RMVT-based finite cylindrical prism methods for multilayered functionally graded circular hollow cylinders with various boundary conditions

Abstract

A unified formulation of finite cylindrical prism methods (FCPMs), based on the Reissner mixed variational theorem (RMVT), is developed for the three-dimensional (3D) analysis of multilayered functionally graded material (FGM) circular hollow cylinders with various boundary conditions and under mechanical loads. In this formulation, the cylinder is divided into a number of finite cylindrical prisms, in which the trigonometric functions and Lagrange polynomials are used to interpolate the circumferential direction and the axial–radial surface variations of the primary field variables of each individual prism, respectively. The material properties of each FGM layer are assumed to obey either a power-law distribution of the volume fractions of the constituents through the thickness coordinate or an exponential law distribution varying exponentially through this. The number of nodes of the nodal surface of each prism can be set at four for linear FCPMs, and eight and nine for quadratic ones. These quadratic FCPM solutions of simply supported, multilayered composite cylinders and sandwiched FGM ones obtained in this way are in excellent agreement with the exact 3D solutions available in the literature, and those solutions for the cylinders with combinations of clamped and simply-supported edge conditions closely agree with the solutions obtained using the ANSYS commercial software.