[1]何芳社,悦 峰.横观各向同性双参数地基上矩形薄板的弯曲[J].西安建筑科技大学学报(自然科学版),2018,50(05):755-0760.[doi:10.15986/j.1006-7930.2018.05.021]
　HE Fangshe,YUE Feng.The bending of rectangular thin plate on the transversely isotropic two-parameter elastic foundation[J].J. Xi’an Univ. of Arch. & Tech.(Natural Science Edition),2018,50(05):755-0760.[doi:10.15986/j.1006-7930.2018.05.021]
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横观各向同性双参数地基上矩形薄板的弯曲()
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西安建筑科技大学学报（自然科学版）[ISSN:1006-7930/CN:61-1295/TU]

卷:
50
期数:
2018年05期
页码:
755-0760
栏目:
出版日期:
2018-10-28

文章信息/Info

Title:
The bending of rectangular thin plate on the transversely isotropic two-parameter elastic foundation
文章编号:
1006-7930(2018)05-
作者:
何芳社; 悦 峰
(西安建筑科技大学 理学院,西安 710055)
Author(s):
HE Fangshe;  YUE Feng
(School of Science, Xian University of Architecture and Technology, Xian 710055 , China)
关键词:
横观各向同性; 双参数地基; 最小势能原理; 矩形薄板; 里兹法
Keywords:
transversely isotropic;  two-parameter foundation;  the principle of minimal potential energy;  rectangular thin plate;  Ritz method
分类号:
TU348
DOI:
10.15986/j.1006-7930.2018.05.021
文献标志码:
A
摘要:
弹性地基板是建筑工程中常见的构件，对其进行分析具有重要意义。对于工程中的大量由沉积作用形成的天然地基和分层碾压填筑而成的人工地基，采用横观各向同性地基模型更接近工程实际地基。本文将地基—板作为一个整体系统，利用最小势能原理，经过变分运算，推导建立了横观各向同性双参数弹性地基上矩形薄板弯曲的控制方程及其相应的边界条件。然后选取合理的挠度试函数，采用里兹法，对受横向荷载作用的四边自由矩形薄板进行了数值分析。计算表明：通过与其他文献的结果对比，两者吻合良好。所用理论在研究地基板的相互作用中具有普适性，为横观各向同性双参数弹性地基的应用奠定了基础。
Abstract:
?The plate on elastic foundation is the common structural component , so it is very important to have a detailed analysis about this plate for researchers. The Transversely isotropic body will be more reasonable due to the experimental evidence, for the large number of natural foundations formed by sedimentation and artificial foundations formed by stratifying and roll ing in the project. The article completed the basic theory of plates by the principle of minimal potential energy and the variational calculus with the foundation and the plate as a whole system. The governing equations and the boundary conditions of plates on the bi-parameter foundations are given. And the displacement function for meeting the correct boundary condition is selected. Ritz method is used to analyze the bending of plate, giving the deflection for the bending of rectangular plate with four free edges under lateral loads. In the end, the numerical calculations are accomplished. And compared to other literature, their results are coincident. The theory has some universality for analyzing the interaction between plate and elastic foundation. The method lays the foundation for the application of the transversely isotropic two-parameter elastic foundation.

参考文献/References:

References

[1] VALLABHAN C V G, DAS Y C. Modified Vlasov model for beams on elastic foundations[J]. Journal of Geotechnical Geoenvironmental Engineering, 1991,117(6):956-966.

[2] YANG T Y. A finite-element analysis of plates on a two-parameter foundation model[J]. Comput. Struct., 1972,(2):593-614.

[3] JONES R, XENOPHONTOS J. The Vlasov foundation model[J].International journal of mechanical sciences, 1977,19(6):317-323.

[4] NOGAMI T, LAM Y C. Two-parameter layer model for analysis of slab on elastic foundation[J]. J. Engrg. Mech., 1987,113(9):1279-1291.

[5] CELEP Z. Rectangular plates resting on tensionless elastic foundation[J]. Journal of Engineering Mechanics, 198 8,114(12):2083-2092.

[6] 王克林, 黄义. 弹性地基上四边自由矩形板[J]. 计算结构力学及其应用, 1985,2(2)47-58.

WANG Kelin, HUANG Yi. Rectangular plates with four free edges on elastic foundations[J]. Computational Structural Mechanics and Applications, 1985,2(2):47-58.

[7] 张福范, 黄晓梅. 弹性地基上的自由矩形板[J]. 应用数学和力学, 1984,5(3):345-353.

ZHANG Fufan, HUANG Xiaomei. A free rectangular plate on the elastic foundation[J]. Applied Mathematics and Mechanics, 1984,5(3):345-353.

[8] 陈叔陶. 弹性地基上的自由边矩形板[J]. 力学学报, 1960,04(1):23-35.

CHEN Shutao. Rectangular plates with free edges on elastic foundations[J]. Acta. Mechanican Sinica, 1960,04(1):23-35.

[9] 阎红梅, 崔维成, 刘应中. 弹性地基上四边自由矩形板问题的一种新型挠度函数[J]. 船舶力学, 2003,7(2):61-63.

YAN Hongmei, CUI Weicheng, LIU Yingzhong. A new deflction fuction for the problem of a rectangular plate on elastic foundation with four free edges[J]. Journal of Ship Mechanics, 2003,7(2):61-63.

[10] VLASOV V Z, LEONTIEV N N. Beams, plates and shells on elastic foundations[M]. Israel Program for Scientific Translations,Jerusalem,Israel, 1966.

[11] VALLABHAN C V G, DAS Y C. Refined model for analysis of plates on elastic foundations[J]. J. Engrg. Mech.,ASCE, 1991,117(12):2830-2843.

[12] VALLABHAN C V G, DAS Y C. Parametric study of beams on elastic foundations[J]. Journal Eng. Mech., 1988,114:2072-2082.

[13] 张福范. 弹性薄板[M]. 北京：科学出版社, 1984.

ZHANG Fufan. Elastic thin plate[M]. Beijing:Science Press, 1984.

[14] 乔世范, 顿志林, 刘宝琛.横观各向同性地基模型的理论分析及其应用[J]. 岩土工程技术 , 2003,(4):213-219.

QIAO Shifan, DUN Zhilin, LIU Baochen. The study on constitutive equations of a transversely isotropic foundation and its application[J]. Geotechnical Engineering Technique, 2003,(4):213-219.

[15] 李婕, 张学民, 顿志林等.横观各向同性地基空间问题的位移函数解法[J]. 岩土工程学报, 2007,29(1):137-142.

LI Jie, ZHANG Xuemin, DUN Zhilin, et al. Displacement function method of space problems for transversely isotropic foundation[J]. Chinese Journal of Geotechnical Engineering, 2007,29(1):137-142.

[16] 何芳社, 黄义, 郭雅云. 双参数弹性地基板的动力问题[J]. 西安建筑科技大学学报 (自然科学版), 2006,38(1):130-134.

HE Fangshe, HUANG Yi, GUO Yayun.The dynamic problem of plates on the bi-parameter elastic foundations[J]. J. Xi’an Univ. Of Arch. & Tech.(Natural Science Edition), 2006,38(1):130-134.

[17] SELVADURAI A P S. Elastic analysis of soil-foundation
interaction[M]. London: Elsevier Scientific Publishing Co., 1979.

[18] 生跃, 黄义. 双参数弹性地基上自由矩形板[J]. 应用数学和力学, 1987,8(4):317-329.

SHENG Yao, HUANG Yi. A free rectangular plate on the two-parameter elastic foundation [J]. Applied Mathematics and Mechanics, 1987,8(4):317-329.

[19] 黄义, 何芳社. 弹性地基上的梁、板、壳[M]. 北京 :科学出版社, 2005.

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备注/Memo

备注/Memo:
收稿日期：2017-05-09 修改稿日期：2018-08-06
基金项目：国家自然科学基金项目（51178387）
第一作者简介：何芳社(1962－)，男，硕士生导师，主要研究结构与复杂介质的相互作用．E-mail: xymmyf0927@sina.com
更新日期/Last Update: 2018-11-22