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; CHENG Chaoyu; YI Fangyu; AN Dongqi

doi:10.21656/1000-0887.450307

Volume 46 Issue 11

Nov. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(11): 1367-1377

HU Bo, CHENG Chaoyu, YI Fangyu, AN Dongqi. Exact Bending Solutions of Rectangular Moderately Thick Plates Resting on 2-Parameter Foundations With 4 Edges Free With the Finite Integral Transform Method[J]. Applied Mathematics and Mechanics, 2025, 46(11): 1367-1377. doi: 10.21656/1000-0887.450307

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

doi: 10.21656/1000-0887.450307

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)

Received Date: 2024-11-12
Rev Recd Date: 2025-01-20

Available Online: 2025-12-05

Abstract

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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References(20)

References

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