Isogeometric Shape Optimization for Compliant Mechanisms With Prescribed Load Paths

Abstract

This paper presents a method for the design of compliant mechanisms with large deflections and prescribed load paths. While the approach is general, this paper treats the shape optimization for two dimensional beams. Due to the geometric non-linearity of the problem the non-linear analysis is nested into the optimization procedure. This requires accurate and efficient analysis of the structural problem. The analysis of the beam is based on the Isogeometric Analysis formulation, an alternative for conventional FEA especially appreciated for its shape-accuracy and efficiency. The method is applied to the synthesis of a balancer for a pendulum, which involves a two step load case: first a prestressing phase and subsequently a motion phase under the influence of gravity. To this end, a prestressed compliant beam was optimized with respect to its initial shape and the preload conditions. The rotationless character of the degrees of freedom of the Isogeometric beam requested the formulation of specific boundary conditions in order to apply rotations on the beam. The results of the shape optimization have been validated with a prototype out of carbon fiber composite material, which has been successfully tested. The experimental results are in agreement with the simulation results, with an error of 3%.