Yl. Hsu et al., THE CURVATURE FUNCTION-METHOD FOR 2-DIMENSIONAL SHAPE OPTIMIZATION UNDER STRESS CONSTRAINTS, Computers & structures, 55(4), 1995, pp. 647-657
The curvature function method for two-dimensional shape optimization u
nder stress constraints is developed. This method uses curvatures alon
g the boundary curve as the design variables. First it is shown that l
ocal curvature has a monotonic relation to stress. Based on this, a ze
ro-order search direction can be defined to search for the optimum cur
vature function which achieves a fully stressed boundary. No sensitivi
ty analysis is required, and the method is completely independent of t
he analysis techniques for calculating the stress. The resulting curve
has C-2 continuity if the curvature function is continuous. Three des
ign examples are presented.