Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories |
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| Affiliation: | 1. Department of Architecture, University of Cukurova, 01330, Balcali, Adana, Turkey;2. Department of Civil Engineering, University of Cukurova, 01330, Balcali, Adana, Turkey;1. Department of Engineering Mechanics, Hohai University, Nanjing 211100, PR China;2. Institute for Research and Development, Duy Tan University, Da Nang, Vietnam;3. Department of Civil and Environmental Engineering, Tokyo Institute of Technology, 2-12-1-W8-22, Ookayama, Meguro-ku, Tokyo 152-8552, Japan;1. Department of Computational Engineering, Vietnamese-German University, Binh Duong New City, Viet Nam;2. Department of Architectural Engineering, Sejong University, 98 Kunja Dong, Kwangjin Ku, Seoul, 143-747, South Korea;3. Department of Mechanical Engineering, University of New Orleans, Lakefront, New Orleans, LA 70148, USA;4. Center for Interdisciplinary Research in Technology (CIRTech), Ho Chi Minh City University of Technology (HUTECH), Viet Nam;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;1. Faculty of Mechanical Engineering, University of Engineering and Technology, Jr. Medrano Silva 165, Barranco, Lima, Peru;2. Faculty of Mechanical Engineering, National University of Engineering, Av. Túpac Amaru 210, Rimac, Lima, Peru |
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| Abstract: | In this study, two dimensional (2D) and quasi three-dimensional (quasi-3D) shear deformation theories are presented for static and free vibration analysis of single-layer functionally graded (FG) plates using a new hyperbolic shape function. The material of the plate is inhomogeneous and the material properties assumed to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori–Tanaka model, in terms of the volume fractions of the constituents. The fundamental governing equations which take into account the effects of both transverse shear and normal stresses are derived through the Hamilton's principle. The closed form solutions are obtained by using Navier technique and then fundamental frequencies are found by solving the results of eigenvalue problems. In-plane stress components have been obtained by the constitutive equations of composite plates. The transverse stress components have been obtained by integrating the three-dimensional stress equilibrium equations in the thickness direction of the plate. The accuracy of the present method is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature. |
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| Keywords: | A Layered structures B Mechanical properties C Analytical modeling D Numerical analysis |
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