Minimum Weight Design of Finite Element Structures

Abstract

Design algorithms for obtaining the minimum weight of finite element structure are presented. The procedures are based upon approximating the structural behavior as a function of the reciprocal of the characteristic crosssectional property of the finite elements. In addition, approximations based upon the compatibility equations are employed. This results in simpler and generally more accurate approximations of the deflection and stress changes as compared to present procedures which utilize the size variables and the equilibrium equations. Algorithms based upon linear programming utilizing linear constraints obtained either from the global equilibrium or compatibility equations plus a gradient search procedure with segmented linear constraints are developed. The efficiency of the linear programming with linear (equilibrium) constraints, which utilizes available digital subprograms, was demonstrated by comparison of solutions of 3- and 10-bar truss problems presented in the literature. All solutions were of equal or less weight than published results and generally were obtained with fewer redesign cycles. The other algorithms are potentially more efficient. They require, however, further development and demonstration.