An efficient shape optimization technique of a two-dimensional body based on the boundary element method

An efficient approximation method to determine the optimum shape of the minimum weight of a body subjected to stress and displacement constraints is suggested by using the boundary element method. The objective function of weight is approximated to an expansion of a second-order Taylor series and the stress and displacement constraints to expansions of a first-order Taylor series, based on the boundary element sensitivity analysis at the current design point. The approximated subproblem is then solved by a linear complementary pivot method. Design variable reduction techniques of isoparametric interpolation and trigonometric series interpolation for the design boundary shape are also adopted for reducing the degrees of freedom of the design problems.