Application of optimality criteria to automated structural design

Abstract

This paper presents a recursive design method for the minimum weight design of linear elastic redundant structures subject to multiple independent static loading conditions and with behavioral constraints on allowable element stresses and nodal displacements and constraints on design variables. This recursive method is based on the Kuhn-Tucker necessary conditions for a local optimum and gives, upon completion, a local optimum design. An iterative procedure is used to resize the structure until a design satisfying the Kuhn-Tucker necessary conditions is obtained. For resizing, it is necessary to identify the current near-active (critical) constraints and to use this data to construct the Kuhn-Tucker test. If the current design is not converged, then the information from the test is used to resize the design variables and improve the design. Each iteration or redesign requires only the solution of a set of linear algebraic equations equal in number to the number of currently active constraints. The method is used to design several well-known truss-type structures, and the results are shown to compare favorably with previous results obtained using mathematical programing algorithms and other optimality criteria methods.