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Structural Engineering and Mechanics Volume 36, Number 6, December20 2010 , pages 669-678 DOI: https://doi.org/10.12989/sem.2010.36.6.669 |
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Analytical studies on stress concentration due to a rectangular small hole in thin plate under bending loads |
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Y. Yang, J.K. Liu and C.W. Cai
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| Abstract | ||
| In general means, the stress concentration problem of elastic plate with a rectangular hole can be investigated by numerical methods, and only approximative results are derived. This paper deduces an analytical study of the stress concentration due to a rectangular hole in an elastic plate under bending loads. Base on classical elasticity theory and FEM applying the U-transformation technique, the uncoupled governing equations with 3-DOF are established, and the analytical displacement solutions of the finite element equations are derived in series form or double integral form. Therefore, the stress concentration factor can then be discussed easily and conveniently. For the plate subjected to unidirectional bending loads, the non-conforming plate bending element with four nodes and 12-DOF is taken as examples to demonstrate the application of the proposed method. The inner force distribution is obtained. The solutions are adequate for the condition when the hole is far away from the edges and the thin plate subjected to any transverse loadings. | ||
| Key Words | ||
| U-transformation; stress concentration; rectangular hole; analytical solution; bending loads. | ||
| Address | ||
| Y. Yang: School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, 510640, P.R. China J.K. Liu: Department of Mechanics, Sun Yat-sen University, Guangzhou, 510275, P.R. China C.W. Cai: Department of Mechanics, Sun Yat-sen University, Guangzhou, 510275, P.R. China | ||