Absolute Nodal Coordinate法による梁の多体動力学解析に関する研究(有限変位・微小歪とした時の弾性力の導出)

抄録

There are three basic finite element formulations which are used in the multibody dynamics of flexible beams. These are the floating frame of reference approach, the incremental finite element approach and the large rotation vector approach. Recently, the absolute nodal coordinate formulation was proposed by A. A. Shabana et al. In this formulation, the mass matrix becomes constant, whereas the stiffness matrix becomes nonlinear function of time, even in case of linear elastic problems. In this paper, a new formulation to calculate the elastic forces is proposed. This formulation is based on the assumption that the deformations within each element remain very small. So, the expression of the resulting elastic force is simple, and this formulation is efficient for large rotation and medium deformation problems. Numerical examples are demonstrated for this formulation by using planar static buckling problems and flexible pendulum problems.