Analytical solution of a cantilever functionally graded beam |
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| Affiliation: | 1. Department of Mechanics, Tianjin University, Tianjin, 300072, China;2. School of Mechanical and Automotive Engineering, Anhui Polytechnic University, Wuhu, 241000, China;3. Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin, 300072, China;1. Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Italy;2. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;3. Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, Egypt;1. College of Civil Engineering, Hebei University of Engineering, Handan 056038, PR China;2. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, PR China;3. Xingtai University, Xingtai 054001, PR China;1. Faculty of Engineering and Environment, Northumbria University, Newcastle upon Tyne NE1 8ST, UK;2. School of Civil and Environmental Engineering, The University of New South Wales, NSW 2052, Australia;3. Faculty of Civil Engineering and Applied Mechanics, University of Technical Education Ho Chi Minh City, 1 Vo Van Ngan Street, Thu Duc District, Ho Chi Minh City, Viet Nam;4. Department of Architectural Engineering, Sejong University, 98 Kunja Dong, Kwangjin Ku, Seoul 143-747, Republic of Korea |
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| Abstract: | The problem of a cantilever functionally graded beam subjected to different loads is studied. In terms of Airy stress function a general two-dimensional solution is presented for a cantilever functionally graded beam, assuming that all the elastic moduli of the material have the same variations along the beam-thickness direction. Explicit expressions of analytical solutions to some specific examples under different boundary conditions are obtained to demonstrate the usefulness of the proposed general solution technique. This solution will be useful in analyzing functionally graded beam with arbitrary variations of material properties and it can serve as a basis for establishing simplified functionally graded beam theories. |
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