Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory
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APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-020-2679-7
Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory∗ Wenjie FENG1,2,† , Zhen YAN1,3 , Ji LIN4 , C. Z. ZHANG3 1. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China; 2. Hebei Key Laboratory of Smart Material and Structure Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China; 3. Department of Civil Engineering, University of Siegen, Siegen D-57068, Germany; 4. China State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, International Center for Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 211100, China (Received May 30, 2020 / Revised Aug. 12, 2020) Abstract Based on the nonlocal theory and Mindlin plate theory, the governing equations (i.e., a system of partial differential equations (PDEs) for bending problem) of magnetoelectroelastic (MEE) nanoplates resting on the Pasternak elastic foundation are first derived by the variational principle. The polynomial particular solutions corresponding to the established model are then obtained and further employed as basis functions with the method of particular solutions (MPS) to solve the governing equations numerically. It is confirmed that for the present bending model, the new solution strategy possesses more general applicability and superior flexibility in the selection of collocation points. Finally, the effects of different boundary conditions, applied loads, and geometrical shapes on the bending properties of MEE nanoplates are evaluated by using the developed method. Some important conclusions are drawn, which should be helpful for the design and applications of electromagnetic nanoplate structures. Key words magnetoelectroelastic (MEE) nanoplate bending, nonlocal theory, Mindlin plate theory, method of particular solution (MPS), polynomial basis function Chinese Library Classification O242 2010 Mathematics Subject Classification
11C08, 30G25, 32W50, 35R15, 65N12
Nomenclature l, b, h,
length, width, and thickness of magnetoelectroelastic (MEE) nanoplate;
Ei , Hi ,
components of electric and magnetic fields;
∗ Citation: FENG, W. J., YAN, Z., LIN, J., and ZHANG, C. Z. Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory. Applied Mathematics and Mechanics (English Edition) (2020) https://doi.org/10.1007/s10483-020-2679-7 † Corresponding author, E-mail: [email protected] Project supported by the National Natural Science Foundation of China (Nos. 11872257 and 11572358) and the German Research Foundation (No. ZH 15/14-1) c
The Author(s) 2020
2
Wenjie FENG, Zhen YAN, Ji LIN, and C. Z. ZHANG
q,
transverse distributed mechanical load; φ, ϕ, electric and magnetic potentials; Di , Bi , components of electric displacements and magnetic inductions; w, ψx , ψy , deflection, rotations of the normal
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