An Efficient Shape Optimization of Minimum Weight Design by Boundary Element Method

An efficient approximation method to determine an optimum shape of minimum weight subjected to stress constraints is suggested. Design variable reduction techniques of isoparametric interpolation and trigonometric series interpolation for the boundary shape are adopted for reducing the degree of freedom of the design problems. The objective function of weight is approximated to an expansion of a second-order Taylor series and the stress constraints to expansions of first-order Taylor series, based on the boundary element sensitivity analysis at a design point. Then the approximated subproblem is solved by a linear complementary pivot method. In the design variable reduction of isoparametric interpolation, an adaptive mesh refinement technique is also adopted to maintain the accuracy of the structural analysis. The efficiency of the approximation method suggested here is confirmed by application to minimum weight design problems to determine hole shapes in a plate under biaxial loadings.