Analytical solution for a functionally graded beam with arbitrary graded material properties |
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| Affiliation: | 1. Department of Mechanics, Northeastern University, Shenyang 110819, China;2. Faculty of Aerospace Engineering, Shenyang Aerospace University, Shenyang 110136, China;1. Mechanical Design and Production Dept., Faculty of Engineering, Zagazig University, Egypt;2. Centre of Nanotechnology, Zagazig University, Egypt;3. Mechanical Engineering Dept., Faculty of Engineering, King Abdulaziz University, Saudi Arabia;1. School of Civil Engineering, the University of Queensland, St Lucia, Brisbane 4072, Australia;2. School of Engineering, RMIT University, PO Box 71, Bundoora, VIC 3083, Australia;1. Faculty of Civil Engineering and Applied Mechanics, Ho Chi Minh City University of Technology and Education, 1 Vo Van Ngan Street, Thu Duc District, Ho Chi Minh City, Viet Nam;2. Duy Tan University, Da Nang, Viet Nam;3. Faculty of Engineering and Environment, Northumbria University, Newcastle upon Tyne NE1 8ST, UK;4. Faculty of Civil Engineering, Thu Dau Mot University, 06 Tran Van On Street, Phu Hoa District, Thu Dau Mot City, Binh Duong Province, Viet Nam;5. Department of Architectural Engineering, Sejong University, 98 Kunja Dong, Kwangjin Ku, Seoul 143-747, Republic of Korea |
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| Abstract: | The plane stress problem of an orthotropic functionally graded beam with arbitrary graded material properties along the thickness direction is investigated by the displacement function approach for the first time. A general two-dimensional solution is obtained for a functionally graded beam subjected to normal and shear tractions of arbitrary form on the top and bottom surfaces and under various end boundary conditions. For isotropic case explicit solutions are given to some specific through-the-thickness variations of Young’s modulus such as exponential model, linear model and reciprocal model. The influence of different grade models on the stress and displacement fields are illustrated in numerical examples. These analytical solutions can serve as a basis for establishing simplified theories and evaluating numerical solutions of functionally graded beams. |
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