Study on the frame structure modeling of the beam element formulated by absolute nodal coordinate approach

Accurate seismic analyses of large deformable moving structures are 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 over the standard procedures on mass matrix, elastic forces and damping forces in the case of large displacement problems. But, it has not been fully studied to build frame structure models by using beam elements in the absolute nodal coordinate formulation. In this paper, we propose the connecting method of the beam elements 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 stiffiness 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 vibration problem and a large displacement problem.