Shape optimization of beam due to lateral buckling problem

Based on a non-linear mathematical model of lateral buckling of a slender beam with a narrow rectangular cross section, the variational formulation of the two-parametric optimization problem is given in the dimensionless form. An optimal shape is obtained by solving the variational problem using the Rayleigh-Ritz method with the orthogonal system of trigonometric functions. By a partial solution of the Euler-Lagrange differential equation of the variational problem, a proof is given that in the case of the optimal shape, a maximal reference stress according to the total strain energy theory is constant along the beam. An example of extrapolation of the two-parametric optimization problem solution is represented. (C) 2011 Elsevier Ltd. All rights reserved.