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Nonlocal and surface effects on the buckling behavior of functionally graded nanoplates: An isogeometric analysis
Institution:1. Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam;2. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Viet Nam;3. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;4. Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, Egypt;5. Laboratory Soete, Faculty of Engineering and Architecture, Ghent University, 9000 Ghent, Belgium;6. Department of Physical Therapy, Graduate Institute of Rehabilitation Science, China Medical University, 40402, Taiwan;7. Center for Interdisciplinary Research in Technology (CIRTech), Ho Chi Minh City University of Technology (HUTECH), 70000, Viet Nam;1. Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran;2. Department of Mechanical Engineering, Lahijan Branch, Islamic Azad University, P.O. Box 1616, Lahijan, Iran;1. School of Mechanical Engineering, Xiangtan University, Xiangtan, Hunan, 411105, PR China;2. Department of Engineering Mechanics, Hohai University, Nanjing, 211100, PR China;3. Institute for Research and Development, Duy Tan University, Da Nang City, Vietnam;4. Department of Civil and Environmental Engineering, Tokyo Institute of Technology, 2-12-1-W8-22, Ookayama, Meguro-ku, Tokyo, 152-8552, Japan;5. Graduate School of Engineering, Hiroshima University, 4-1, Kagamiyama 1-chome, Higashi-Hiroshima, 739-8527, Japan;6. Key Laboratory of Welding Robot and Application Technology of Hunan Province, Xiangtan University, Xiangtan, 411105, PR China
Abstract:The size-dependent static buckling responses of circular, elliptical and skew nanoplates made of functionally graded materials (FGMs) are investigated in this article based on an isogeometric model. The Eringen nonlocal continuum theory is implemented to capture nonlocal effects. According to the Gurtin–Murdoch surface elasticity theory, surface energy influences are also taken into account by the consideration of two thin surface layers at the top and bottom of nanoplate. The material properties vary in the thickness direction and are evaluated using the Mori–Tanaka homogenization scheme. The governing equations of buckled nanoplate are achieved by the minimum total potential energy principle. To perform the isogeometric analysis as a solution methodology, a novel matrix-vector form of formulation is presented. Numerical examples are given to study the effects of surface stress as well as other important parameters on the critical buckling loads of functionally graded nanoplates. It is found that the buckling configuration of nanoplates at small scales is significantly affected by the surface free energy.
Keywords:Critical buckling load  Nanoplate  Surface energy  Nonlocal continuum theory  Isogeometric analysis  Functionally graded material
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