Optimisation of columns and frames against buckling

A simple method using the finite element analysis is presented for the optimum design of columns and frames to enhance the elastic buckling resistance of structures. From the results of finite element analysis, the effect on the fundamental buckling load due to the local modification of each element is assessed. Based on this assessment, an iterative procedure is set up for gradually shifting the material from the strongest part of the structure to the weakest part while keeping the structural weight constant. A simple procedure for bimodal and multimodal optimisation is also introduced. Numerical examples are included to demonstrate the efficiency and effectiveness of the proposed method for the optimum design of columns and frames with single modal, bimodal and trimodal buckling failures.