[1]徐业鹏,周 叮.简支功能梯度变厚度梁的弹性力学解[J].南京理工大学学报(自然科学版),2009,(01):132-136.
 XU Ye-peng,ZHOU Ding.Elasticity Solution of Simply-supported Functionally Graded Beams with Variable Thickness[J].Journal of Nanjing University of Science and Technology,2009,(01):132-136.
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简支功能梯度变厚度梁的弹性力学解
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《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

卷:
期数:
2009年01期
页码:
132-136
栏目:
出版日期:
2009-02-28

文章信息/Info

Title:
Elasticity Solution of Simply-supported Functionally Graded Beams with Variable Thickness
作者:
徐业鹏1 周 叮2
1. 南京理工大学理学院, 江苏南京210094; 2. 南京工业大学土木工程学院, 江苏南京210009
Author(s):
XU Ye-peng1ZHOU Ding2
1.School of Sciences,NUST,Nanjing 210094,China;2.College of Civil Engineering,Nanjing University of Technology,Nanjing 210009,China
关键词:
功能梯度材料 变厚度 傅里叶展开 弹性力学解
Keywords:
beams functionally graded materials variable thickness Fourier expansion elasticity solutions
分类号:
O343.1
摘要:
该文假设弹性模量为沿厚度变化的指数函数,泊松比为常数,利用平面应力问题的基本方程,导出满足控制微分方程和两端简支边界条件的位移函数的一般解,对上下表面的边界方程作傅里叶级数展开确定待定系数,结果具有很好的收敛性,精度可达三位有效数字。考察了弹性模量变化对功能梯度梁位移和应力的影响,为检验其它功能梯度梁近似理论和数值结果的有效性提供了依据。该文的方法可应用于对应力分析有较高精度要求的航空工程以及微型机械仪器设计等工程。
Abstract:
In this paper,the Young’s modulus is graded through the thickness following the exponential-law and the Poisson’s ratio keeps constant.According to the governing equations of plane stress problems,the general expressions of displacements,which exactly satisfy the governing differential equations and the simply-supported boundary conditions at two ends of the beam,are deduced.The unknown coefficients in the solution are determined by using the Fourier sinusoidal series expansion to the boundary equations on the upper and lower surfaces of the beams.The excellent convergence of the solution is demonstrated.The results are accurately up to the third significant digit.The effect of the Young’s modulus varying rules on the displacements and stresses of functionally graded beams is investigated.The proposed elasticity solution can be used to assess the validity of various approximate solutions and numerical methods for functionally graded beams.It is applicable in aerospace engineering and other projects with highly accurate demand on stress analysis such as the design of micro-mechanical apparatus.

参考文献/References:

[ 1] ?H ira i T, Chen L. Recent and prospec tive deve lopm ento f functiona lly graded m ater ia ls in Japan[ J]. M aterialsSc ience Fo rum, 1999, 308- 311: 509- 514.

[ 2] Sankar B V. An e lastic ity solution for functiona lly g raded beam s[ J] . Composites Sc ience and Techno logy,2001, 61: 689- 696.
[ 3] 仲政, 于涛. 功能梯度悬臂梁弯曲问题的解析解[ J].同济大学学报(自然科学版), 2006, 34: 443- 447.
[ 4] 于涛, 仲政. 均布荷载作用下功能梯度悬臂梁弯曲问题的解析解[ J]. 固体力学学报, 2006, 27: 15- 20.
[ 5] Y ing J, Lu C F, ChenW Q. Tw odim ensional e lasticity so lutions for functiona lly g raded beam s resting on elastic foundations [ J]. Com po site Structu res, 2008,84: 209- 219.
[ 6] DingH J, H uang D J, ChenW Q. Elastic ity so lutionfor p lane anisotropic functionally graded beam s [ J].Inte rna tiona l Journa l of So lids and S tructures, 2007,44: 176- 196.

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备注/Memo

备注/Memo:
基金项目: 南京理工大学博士研究生创新基金
作者简介: 徐业鹏( 1982- ), 男, 博士, 主要研究方向: 结构三维弹性力学分析, Em a il: xuyepeng285@ yahoo. com. cn;通讯作者: 周叮( 1957- ), 男, 教授, 主要研究方向: 结构动力学, Em a il:dingzhou57@ yahoo. com。
更新日期/Last Update: 2012-11-19