Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory

doi:10.1007/s10483-020-2679-7

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (12): 1769-1786.doi: https://doi.org/10.1007/s10483-020-2679-7

Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory

Wenjie FENG^1,2, Zhen YAN^1,3, 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

收稿日期:2020-05-30 修回日期:2020-08-12 发布日期:2020-11-21
通讯作者: Wenjie FENG E-mail:wjfeng9999@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11872257 and 11572358) and the German Research Foundation (No. ZH 15/14-1)

Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory

Wenjie FENG^1,2, Zhen YAN^1,3, 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:2020-05-30 Revised:2020-08-12 Published:2020-11-21
Contact: Wenjie FENG E-mail:wjfeng9999@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11872257 and 11572358) and the German Research Foundation (No. ZH 15/14-1)

摘要/Abstract

摘要： 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. 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.

关键词: magnetoelectroelastic (MEE) nanoplate bending, nonlocal theory, Mindlin plate theory, method of particular solution (MPS), polynomial basis function

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. 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

中图分类号:

Wenjie FENG, Zhen YAN, Ji LIN, C. Z. ZHANG. Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(12): 1769-1786.

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Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory

Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory

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