Two-Dimensional Geometrically Nonlinear Hyperelastic Wave Propagation Analysis in FG Thick Hollow Cylinders using MLPG Method

The idea of using a meshless method for geometrically nonlinear problems due to its advantage of eliminating mesh distortion has been attracted many researchers. In this paper, the nonlinear wave propagation analysis in two-dimensional functionally graded (2D FG) thick hollow cylinders is studied using the meshless method. For this purpose, the meshless local Petrov-Galerkin (MLPG) method is developed for geometrically nonlinear dynamic analysis based on the total Lagrangian approach. The radial point interpolation, which possesses the delta function property, is used to construct the shape functions. Since the cylinder is assumed to have large deformations, the neo-Hookean hyperelastic model is employed for constitutive modeling of material. The incremental-iterative Newmark/Newton-Raphson technique is applied to iteratively solve the nonlinear equations of motion. The 2D FG cylinder is analyzed under uniform and non-uniform mechanical shock loading. The mechanical properties of the cylinder are assumed to vary nonlinearly through the radial and longitudinal directions which are simulated using two-dimensional volume fractions. Rayleigh damping is utilized to model energy dissipation in analyses. Numerical examples demonstrate the applicability and accuracy of the present approach in tracking the nonlinear wave propagation in two-dimensional FG thick hollow cylinders. The effects of grading patterns on the time history and wave propagation are discussed in detail.