Optimal Design of Planar Frames Based on Stability Criterion

This paper suggests an optimization-based design methodology for improving the strength and overall stability of framed structures, the capacities of which are governed by inelastic limit-load behavior. The optimization objective function, comprising the dominant linearized buckling eigenvalue of the structure weighted by a frequency-dependent penalty function, is motivated by a simple model of nonlinear frame behavior. Designs are constrained to have constant weight. The method requires only the linearized buckling eigenvalues and eigenvectors of the structure, avoiding computationally intensive nonlinear structural analyses in the design cycle. An iterative optimality-criteria method is used to solve the optimization problem. Several examples are given to examine the performance of the procedure, both in terms of robustness of the numerical algorithm and the quality of the designs it produces. By way of example, it is shown that by improving the overall stability characteristics of a structure under static loading, the dynamic performance of the structure is often improved.