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SUMMARY '.S.AThis paper presents an optimization method based on optimality criterion for minimum weight of structures with stability requirements. A recurrence relation is derived and the method is explained in the context of the displacement method of finite element analysis. The incipient buckling of the structure is determined by a linear eigenvalue solution. The method is programmed for trusses and frames. Illustrative problems are given to show the applicability of the method to design of structures with a large number of design variables.

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The merits and limitations of the Optimality Criteria (OC) method for the minimum weight design of structures subjected to multiple load conditions under stress, displacement and frequency constraints were investigated by examining several numerical examples. The examples were solved utilizing the OC design code that was developed for this purpose at the NASA Lewis Research Center. This OC code incorporates OC methods available in the literature with generalizations for stress constraints, fully utilized design concepts, and hybrid methods that combine both techniques. It includes multiple choices for Lagrange multiplier and design variable update methods, design strategies for several constraint types, variable linking, displacement and integrated force method analysers, and analytical and numerical sensitivities. On the basis of the examples solved, the optimality criteria for general application were found to be satisfactory for problems with few active constraints or with small numbers of design variables. However, the OC method without stress constraints converged to optimum even for large structural systems. For problems with large numbers of behaviour constraints and design variables, the method appears to follow a subset of active constraints that can result in a heavier design. The computational efficiency of OC methods appears to be similar to some mathematical programming techniques.