Flexural-Torsional Buckling of Cantilever Strip Beam-Columns with Linearly Varying Depth
Résumé
In this paper, one investigates the elastic flexural-torsional buckling of linearly tapered cantilever strip beam-columns acted by axial and transversal point loads applied at the tip. For prismatic and wedge-shaped members, the governing differential equation is integrated in closed form by means of confluent hypergeometric functions. For general tapered members (0 <(h(max)-h(min))/h(max)< 1), the solution to the boundary value problem is obtained in the form of a Frobenius' series, which is shown to converge in the interior of the domain and at the boundary if and only if 0 <(h(max)-h(min))/h(max)< 1/2. Therefore, for 1/2 <=(h(max)-h(min))/h(max)< 1 the Frobenius' series solution cannot be used to establish the characteristic equation for the cantilever beam-columns; the problem is then solved numerically by means of a collocation procedure. Some of the analytical solutions (buckling loads) were compared with the results of shell finite-element analyses and an excellent agreement was found in all cases, thus validating the mathematical model and confirming the correctness of the analytical results. The paper closes with a discussion on the convexity of the stability domain (in the load parameter space) and the accuracy of approximations based on Dunkerley-type theorems.