Topology Optimization of Blank Geometry for the Sheet Forming Process

Abstract

The newly developed element exchange method (EEM) for topology optimization is applied to the problem of blank shape optimization for the sheet-forming process. EEM uses a series of stochastic operations guided by the structural response of the model to switch solid and void elements in a given domain to minimize the objective function while maintaining the specified volume fraction. In application of EEM to blank optimization, a sheet forming simulation model is developed using Abaqus/Explicit. With the goal of minimizing the variability in wall thickness of the formed component, a subset of solid (i.e., high density) elements with the highest increase in thickness is exchanged with a consistent subset of void (i.e., low density) elements having the highest decrease in thickness so that the volume fraction remains constant. The EEM operations coupled with finite element simulations are repeated until the optimum blank geometry (i.e., boundary and initial thickness) is found. The developed numerical framework is applied to blank optimization of a benchmark problem. The results show that EEM is successful in generating the optimum blank geometry efficiently and accurately.