Finite Element Synthesis of Structure Shapes Due to Stress Criteria

Abstract

An iteration method of the finite element synthesis is presented on the basis of a new notion: that the objective design is searched for in the vicinity of the initial design, while the structural response to the objective value ia approximated by the first-order Taylor series expansion of the response with respect to the design variables. A functional is composed of the squared sum of the design variables and the equality constraint conditions representing the response approach to the objective value incorporated by the Lagrange multipliers. The design variables are determined by the minimization of the functional. The numerical examples are concerned with the contour adaptation of two-dimensional elastic structures so as to decrease the concentrated stresses around the hole in a square plate under bi-axial tension and the fillet bending stress in a gear tooth.