Application of Optimality Criteria to Stress Limited Structural Design.

摘要

This report 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 internal stresses and side constraints on design variables. This recursive method is based on the Kuhn-Tucker test for a local optimum and gives, upon completion, a true local optimum design. In this method the values of the design variables are modified to drive the design to a point in the design space satisfying the Kuhn-Tucker test. Satisfaction of the Kuhn-Tucker test requires knowledge of which constraints are active, that is, critical at the optimum design. Selecting the set of active constraints for stress limited design is difficult because many more stress constraints exist than are active in the final design. Therefore, one or more iterations or redesigns are necessary. The recursive method presented herein allows automatic constraint selection and requires only the solution of a set of simultaneous linear algebraic equations at each iteration. The results of the application of the recursive method to several well known truss type structures are shown to compare favorably to results obtained using mathematical programming and other optimality criteria methods.