Examination of Shape Optimization for the Nonlinear Buckling Phenomenon of Suspension Parts

Abstract

This paper presents a numerical solution to a non-parametric shape optimization problem for design of suspension arm in which strength of suspension arm is evaluated by reaction force to plastic buckling load due to compulsory displacement. To deal with buckling phenomena, the geometrical non-linearity and material non-linearity are considered. Hyper-elastic theory is applied to calculate the deformation of suspension arm, under assumption of monotonous loading. Mass and the reaction force integral to the buckling phenomena are chosen as an objective function and a constraint function, respectively. The shape derivatives of these functions are evaluated by the shape optimization theory. A numerical scheme based on a sequential quadratic approximation method is applied to reshape by using the shape gradients. In this scheme, the traction method is used to find the decent directions of the cost functions. The scheme is implemented by using a commercial shape optimization program. In this program, the shape gradients are calculated by a user sub-program which is developed by using the result of non-linear FEM analysis of a commercial solver. The numerical example for a suspension arm model shows 12% of mass reduction while keeping the reaction force integral constant.