Geometrically nonlinear elastodynamic analysis of hyper-elastic neo-Hooken FG cylinder subjected to shock loading using MLPG method

In this paper, geometrically nonlinear dynamic behavior of FG thick hollow cylinder under axisymmetric mechanical shock loading is investigated using meshless local Petrov–Galerkin (MLPG) method. The FG cylinder is assumed to be made of large deformable materials such as carbon-based polymers. Thus, the neo-Hooken hyper-elastic constitutive model is employed for the problem. The material properties of FG cylinder are varied as nonlinear function of radius in volume fraction forms. Radial point interpolation method is used to approximate the field variables in the local integral equations. Weak formulation on local sub-domains using a Heaviside test function is adopted to get the system of equations. It should be emphasized that the formulations are derived using total Lagrangian approach, which refers all variables to the initial configuration. The iterative Newmark/Newton–Raphson technique is used to solve the equilibrium equations. In order to verify the feasibility and accuracy of the presented method, a thick hollow FG cylinder is linearly analyzed and compared with published data. The dynamic behaviors of displacements and stresses are obtained using nonlinear analysis and discussed in details for various kinds of neo-Hooken FGMs.