Dynamic characteristics analysis of hyperelastic flexible beam based on MLS-ANCF

Due to the dual characteristics of material nonlinearity and geometric nonlinearity exhibited by silicone rubber-like hyperelastic incompressible materials, the dynamic problems involving such materials become complex and challenging. In previous research, the Absolute Nodal Coordinate Formulation (ANCF) has demonstrated its effectiveness in addressing geometric nonlinearities during large deformations. However, ANCF tends to suffer from mesh distortion and configuration distortion issues. On the other hand, the Moving Least Squares Method (MLS) from meshfree methods uses a substantial number of nodes when constructing shape functions, which effectively improves mesh distortion problems in finite element methods when dealing with large deformations. Therefore, this paper employs Hermite-type MLS approximation functions to construct three-dimensional interpolation shape functions that replace the finite element shape function used in the traditional ANCF, thus creating an MLS-ANCF(Absolute node coordinate method based on the moving least square method) approach. Additionally, three nonlinear material models are introduced to tackle the material nonlinearity of hyperelastic beams. Moreover, Lagrange multipliers and Hamilton's principle are used to derive the static and dynamic equations for the hyperelastic beams system. To further validate the correctness of the MLS-ANCF method, this study first compares its results with those obtained from commercial software ABAQUS and static equilibrium experiments, thereby demonstrating the accuracy and effectiveness of MLS-ANCF; Next, dynamic analysis of a cantilevered silicone rubber beam under gravity alone is conducted to show the advantages of MLS-ANCF over other methods and effectively solve the issue of geometric configuration distortion caused by meshing; Furthermore, this paper also investigates the influencing factor of dynamics analysis, such as the incompressibility constant k, weight function, damping coefficient, number of elements, and different nonlinear material models; Ultimately, a comparison with experimental data reveals that MLS-ANCF outperforms conventional ANCF beam elements in terms of agreement with experimental data. This demonstrates the significant role of MLS-ANCF in analyzing the dynamic characteristics of nonlinear hyperelastic beams.