Hygrothermal deformation of orthotropic nanoplates based on the state-space concept |
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| Affiliation: | 1. Department of Mathematics and Statistics, Faculty of Science, King Faisal University, P.O. Box 400, Hofuf 31982, Saudi Arabia;2. Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt;1. Department of Chemical Engineering, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Jalan Genting Kelang, 53300 Setapak, Kuala Lumpur, Malaysia;2. Radiation Processing Technology Division, Malaysian Nuclear Agency, Bangi, 43000 Kajang, Selangor, Malaysia;3. Department of Mechanical Engineering, University of New Orleans, New Orleans, LA 70148, USA;4. Department of Polymer Engineering, Faculty of Chemical Engineering, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia;1. AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland;2. Delphi Technical Center Krakow, ul. Podgorki Tynieckie 2, 30-399 Krakow, Poland;1. Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education, Beijing Key Laboratory of Bio-Inspired Energy Materials and Devices, School of Chemistry and Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, PR China;2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, PR China;3. AFM, School of Aerospace, Tsinghua University, Beijing 100084, PR China;4. China Academy of Machinery of Science & Technology, Beijing 100044, PR China;1. Department of Molecular Science and Engineering, National Taipei University of Technology, Taipei 10608, Taiwan, Taiwan, ROC;2. Materials and Chemical Research Laboratories, Industrial Technology Research Institute, Hsinchu 30011, Taiwan, Taiwan, ROC |
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| Abstract: | This paper deals with the investigation of the effect of hygrothermal conditions on the bending of nanoplates using Levy type solution model employing the state-space concept. The nanoplates are assumed to be subjected to a hygrothermal environment. The two-unknown function plate theory is used to derive the governing differential equations on the basis of Eringen's nonlocal elasticity theory. The governing equations contain the small scale effect as well as hygrothermal and mechanical effects. These equations are converted into a set of first-order linear ordinary differential equations with constant coefficients. Analytical solution of bending response for nanoplates under combinations of simply supported, clamped and free boundary conditions is obtained. Comparison of the results with those being in the open literature is made. The influences played by small scale parameter, temperature rise, the degree of moisture concentration, boundary conditions, plate aspect ratio and side-to-thickness ratio are studied. |
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| Keywords: | A Nano-structures B Thermal properties C Analytical modeling Levy type solution |
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