Geometric Nonlinear Analysis for Frame Structures, Part 2: Dynamic Analysis

Abstract

Abstract:In this paper, the governing equation of dynamic analysis for frame structures is derived, with geometric nonlinearity considered. In the process of derivation, the updated Lagrange format is adopted and the elemental equilibrium equation is established at current configuration and then transformed into the initial configuration. To simplify the calculation of mass matrix, it is assumed that the beam's mass is only related with its rigid configuration. In other words, the mass effect due to the beam's deformation is ignored. Finally, a numerical example about dynamic buckling analysis of a circular arch subjected to a uniformly distributed step load is presented and discussed detailedly, demonstrating the validity and accuracy of the present method.