[1]黄会荣,等.考虑横向剪切变形简支矩形中厚板的屈曲分析[J].西安建筑科技大学学报:自然科学版,2011,43(05):638-643.[doi:DOI :10.15986/j .1006-7930.2011.05.005]
　HUAN G Hui-rong,HAO J i-ping,et al.Study on buckling of simply supported rectangular medium plateconsidering the transverse shearing deformation[J].J.Xi’an Univ. of Arch. & Tech.:Natural Science Edition,2011,43(05):638-643.[doi:DOI :10.15986/j .1006-7930.2011.05.005]
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考虑横向剪切变形简支矩形中厚板的屈曲分析()
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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:
43
期数:
2011年05期
页码:
638-643
栏目:
出版日期:
2011-10-31

文章信息/Info

Title:
Study on buckling of simply supported rectangular medium plate
considering the transverse shearing deformation
文章编号:
1006-7930(2011)05-0638-06
作者:
黄会荣1 ;  2 ;  郝际平2 ;  张海霞3 ;  郭家元1
(1.西安建筑科技大学机电工程学院;2.西安建筑科技大学土木工程学院;
3.山东省泰安市建筑设计院, 山东泰安271000)
Author(s):
HUAN G Hui-rong1 ;  2 ;  HAO J i-ping 2 ;  Z H ANG Hai-x ia3 ; GUO J ia-yuan1
(1 .Co lleg e of Mechanical & Electrical Eng ineering , 2.College o f Civil Engineering ,
3 .Taian Institute of Ar chitec tur al Desig n, Taia n 271000 , China)
关键词:
横向剪切变形; 位移型控制微分方程; 小挠度屈曲; 简支矩形中厚板; 双重三角级数; 临界荷载
Keywords:
transverse shearing de f ormation ; displacement governing di f f erential equation ; small-de f lection buck ling ; simp ly supported rectangular medium plates ; double trigonometric series ; critical load ..
分类号:
TU33
DOI:
DOI :10.15986/j .1006-7930.2011.05.005
文献标志码:
A
摘要:
 基于考虑横向剪切变形中厚板的几何方程、物理方程及平衡方程, 建立关于一个中面挠度和两个中面
转角为独立变量的中厚板大挠度弯曲的位移型控制微分方程, 从而获得中厚板小挠度屈曲的位移型控制微
分方程.该方程退化为薄板屈曲的控制微分方程的正确性说明推导过程的正确性及一般性.文中中厚板小挠
度屈曲的位移型控制微分方程是一个六阶耦合微分方程, 对其使用双重三角级数并作为广义坐标, 将两个中
面转角解耦为中面挠度的函数, 进一步建立中厚板小挠度屈曲的特征方程, 从而借助MATLAB 工具得到简
支矩形中厚板小挠度屈曲的临界荷载表达式, 最后应用MATLAB 工具通过临界荷载表达式获得临界荷载系
数的曲线, 整个求解过程简便, 且其曲线退化后符合经典的薄板临界荷载曲线.
Abstract:
Ba sed on the theo ry o f g eometric equatio n, phy sical equatio n and equilibrium equatio n of medium pla te co nsider
ed t ransve rse shearing defo rma tion , the displacement g ove rning differential equatio n for the la rge-deflectio n bending o f
medium plate is established, co ncerning three inde pendent variables including o ne middle surface displacement and two
middle surface angles o f ro tatio n.So the displacement go verning diffe rential equa tion fo r the small-deflection buckling o f
medium plate is o btained .Furthermo re , the equa tion could degenerate into the g ove rning differentia l equation for the
buckling o f thin plate , w hich demonstra te s the validity and generality of the solv ing pro cess .The displacement go ver ning
the differ ential equatio n fo r the small-deflectio n buckling of medium plate is a sixth-o rde r diffe rential equatio n by applying
do uble trig onometric se ries as g ene ralized coo rdinates .The characteristic equa tion fo r the small-def lectio n buckling o f medium
plate is obtained throug h deco upling of tw o middle surface ang les of ro tatio n into middle surface deflection functio n.
Thus, the critical lo ad fo rmula f or the small-deflection buckling of simply suppo rted rectangular medium plate is gained
throug h M ATLAB.Finally , the curves of c ritical lo ad coefficient th rough the critical load formula by MAT LAB are obtained
.Gener ally , it’ s a simplified and co nvenient solv ing pro ce ss , and the deg ener ative curve is in line with the classical
critical lo ad curv e of thin plate

参考文献/References:

References
[ 1] 　曹志远, 杨昇田.厚板动力学理论及其应用[ M] .北京:科学出版社, 1983 .
CAO ZHi-yuan, YANG Sheng-tian .Dy namics Theory and Application of Thick Plates[ M] .Beijing :Science Press, 1983 .
[ 2] 　曹志远.板壳振动理论[ M] .北京:中国铁道出版社, 1989.
CAO ZH i-y uan .Vibr atio n Theo ry o f Plates a nd Shells [ M] .Beijing :China Railw ay Press , 1989 .
[ 3] 　吴连元.板壳理论[ M] .上海:上海交通大学出版社, 1989.
WU Lian-Yua n.Theory of Plates and Shells[ M] .Shang hai :Shanghai Jiao tong Univ ersity Press, 1989.
[ 4] 　吴连元.板壳稳定性理论[ M] .武汉:华中科技大学出版社, 1996.
WU Lian-Yua n.S tability Theo ry o f Plates and Shells[ M] .Wuhan :Huang zho ng keji Univ ersity Pr ess , 1996.
[ 5] 　何福保, 沈亚鹏.板壳理论[ M] .西安:西安交通大学出版社, 1993 .
H E Fu-bao , SH ENGYa-peng .Theo ry of Plates and She lls[ M] .Xi′an :Xi′an Jiaoto ng Univer sity Press , 1993 .
[ 6] 　Clive .L.DYM .Intro duction to the Theo ry of Shells[ M] .New Yor k:Per gamo n Press, 1974 .
[ 7] 　贾春元.板的非线性分析[ M] .北京:科学出版社, 1989.
JIA Chun-y uan.No nlinear Analy sis of Plates[ M] .Beijing :Science Pre ss , 1989.
[ 8] 　沈惠申.板壳后屈曲行为[ M] .上海:上海科学技术出版社, 2002.
SH EN H ui-shen .Post-buckling Behavior of Plates and Shells[ M] .Shang hai :Shanghai Pr ess o f Science and Techno
lo gy , 2002 .
[ 9] 　黄会荣, 郝际平, 黄　义.考虑横向剪切变形厚板弯曲的位移型方程及简支矩形板的一般解[ J] .西安建筑科技大学
学报:自然科学版, 2009 , 41(6):780-784 .
H UANG H ui-ro ng H AO Ji-ping H UANG Yi.Displacement fundamental equatio ns o f the thick plates bending and
the general so lutio n to simply suppo rted rectang ular pla te s by transver s shea ring defomatio n[ J] .J.Xi′an Univ ersity
of Ar chitecture & Techno lo gy :Natural Scie nce Edition , 2009, 41(6):780-784.

备注/Memo

备注/Memo:
＊收稿日期:2010-05-24 　　修改稿日期:2011-07-12
基金项目:国家自然科学基金资助项目(50878181);陕西省教育厅专项基金资助项目(11JK0958)
作者简介:黄会荣(1963-), 女, 陕西西安人, 教授, 主要从事钢结构理论与设计研究.
更新日期/Last Update: 2015-11-05