Structural optimization: A new dual method using mixed variables

TLDR

The paper introduces a powerful mathematical programming method for solving a broad class of structural optimization problems. The method uses mixed direct/reciprocal design variables to create conservative first‑order approximations, reformulates the problem into a sequence of convex, separable subproblems solved efficiently with a dual formulation, and demonstrates its applicability to aerospace structures. The method consistently produces a sequence of steadily improving feasible designs.

Abstract

Abstract A new and powerful mathematical programming method is described, which is capable of solving a broad class of structural optimization problems. The method employs mixed direct/reciprocal design variables in order to get conservative, first‐order approximations to the objective function and to the constraints. By this approach the primary optimization problem is replaced with a sequence of explicit subproblems. Each subproblem being convex and separable, it can be efficiently solved by using a dual formulation. An attractive feature of the new method lies in its inherent tendency to generate a sequence of steadily improving feasible designs. Examples of application to real‐life aerospace structures are offered to demonstrate the power and generality of the approach presented.