Dynamic analysis of highly deformable bodies undergoing large rotations.

Abstract

A new approach in which element reference frames are placed at each element and deformed with the elements at all times is introduced with the purpose of computing large deformations in the dynamic analysis of highly deformable bodies. Since the deformation rate of a deformable body is generally not zero, the time derivatives of the motions of these element frames do not vanish. This co-rotational-time-dependent frame approach (named CRTD in this work) is applied to flexible rotating beams undergoing large deformations. A novel numerical scheme based on the Newmark method is presented for the fast integration of the nonlinear equations obtained from the CRTD approach, and mesh partitioning/recombining algorithms are investigated as a means of achieving computational efficiency. A flexible rotating plate undergoing large and fast rotation but small deformation is also examined. Numerical results, which include comparisons between the CRTD approach and other related approaches including nonlinear finite element approaches are presented. The effects of bending stiffness and density on the maximum deflection of highly deformable rotating beams, and differences between the rotating plate and rotating beam approaches are discussed.