Buckling Optimization of Wood Composite Columns with Variable Cross-Sectional Area: A Comparison between two Tree Species

Abstract

The minimization of structural weight and the maximization of critical buckling load are problems that have been addressed many times. The problem of maximizing the buckling load of a wood composite column of given volume, length and material is studied. Tadjbakhsh and Keller were the first to obtain an optimum solution analytically for the case of clamped-clamped case. Unimodal solutions obtained by Tadjbaksh-Keller are not optimal because they buckle by the modes with discontinuities of the slope corresponding to the lower critical load. This leads to taking into account bimodal formulation of the optimization problem. Olhoff-Rasmussen (1977) first discovered that the unimodal solution given for the clamped by Tadjbaksh-Keller (1962) is incorrect. The optimal columns must be considered from the point of view of practical design. In this paper, it will be shown that bimodal solution is not practical and optimal since in points of minimum thickness crush occurred but not buckling. This leads to the necessity of both stability and crush formulation of the optimization problem. The present contribution of this paper is that crush is taken into account in the formulation of column optimization problem allowing for bimodal optimum solution. To test the accuracy of our new optimization column with clamped ends, experimental data were compared to numerical analysis using ANSYS. Both necessary and sufficient optimality conditions are derived. One important conclusion of this paper is that our new optimal solution is in agreement with results obtained by numerical analysis and by experiments.