Design of 2D and 3D Non-linear Compliant Mechanisms using Hybrid Cellular Automata

Abstract

The field of topology design of compliant mechanisms has developed from infancy to well grown state in last 15 years. Born from the need of hingeless mechanisms in MicroElectroMechanical Systems (MEMS), compliant mechanims are finding their use in wide range of applications like snap-through mechanisms, piezoelectric actuators and wing flapping mechanisms among many others. Most of the work developed so far, consider linear elastic material behavior and small displacment theory to design compliant mechanisms. In order to account for the effect of large displacements in mechanism design, geometric nonlinearity is considered by many researchers, however, nonlinearities arising from plasticity and contact are seldomly studied. One of the major challenges in the design of mechanisms considering nonlinearities is sensitivity analysis. Analytical expressions for sensitivities of objective function with respect to design variables can not be expressed in closed form when nonlinear finite element methods are used. Moreover, commercial finite element softwares which use implicit/explict solvers can not be used for such sensitivity calculations as they do not store stiffness matrices. In this work, optimal design for compliant mechanisms using control based material update scheme (HCA) is developed for linear case and the idea is extended to obtain concept topologies for nonlinear cases. Since this method does not involve sensitivity calculations when nonlinearities are considered, commercial FEA packages can be used which help in handling complex design problems in 2D and 3D. Although the final designs for nonlinear cases can not be claimed ‘optimal’, this method gives designer, a candidate designs which perform satisfactorily well under nonlinear conditions. This method is developed particularly for potential applications of compliant mechanisms in crashworthy designs where considering nonlinearity becomes essential. The applicability of the proposed method is shown by considering 2 examples.