Structural Synthesis by Combining Approximation Concepts and Dual Methods
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Abstract
Approximation concepts and dual methods are combined to create an efficient procedure for minimum weight sizing of structural systems. Approximation concepts convert the basic mathematical programming statement of the structural synthesis problem into a sequence of explicit primal problems of convex and separable form. These problems are solved by constructing explicit dual functions which are maximized subject to non-negativity constraints on the dual variables. A specially devised Newton type maximization algorithm called DUAL 2 operates in a sequence of dual subspaces, with gradually increasing dimensionality, such that the maximum dimensionality of the dual subspace never exceeds the number of strictly critical constraints by more than one. The power of the method presented is demonstrated by giving numerical results for several example problems, including a metallic swept wing and a thin delta wing with fiber composite skins.