Some Approximation Concepts for Structural Synthesis

TLDR

The study considers static stress and displacement constraints under alternative loading conditions. The paper presents an efficient automated minimum‑weight design procedure for sizing structural systems such as trusses, shear panels, and constant‑strain triangles. The optimization algorithm adapts the method of inscribed hyperspheres, employing temporary deletion of noncritical constraints, design‑variable linking, and Taylor‑series expansions to achieve high efficiency. The method yields optimum designs for multiple planar and space truss examples, demonstrating significant efficiency gains from the approximation concepts.

Abstract

An efficient automated minimum weight design procedure is presented which is applicable to sizing structural systems that can be idealized by truss, shear panel, and constant strain triangles. Static stress and displacement constraints under alternative loading conditions are considered. The optimization algorithm is an adaptation of the method of inscribed hyperspheres and high efficiency is achieved by using several approximation concepts including temporary deletion of noncritical constraints, design variable linking, and Taylor series expansions for response variables in terms of design variables. Optimum designs for several planar and space truss examples problems are presented. The results reported support the contention that the innovative use of approximation concepts in structural synthesis can produce significant improvements in efficiency.