Nonlinear dynamic analysis of frame structures

Abstract

A geometrically nonlinear dynamic analysis method is presented for frames which may be subjected to finite rotations in three-dimensional space. The proposed method is based on the static geometrically nonlinear analysis method reported by Yoshida et al., in which the governing incremental equilibrium equation is represented by the coordinates after the deformation themselves rather than conventional displacements. The governing dynamic equilibrium equation for each element is obtained from the static equation by adding the inertia term. In the solution procedure, a modified Steffensen's iteration process is introduced and combined with the two-step approximation and iterative correction solution procedure developed for static analysis. A numerical example of a curved cantilever beam under lateral loads indicates the effectiveness of the proposed method in cases with three-dimensional finite rotations. Forced vibration analyses of a two-hinged shallow arch are conducted under centrally concentrated loading with several loading amplitudes. The resulting dynamic buckling load is compared with that given by Gregory and Plaut in 1982, who used Galerkin method, and shows good agreement.