THE CURVATURE FUNCTION-METHOD FOR 2-DIMENSIONAL SHAPE OPTIMIZATION UNDER STRESS CONSTRAINTS

The curvature function method for two-dimensional shape optimization under stress constraints is developed. This method uses curvatures along the boundary curve as the design variables. First it is shown that local curvature has a monotonic relation to stress. Based on this, a zero-order search direction can be defined to search for the optimum curvature function which achieves a fully stressed boundary. No sensitivity analysis is required, and the method is completely independent of the analysis techniques for calculating the stress. The resulting curve has C-2 continuity if the curvature function is continuous. Three design examples are presented.