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
计量
- 文章访问数: 21
- HTML全文浏览量: 2
- PDF下载量: 1
- 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)

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