The Large Deformation Analysis of Thin Beam Using Absolute Nodal Coordinate Formulation and Newmark Integration Method

Nowadays, large deformation analysis of thin beam has become a research hotpot of the computational mechanics when the high performance lightweight materials are used in lots of engineering structure. Absolute nodal coordinate formulation (ANCF) is a powerful method to calculate the dynamic response of the large deformation beams. In this study, the modeling of thin beams with large deformations and large motions is conducted based on ANCF, and the dynamics equations of system are solved using Newmark integration method. First, the ANCF low-order elements utilize Green strains and exact curvatures to describe the deformation of slender beams. The inertia forces, elastic forces, and generalized moment matrices are derived in detail. The dynamics equations for thin bodies with large motions and large deformations are established. Then, following Newmark's integration method, the dynamic equations of motion are discretized into algebraic equations for solution. Through this modeling and computational approach, it is possible to effectively perform dynamic analysis of flexible bodies with large motions and large deformations, thereby improving computational efficiency while avoiding shear locking. Numerical examples have been conducted to validate the accuracy of the dynamic response. The proposed approach is a powerful technique in the dynamic analysis of beams with large deformations.