the topological diagram. And a new topology extraction method for compliant mechanisms is presented. In the fist stage, the grey image is transferred into the black-and white finite element topology optimization results. The threshold value meeting to objective function is obtained so that each element is either empty or solid; in the second stage, the density contour approach is used by redistributing nodal densities to generate the smooth boundaries; in the third stage, Smooth boundaries are represented by parameterized B-spline curves whose control points selected from the viewpoint of stiffness and flexibility constitute the parameters ready to undergo shape optimization; Then shape optimization is executed to improve stress-based local performance, The parameters that present the outer shape of the compliant mechanism are used as design variables; In the final stage, simulations of numerical examples are presented to show the validity of the proposed method.