Nonlinear dynamic analysis of elastic frames

Abstract

A co-rotational formulation and numerical procedure for the dynamic analysis of in-plane frames is presented. The nodal coordinates, incremental displacements and rotations, velocities, acceler-ations, and equations of motion of the system are defined in terms of fixed global coordinates, whereas the total strains in the beam element are measured in an element coordinate system which rotates and translates with the element but does not deform with the element. The element equations are constructed using the small deflection beam theory with the inclusion of the effect of axial force first in the element coordinate system, and then transformed to the global coordinate system by standard procedure. An incremental-iterative method based on the Newmark direct integration method and the Newton-Raphson method is used here for the solution of the nonlinear dynamic equilibrium equations. To improve convergence properties of the equilibrium iterations, the previous convergent axial force is used to calculate the geometric stiffness matrix. Numerical examples show the accuracy and efficiency of the present method.