Iterative Elastic and Plastic Optimal Design of Steel Frames by a Mixed Method Including Double Secant Method for Nonlinear Mathematical Programming

Abstract

Recent applications of optimization methods in building frame design practice include optimality criteria method [1,2,3] and the conventional LP method. To use the recurrence relationship in the optimality criteria method, the Lagrange multipliers associated with each active constraint, and the gradients of the weight function and the active constraints must first be determined. But there derivations are lengthy and tedius. Therefore, we try to use the ‘double secant method for nonlinear mathematical programming ‘developed by Tsung-Wu Lin [4] for elastic optimal design. The major advantage of the latest method is that it provides double secants to make the search of correct direction quickly with smaller maximum error at each iterate. Nevertheless, there are still too many iterations required to reach an optimum design if the double secant method alone is used. It can become more effective if we determine first the initial design variables, or the initial member sizes, by applying the stress-ratio method and the shifting method alternatively. The amount of calculation can also be reduced by applying the reanalysis technique or Gauss-Seidal iteration method in the process of nonlinear mathematical programming. Numerical examples have shown that after the initial design variables were determined after two or more iterations, only several iterations were needed for the double secant method.