An asymptotic meshless method for sandwich functionally graded circular hollow cylinders with various boundary conditions

Abstract

An asymptotic meshless method using the differential reproducing kernel interpolation and perturbation method is formulated for the three-dimensional bending analysis of sandwich functionally graded circular hollow cylinders and laminated composite ones with clamped and simply-supported edge conditions, in which the effective material properties of the functionally graded layer are evaluated using the Mori–Tanaka scheme. In the formulation, we perform the mathematical processes of nondimensionalization, asymptotic expansion and successive integration to obtain recurrent sets of governing equations for various order problems. Classical shell theory is derived as a first-order approximation of the three-dimensional theory of elasticity, and the governing equations for higher order problems retain the same differential operators as those of classical shell theory, although with different nonhomogeneous terms. Expanding the primary field variables of each order as the Fourier series functions in the circumferential direction, and interpolating these in the axial direction using the differential reproducing kernel interpolation, we can obtain the leading-order solutions of this analysis, and the higher order modifications can then be determined in a systematic manner. Some benchmark solutions for the bending analysis of sandwich functionally graded circular hollow cylinders and laminated composite ones subjected to mechanical loads are given to demonstrate the performance of the asymptotic meshless method.