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Structural Engineering and Mechanics Volume 53, Number 3, February10 2015 , pages 411-427 DOI: https://doi.org/10.12989/sem.2015.53.3.411 |
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The refined theory of 2D quasicrystal deep beams based on elasticity of quasicrystals |
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Yang Gao, Lian-Ying Yu, Lian-Zhi Yang and Liang-Liang Zhang
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| Abstract | ||
| Based on linear elastic theory of quasicrystals, various equations and solutions for quasicrystal beams are deduced systematically and directly from plane problem of two-dimensional quasicrystals. Without employing ad hoc stress or deformation assumptions, the refined theory of beams is explicitly established from the general solution of quasicrystals and the Lur\'e symbolic method. In the case of homogeneous boundary conditions, the exact equations and exact solutions for beams are derived, which consist of the fourth-order part and transcendental part. In the case of non-homogeneous boundary conditions, the exact governing differential equations and solutions under normal loadings only and shear loadings only are derived directly from the refined beam theory, respectively. In two illustrative examples of quasicrystal beams, it is shown that the exact or accurate analytical solutions can be obtained in use of the refined theory. | ||
| Key Words | ||
| deep beams; two-dimensional quasicrystals; the refined theory; general solution | ||
| Address | ||
| Yang Gao, Lian-Ying Yu: College of Science, China Agricultural University, Beijing 100083, P.R. China Lian-Zhi Yang, Liang-Liang Zhang: College of Science, China Agricultural University, Beijing 100083, P.R. China; College of Engineering, China Agricultural University, Beijing 100083, P.R. China | ||