An Efficient Technique in Shape Optimization*, †

Abstract

ABSTRACT A shape optimization method is presented for smoothing stress peaks that are caused by notch effects on unloaded edges of holes in plates or shell structures with linear-elastic, homogeneous, isotropic material under external forces. The optimization problem is first formulated as a functional whose integrand contains the difference between the stresses at the hole edge and the optimal stress. This mechanical problem is approximated by a sequence of purely geometric, substitute functionals. The substitute functional is discretized by means of splines and formulated as a nonlinear constrained optimization problem which is solved with a quasi-Newton method. The efficiency of the method is demonstrated on the basis of examples.