Abstract
A bi-harmonic stress function is constructed in this work. Ariy stress function methodology is used to obtain a set of analytical solutions for both ends fixed beams subjected to uniform load. The treatment for fixed-end boundary conditions is the same as that presented by Timoshenko and Goodier (1970). The solutions for propped cantilever beams and cantilever beams are also presented. All of the analytical plane-stress solutions can be obtained for a uniformly loaded isotropic beam with rectangular cross section under different types of classical boundary conditions.
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References
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Project (No. 10472102) supported by the National Natural Science Foundation of China
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Ding, Hj., De-jin, H. & Hui-ming, W. Analytical solution for fixed-end beam subjected to uniform load. J. Zheijang Univ.-Sci. A 6, 779–783 (2005). https://doi.org/10.1631/jzus.2005.A0779
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DOI: https://doi.org/10.1631/jzus.2005.A0779