Geometrically nonlinear dynamic analysis of functionally graded thick hollow cylinders using total Lagrangian MLPG method

Abstract

In this article, geometrically nonlinear transient analysis based on the meshless local Petrov-Galerkin method (MLPG) is presented for functionally graded material thick hollow cylinders with infinite length subjected to a mechanical shock loading. The cylinder is assumed to be axisymmetric and in plane strain conditions. The mechanical properties of functionally graded cylinder are assumed to vary across the thickness. In MLPG analysis, the total Lagrangian formulation, radial base function, and Heaviside test function are used for approximation of displacement field in the weak form of the equation of motion. The system nonlinear equations are solved by Newmark finite difference and Newton-Raphson iteration methods. The time history of the radial displacement and stress for various values of the power law exponents, radii and thicknesses are investigated. The effects of different loading types and also the duration of loading on the dynamic behaviors of displacement and stress fields are obtained and discussed in details. Moreover, the obtained results from nonlinear analysis are compared with those obtained from linear analysis.