Study on the Frame Structure Modeling of the Beam Element Formulated by Absolute Nodal Coordinate Approach

Abstract

Accurate seismic analysis of large deformable moving structures is still unsolved problems in the field of earthquake engineering. In order to analyze these problems, the nonlinear finite element method formulated by the absolute nodal coordinate approach is noticed. Because, this formulation has several advantages on mass matrix, elastic forces and damping forces in the case of large displacement problems. But, it has not been fully studied to build a frame structure model by using the beam element in the absolute nodal coordinate formulation. In this paper, we propose the connecting method of the beam element formulated by the absolute nodal coordinate. The coordinate transformation matrix of this element is introduced into the frame structure. This beam element has the characteristic that the mass matrix and bending stiffness matrix are constant even if in the case of large displacement problems, and this characteristic is being kept after the transformation. In order to verify the proposed method, we show the numerical simulation results of frame structures for a static problem and a vibration problem.