Optimal Design of Frames to Resist Buckling under Multiple Load Cases

Abstract

This paper suggests an optimization‐based design methodology for improving the strength and the overall stability characteristics of framed structures whose capacities are governed by limit‐load behavior. Attention is focused on space‐framed structures under static loads, and represents a natural extension of the basic ideas presented in the companion paper. The optimization objective function is taken here to be a linear combination of the critical buckling eigenvalues of the structure. A constant volume constraint with bounds on the design variables is used in conjunction with an optimality‐criterion approach for search. The present approach avoids the need to know the eigenvector that dominates the response as the structure passes a limit load. A novel approach to solving problems with multiple loading conditions is introduced wherein each eigenvalue in the objective is weighted in accordance with the participation of that mode in the loading. Several examples are given to demonstrate aspects of the behavior of the proposed design procedure.