[1]吴 晓,黄 翀,杨立军.非线性基础上拉压弹性模量不同矩形板的弯曲[J].西安建筑科技大学学报:自然科学版,2013,45(06):778-783.[doi:10.15986/j.1006-7930.2013.06.004]
　WU Xiao,HUANG Chong,YANG Li-jun.Bending of rectangular plate with difference elastic modulus intension and compression based on nonlinear foundation[J].J.Xi’an Univ. of Arch. & Tech.:Natural Science Edition,2013,45(06):778-783.[doi:10.15986/j.1006-7930.2013.06.004]
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非线性基础上拉压弹性模量不同矩形板的弯曲()
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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:
45
期数:
2013年06期
页码:
778-783
栏目:
出版日期:
2013-12-31

文章信息/Info

Title:
Bending of rectangular plate with difference elastic modulus intension and compression based on nonlinear foundation
文章编号:
1006-7930(2013)06-0778-06
作者:
吴 晓; 黄 翀; 杨立军
(湖南文理学院土木建筑工程学院,湖南 常德 415000)
Author(s):
WU Xiao;  HUANG Chong;  YANG Li-jun
(Dept. of Civil and Architectural Engineering, Hunan University of Arts and Science, Changde 415000, China)
关键词:
非线性; 基础; 弹性模量; 矩形板; 弯曲
Keywords:
nonlinearity;  foundation;  elastic modulus;  rectangular plate;  bending
分类号:
O 343.5
DOI:
10.15986/j.1006-7930.2013.06.004
文献标志码:
A
摘要:
采用弹性理论研究了非线性基础上拉压弹性模量不同矩形板的弯曲问题.建立了非线性基础上拉压弹性模量不同材料板的弯曲微分方程.对于非线性基础上拉压弹性模量不同材料板弯曲变形问题,选取梁函数作为试函数,采用Kantorovich及Galerkin联合法推导出了非线性基础上拉压弹性模量不同材料板的解析解,该方法计算结果与有关文献计算结果的误差很小.所以,选取梁函数作试函数,采用Kantorovich及Galerkin联合法研究拉压弹性模量不同矩形板的弯曲变形问题是可行的.把该方法计算结果与有限元法计算结果进行比较分析,验证了此方法计算精度比较高.算例分析表明,拉压弹性模量相差较大时,矩形板弯曲计算不宜采用相同弹性模量经典薄板理论,而应采用拉压弹性模量不同弹性理论.
Abstract:
Bending of rectangular plate with difference elastic modulus in tension and compression based on nonlinear foundation is studied by using elastic theory. Bending differential equations of plate with difference elastic modulus in tension and compression based on nonlinear foundation are established. For bending of plate with difference elastic modulus intension and compression based on nonlinear foundation, by taking beam functions as trial functions, analytical solutions of plate with difference elastic modulus in tension and compression based on nonlinear foundation are deduced with the combination method of Kantorovich with Galerkin, and calculation errors between analytical solutions and relevant literatures proved to be small. So, it is feasible that the combination method of Kantorovich with Galerkin is used in studying bending of rectangular plate with difference elastic modulus in tension and compression based on nonlinear foundation by taking beam functions as trial functions. Calculation results are compared with that obtained by finite element, and the accuracy of this method is verified relatively high. The analysis of examples indicated that bending calculation of rectangular plate which has larger difference between tensile elastic modulus and compressive elastic modulus may not apply classical elastic theory with the same elastic modulus, and elastic theory of difference elastic modulus in tension and compression can not be used either.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2013-01-22 修改稿日期:2013-11-30
基金项目:湖南省科技计划项目(湘财企指[2011]65号);湖南“十二五”重点建设学科项目资助
作者简介:吴 晓(1965-),男,湖南常德人,教授,主要从事结构振动理论研究.
更新日期/Last Update: 2015-10-05