Nonconservative Stability Problems via Generalized Differential Quadrature Method

In this paper, the generalized differential quadrature (GDQ) method is applied to solve classical and nonclassical nonconservative stability problems. Various cantilever beams subjected to slope-dependent forces are considered. First, the governing differential equation for a nonuniform column subjected to an arbitrary distribution of compressive subtangential follower forces is obtained. The effect of the variability of the mechanical properties along the beam length is also considered. Then, the application of the GDQ procedure leads to a discrete system of algebraic equations from which the system critical loads can be obtained by solving an associated eigenvalue problem. A parametrical study for different levels of nonconservativeness of the applied load is carried out for some classical benchmark cases such as Beck’s, Leipholz’s and Hauger’s column problems. Finally, applications to geometrically and mechanically tapered beams subjected to nonpotential subtangential follower forces are investigated as nonclassical cases. It has been proved that the method can efficiently solve structural nonconservative elastic problems and, more in general, problems governed by a nonsymmetric system of algebraic equations.