双参数地基上四边自由矩形中厚板弯曲的有限积分变换精确解

胡波; 程超宇; 宜芳宇; 安东琦

doi:10.21656/1000-0887.450307

双参数地基上四边自由矩形中厚板弯曲的有限积分变换精确解

doi: 10.21656/1000-0887.450307

胡波^1,2,
程超宇³,
宜芳宇³,
安东琦^3, ,

1. 海南大学土木建筑工程学院，海口 570228;
2. 海南省交通工程建设局，海口 570208;
3. 大连理工大学力学与航空航天学院工业装备结构分析优化与CAE软件全国重点实验室，辽宁大连 116024

基金项目:

中央高校基本科研业务费（DUT25Z2712）

辽宁省杰出青年基金（2025JH6/101100005）

国家自然科学基金（12372067）

详细信息

作者简介:
胡波（1984—），男，高级工程师，硕士(E-mail: 99975161@qq.com);程超宇（2000—），女，硕士生(E-mail: cheng111@mail.dlut.edu.cn);;宜芳宇（2001—），女，硕士生(E-mail: yifangyu@mail.dlut.edu.cn);安东琦（1996—），男，助理教授(通讯作者. E-mail: adq96@mail.dlut.edu.cn).

通讯作者:
安东琦（1996—），男，助理教授(通讯作者. E-mail: adq96@mail.dlut.edu.cn).

中图分类号: O343
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- 文章访问数: 24
- HTML全文浏览量: 2
- PDF下载量: 3
- 被引次数: 0
出版历程
- 收稿日期: 2024-11-12
- 修回日期: 2025-01-20
- 网络出版日期: 2025-12-05

Exact Bending Solutions of Rectangular Moderately Thick Plates Resting on 2-Parameter Foundations With 4 Edges Free With the Finite Integral Transform Method

HU Bo^1,2,
CHENG Chaoyu³,
YI Fangyu³,
AN Dongqi^{3
, ,}

1. School of Civil Engineering and Architecture, Hainan University, Haikou 570228, P.R.China;
2. Hainan Provincial Transportation Engineering Construction Bureau, Haikou 570208, P.R.China;
3. State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds:

The National Science Foundation of China(12372067)

摘要

摘要: 弹性地基上的中厚板是一类重要的工程承载结构，其承载后弯曲行为的研究具有重要理论意义和实用价值.同时考虑反力系数和剪切模量的双参数弹性地基模型可以准确描述板和地基之间的相互作用，利用二维有限积分变换方法推导出了双参数地基上四边自由矩形中厚板弯曲问题的精确解.由于在求解过程中不需要预先人为地选取位移函数，而是直接从问题的基本方程出发，利用有限积分变换的数学方法求出满足四边自由边界条件的精确解，因此问题的求解更加严格.通过计算实例验证了有限积分变换得到的精确解的正确性，相应的参数分析可以为工程设计提供理论基础.
- 双参数地基 /
- 四边自由 /
- 中厚板 /
- 有限积分变换 /
- 精确解
Abstract: Moderately thick plates resting on elastic foundations are an important type of engineering load-bearing structure. The study of their bending behaviors under loads has significant theoretical significance and practical value. The 2-parameter elastic foundation with both the reaction constant and the shear modulus can accurately model the interaction between the plate and the foundation. With the 2D finite integral transform technique, the exact solutions of the displacements and internal forces of a moderately thick rectangular plate with all 4 edges free and supported by a 2-parameter elastic foundation, were derived. The displacement function was not manually selected in advance during the solution process, and instead, the exact solution satisfying the free boundary conditions on all 4 edges was derived directly from the fundamental equations for the problem with the finite integral transform method. The results show that, the exact solution is more rigorous. The accuracy of the exact solution derived from the finite integral transform was validated through computational examples. The presented parameter analysis can provide a theoretical basis for engineering design.
- 2-parameter foundation /
- 4 edges free /
- moderately thick plate /
- finite integral transform /
- exact solution

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参考文献(20)

张福范. 弹性薄板[M]. 北京: 科学出版社, 1984: 89-91. (ZHANG Fufan.Elastic Thin Plate[M]. Beijing: Science Press,1984: 89

-91. (in Chinese))

[2]曲庆璋. 弹性板理论[M]. 北京: 人民交通出版社, 2000.(QU Qingzhang.Elastic Plate Theory[M]. Beijing: China Communications Press, 2000. (in Chinese))

[3]HENWOOD D J, WHITEMAN J R, YETTRAM A L. Finite difference solution of a system of first-order partial differential equations[J].International Journal for Numerical Methods in Engineering,1981,17(9): 1385-1395.

[4]FALLAH A, AGHDAM M M, KARGARNOVIN M H. Free vibration analysis of moderately thick functionally graded plates on elastic foundation using the extended Kantorovich method[J].Archive of Applied Mechanics,2013,83(2): 177-191.

[5]JAHROMI H N, AGHDAM M M, FALLAH A. Free vibration analysis of Mindlin plates partially resting on Pasternak foundation[J].International Journal of Mechanical Sciences,2013,75: 1-7.

[6]HAN J B, LIEW K M. Numerical differential quadrature method for Reissner/Mindlin plates on two-parameter foundations[J].International Journal of Mechanical Sciences,1997,39(9): 977-989.

[7]NOBAKHTI S, AGHDAM M M. Static analysis of rectangular thick plates resting on two-parameter elastic boundary strips[J].European Journal of Mechanics A: Solids,2011,30(3): 442-448.

[8]HENWOOD D J, WHITEMAN J R, YETTRAM A L. Fourier series solution for a rectangular thick plate with free edges on an elastic foundation[J].International Journal for Numerical Methods in Engineering,1982,18(12): 1801-1820.

[9]YOO H H, PIERRE C. Modal characteristic of a rotating rectangular cantilever plate[J].Journal of Sound and Vibration,2003,259(1): 81-96.

[10]石小平, 姚祖康. 弹性地基上四边自由矩形厚板的解[J]. 河北工学院学报, 1985,14(1): 54-72.(SHI Xiaoping, YAO Zukang. The solution of a rectangular thick plate with free edges on an elastic foundation[J].Journal of Hebei University of Technology,1985,14(1): 54-72. (in Chinese))

[11]TIMOSHENKO S, WOINOWSKY-KRIEGER S.Theory of Plates and Shells[M]. 2nd ed. New York: McGraw-Hill Inc, 1959: 126-130.

[12]QIAO J, HOU G, LIU J. Analytical solutions for the model of moderately thick plates by symplectic elasticity approach[J].AIMS Mathematics,2023,8(9): 20731-20754.

[13]李锐, 田宇, 郑新然, 等. 求解弹性地基上自由矩形中厚板弯曲问题的辛-叠加方法[J]. 应用数学和力学, 2018,39(8): 875-891.(LI Rui, TIAN Yu, ZHENG Xinran, et al. A symplectic superposition method for bending problems of free-edge rectangular thick plates resting on elastic foundations[J].Applied Mathematics and Mechanics,2018,39(8): 875-891. (in Chinese))

[14]丁凯文, 高芳清, 郑双星. 弹性地基上任意边界条件矩形中厚板的振动特性分析[J]. 四川轻化工大学学报(自然科学版), 2021,34(3): 69-76.(DING Kaiwen, GAO Fangqing, ZHENG Shuangxing. Vibration behavior analysis of rectangular thick plates with arbitrary boundary conditions on elastic foundation[J].Journal of Sichuan University of Science & Engineering (Natural Science Edition), 2021,34(3): 69-76. (in Chinese))

[15]LI H, PANG F, WANG X, et al. Benchmark solution for free vibration of moderately thick functionally graded sandwich sector plates on two-parameter elastic foundation with general boundary conditions[J].Shock and Vibration,2017,2017: 4018629.

[16]夏平, 龙述尧, 胡玮军. 弹性地基中厚板弯曲问题的无网格LRPIM分析[J]. 岩土力学, 2010,31(2): 656-660.(XIA Ping, LONG Shuyao, HU Weijun. Bending analysis of moderately thick plates on elastic foundation by meshless local radial point interpolation method[J].Rock and Soil Mechanics,2010,31(2): 656-660. (in Chinese))

[17]SNEDDON I H.The Use of Integral Transforms[M]. New York: McGraw-Hill Inc, 1972: 169-182.

[18]钟阳, 孙爱民, 周福霖, 等. 弹性地基上四边自由矩形薄板分析的有限积分变换法[J]. 岩土工程学报, 2006,28(11): 2019-2022.(ZHONG Yang, SUN Aimin, ZHOU Fulin, et al. Analytical solution for rectangular thin plate on elastic foundation with four edges free by finite cosine integral transform method[J].Chinese Journal of Geotechnical Engineering,2006,28(11): 2019-2022. (in Chinese))

[19]TIANB, LI R, ZHONG Y. Integral transform solutions to the bending problems of moderately thick rectangular plates with all edges free resting on elastic foundations[J].Applied Mathematical Modelling,2015,39(1): 128-136.

[20]郑健龙, 张起森. 刚性路面设计理论新探[J]. 长沙交通学院学报, 1989,5(2): 55-64.(ZHENG Jianlong, ZHANG Qisen. A new approach for the design theories of the rigid pavements[J].Journal of Changsha Communications University,1989,5(2): 55-64. (in Chinese))

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