回転成分の多項式補間を用いたANCFせん断はりの弾性力の計算法

抄録

The absolute nodal coordinate formulation (ANCF) has been widely used for nonlinear dynamic problems in multibody systems with large rotation and deformation. A distinctive feature of the ANCF is that the mass matrix is constant and symmetric by employing absolute nodal coordinates and global slopes as the element nodal coordinates. On the other hand, a mathematical description of elastic forces is one of significant topics in implementation of the ANCF due to the description with highly nonlinear terms from the standpoint of computational performance. This study focuses on the elastic forces for the ANCF shear deformable beam element utilizing strain measures based on the geometrically exact beam. Due to the mathematical descriptions of the rotation in the strain measures, numerical (spatial) integration techniques, such as the Gaussian quadrature rules, are implemented every time step for evaluating the elastic forces. The present method introduces interporlation of the rotation by polynomials with discrete rotation parameters at nodes on each element. It could contribute to reduction of computational costs regarding the evaluation of elastic forces. In addition, this study employs an augmented formulation technique based on the Lagrange’s equation for constrained systems in order to introduce the discrete rotation parameters as redundant degrees of freedom.