局所回転自由度を用いたANCFせん断はりの数値積分法

抄録

The absolute nodal coordinate formulation (ANCF) has been applied to a problem for large rotation and deformation in multibody system. A distinctive feature of the ANCF is to employ absolute nodal coordinates and global slopes as the element nodal coordinates. Accordingly, it gives a constant and symmetric mass matrix. On the other hand, elastic forces, which are gieven by highly nonlinear terms, affects computational performance. Therefore, one of significant topics in the implementation of the ANCF is to derive mathematical descriptions of the elastic forces which can be calculated efficiently. This study focuses on the elastic forces for the ANCF shear deformable element based on a crosssectional coordinates system approach and a mixed interpolation technique for the strain components of the beam element. Then, in order to improve a mathematical treatment of the rotation for the cross section, the present method introduces an augmented formulation technique with algebraic constraints regarding the definition of the shear angles at nodes of discretized elements defined as the functions of nodal coordinate. The equations of motions of this constrained system are derived by the Lagrange's equation for constrained systems. As the result, equations of motion are given by the differential algebraic equations (DAEs) with index-1. Then, outlines of numerical procedures for simple explicit and implicit schemes are introduced. Moreover, a reduction techniques for the derived DAEs with index-1 is presented. In order to calculate the DAEs formulated by the present method, this study employed a numerical integration technique incorporating the mid-point schemes with the Newton-Raphson iterative procedures. After that, in order to evaluate the proposed method,it is applied to the large deformation problem in the plane case.