A Relative-Stress Based Method for Structural Shape Optimization

A gradientless method for two-dimensional shape optimization is developed based on the magnitude of local relative-stress difference along the design boundary. The design boundary is modeled by using cubic splines, which are determined by a number of control points. The optimal shape of a design boundary with constant stress is achieved iteratively by moving control points consecutively (correspondingly, changing the shape of the design boundary) by an amount depending on the relative-stress difference between two neighboring boundary points. The key feature of the optimization method is that no arbitrary threshold stress is required. The result quality in terms of accuracy and efficiency are tested and discussed with several finite element analysis examples.