A high-order theory for functionally graded axially symmetric cylindrical shells

Abstract

A high-order theory for functionally graded axially symmetric cylindrical shell based on expansion of the axially symmetric equations of elasticity for functionally graded materials into Legendre polynomials series has been developed. The axially symmetric equations of elasticity have been expanded into Legendre polynomials series in terms of a thickness coordinate. In the same way, functions that describe functionally graded relations has been also expanded. Thereby, all equations of elasticity including Hook’s law have been transformed to corresponding equations for coefficients of Legendre polynomials expansion. Then system of differential equations in terms of displacements and boundary conditions for the coefficients of Legendre polynomials expansion coefficients has been obtained. Cases of the first and second approximations have been considered in more details. For obtained boundary-value problems’ solution, a finite element has been used and numerical calculations have been done with COMSOL MULTIPHYSICS and MATLAB.