Non-linear static analysis of a hyperelastic plate with geometrical imperfection using meshless radial basis functions

In this research, static analysis of a square hyperelastic plate with initial geometry imperfection is investigated. The non-linear strains are defined using the right Cauchy-Green Tensor, and the neo-Hookean strain energy function is utilized to propose the hyperelastic plate's non-linear behaviour. The strong form of the hyperelastic plate's governing equations with initial imperfection is derived for the first time using Euler-Lagrange equations. Meshless collocation method based on radial basis function with thin-plate basis function is used to discretizing the governing equations. Eventually, the non-linear system of equations is solved using the arc-length continuation algorithm. The meshless collocation method (MCM) results are compared to those of the Abaqus finite element method (FEM). The results show that the maximum difference between MCM and FEM is ۴.۱۶% for clamped and ۶.۲۴% for simply supported boundary conditions