Meshless method and experimental analysis of hyperelastic plates using Mooney-Rivlin strain energy function subjected to concentrated loading

Abstract

The purpose of this research is to investigate a strong-form meshless method for experimentally and numerically analyzing hyperelastic plates subjected to concentrated loading. The silicone hyperelastic plate was formulated utilizing Mooney-Rivlin strain energy function and Lagrangian strains. The displacements and Lagrangian strains of the plate are also calculated using the first-order shear deformation plate theory (FSDPT). The hyperelastic plate’s governing equations are deduced in strong form and analyzed using the logarithmic thin-plate spline radial basis function (LTPS-RBF) and the meshless method for the first-time. The nonlinear system of governing equations is solved using the arc-length continuation algorithm. In the meshless method, the concentrated loading is modeled using the Kronecker delta function in the expression of external work. A silicone plate is employed experimentally to evaluate the accuracy of the meshless method’s results. Furthermore, the finite element method is utilized to compare the contours obtained from the meshless method. Concentrated loading is considered at various points to validate the meshless methods and results from the experimental analysis. The most significant difference between the meshless method and the experimental results is less than 15%. The results indicate that the meshless method is highly accurate when analyzing hyperelastic plates subjected to concentrated loading.

Keywords:

• Hyperelastic plate
• meshless method
• radial basis function
• concentrated loading
• Kronecker delta function