A new quadrature method for the computation of critical loads in problems of elastic buckling (Q1072756)

The computation of critical loads in problems of elastic buckling of bars and frames is generally reduced to the numerical solution of a transcendental equation. In this paper, we apply a new method, based on Gaussian quadrature rules, for the solution of transcendental equations to the determination of critical loads in buckling problems. Two such problems of practical interest are completely solved for the illustration of the method and numerical results are presented. The main advantages of the present method are its simplicity and the availability of closed-form formulae for the critical loads, from which the numerical results are obtained by using Gaussian quadrature rules. A comparison between the present method and the method of \textit{E. E. Burniston} and \textit{C. E. Siewert} [e.g. SIAM J. Appl. Math. 24, 460-466 (1973; Zbl 0271.33002) and J. Math. Anal. Appl. 43, 626-632 (1973; Zbl 0271.33003)] is also made.