Reissner 混合變分原理有限圓柱層殼元素法於功能性梯度材料中空圓柱殼承受軸、圍壓組合載重之三維挫屈分析

Abstract

The unified formulations of finite cylindrical layer methods (FCLMs) based on the Reissner mixed variational theorem (RMVT) are developed for the three-dimensional (3D) linear buckling analysis of simply-supported, multilayered functionally graded material (FGM) circular hollow cylinders and laminated composite ones under pure axial compression, external pressure, and combined axial compression with external pressure. The material properties of the FGM layer are assumed to obey the power-law distributions of the volume fraction of the constituents through the thickness coordinate. In these formulations, the cylinder is divided into a number of finite cylindrical layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-surface variations of the primary variables of each individual layer, respectively, as well as the related order of each primary variable can be freely chosen, such as the layerwise linear, quadratic or cubic function distribution through the thickness coordinate. The accuracy and convergence of the RMVT-based FCLMs developed in this article are assessed by comparing their solutions with both the exact 3D and accurate two-dimensional (2D) solutions available in the literature. A parametric study for variations of the lowest critical load parameters with the material-property gradient index, and the load intensity, orthotropic, length-to-radius ratio, and radius-to-thickness ratios is carried out.