Two-dimensional complete rational analysis of functionally graded beams within symplectic framework |
| |
Authors: | Li Zhao Wei-qiu Chen Chao-feng Lü |
| |
Institution: | 1. Department of Civil Engineering, Ningbo University of Technology, Ningbo 315016,Zhejiang Province, P. R. China 2. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, P. R. China 3. Department of Civil Engineering, Zhejiang University, Hangzhou 310058, P. R. China |
| |
Abstract: | Exact solutions for generally supported functionally graded plane beams are given within the framework of symplectic elasticity. The Young’s modulus is assumed to exponentially vary along the longitudinal direction while the Poisson’s ratio remains constant. The state equation with a shift-Hamiltonian operator matrix has been established in the previous work, which is limited to the Saint-Venant solution. Here, a complete rational analysis of the displacement and stress distributions in the beam is presented by exploring the eigensolutions that are usually covered up by the Saint-Venant principle. These solutions play a significant role in the local behavior of materials that is usually ignored in the conventional elasticity methods but possibly crucial to the material/structure failures. The analysis makes full use of the symplectic orthogonality of the eigensolutions. Two illustrative examples are presented to compare the displacement and stress results with those for homogenous materials, demonstrating the effects of material inhomogeneity. |
| |
Keywords: | functionally graded material (FGM) exact solution expansion of eigenfunction symplectic elasticity |
本文献已被 CNKI 维普 万方数据 SpringerLink 等数据库收录! |
|