Dynamic Analysis of Functionally Graded Fiber Reinforced Cylinders under an Impact Load by a Three Dimensional Mesh Free Approach

Abstract

In this paper three dimensional (3D) moving least squares (MLS) shape functions in cylindrical coordinates are developed and used for the dynamic analysis of functionally graded fiber reinforced cylinders via a mesh free method. The solution is based on the weak form of the equations of motion and the MLS approximation is used to construct the 3D shape functions in cylindrical coordinates. Essential boundary conditions are imposed using transformation method. Two kinds of variations of the mechanical properties in the thickness direction are considered. In the first model the fibers are assumed to be oriented in the axial direction and the volume fractions of the fibers and matrix are changed continuously according to the power-law distribution. In the second model the volume fractions of constituents are constant and the fibers orientation is changed continuously in the thickness direction according to the power-law distribution. The resulted set of differential equations is solved by the Wilson method. Effects of fiber volume fraction, geometry of cylinder, fiber orientation and boundary conditions on dynamic response of these cylinders are investigated by the proposed model.