A gradientless finite element procedure for shape optimization

Abstract

This paper presents an iterative gradientless method for the shape optimization of stress concentrators, from the context of structural fatigue life extension. The method has been implemented to interface with the finite element code PAFEC, which does not normally have an optimization capability. The key feature of the approach is to achieve constant boundary stresses, in regions of interest, by moving nodes on the stress concentrator boundary by an amount dependent on the sign and magnitude of the local hoop stress obtained from a previous iteration of a standard finite element analysis. The results of example problems are presented which include the optimization of hole shapes in flat plates and the optimization of the design of bonded reinforcements with a focus on minimizing adhesive stress while maintaining the effectiveness of the reinforcement. In all cases, it was found that significant stress reductions were achieved by way of the local shape changes due to the optimization. The method presented is considered an effective and robust alternative to the use of more expensive and complex gradient-based finite element optimization software, which is currently available commercially.