Reliability Based Structural Design Using Probabilistic Optimality Criteria for Stress and Displacement

Abstract

A number of studies have been carried out in past years on optimum design under the condition of probabilistic constraints. For example, Switzky derived a probabilistic optimality criterion for the structural design with stress constraints. However, few attempts have been made to formulate the probabilistic optimality criterion for the displacement constraint. In the present study, an attempt was made first to derive the probabilistic optimality displacement criterion for the minimum weight design by using the Lagrange multiplier method. Then, a new probabilistic optimality criteria method was proposed, which unifies Switzky's probabilistic optimality stress criterion and the present probabilistic optimality displacement criterion by using the envelope method. Two design examples were presented to demonstrate the efficiency and convergency of the method developed herein.
The results shows that the proposed method can be used to optimize the structure having probabilistic stress and displacement constraints only in few cycles of trials, and hence it has a good convergency in comparison with other probabilistic optimum design methods using mathematical programming.