Structural Shape Optimization of Hyperelastic Material by Discrete Force Method

Abstract

In this paper, a shape optimization procedure for a flexible structure which shows strong nonlinearity like rubber is presented. This method follows the idea of the traction method proposed by Azegami but is extended to handle any kinds of nonlinearity. It is formulated in a complete discrete form and not the surface traction force but the body force is applied, so the method is termed as ‘discrete force method’. In this study, in order to verify the validity and effectiveness of the present method, some shape optimization problems of rubber like structures are considered with the nonlinear finite element program for hyperelastic material using the Mooney-Rivlin law and combined with the present method. The first simple numerical example of the plate with a center hole shows the validity of the present method and the second analysis of the flexible micromanipulator shows applicability to the practical problem.