力学与实践 ›› 2015, Vol. 37 ›› Issue (1): 91-94.DOI: 10.6052/1000-0879-14-118

• 应用研究 • 上一篇    下一篇

梯度弹性基础上正交异性薄板的屈曲分析

陈亮1, 李华东2   

  1. 1. 海军驻426 厂军代表室, 上海 202100;
    2. 海军工程大学舰船工程系, 武汉 430033
  • 收稿日期:2014-04-24 修回日期:2014-07-16 出版日期:2015-02-15 发布日期:2015-02-14
  • 通讯作者: 李华东,博士,讲师. E-mail:lhd0727@163.com
  • 基金资助:

    国家自然科学基金资助项目(50979110).

BUCKLING ANALYSIS OF ORTHOTROPIC THIN PLATE ON GRADED ELASTIC FOUNDATION

CHEN Liang1, LI Huadong2   

  1. 1. Naval Representative Office Stationed at No.426 Factory, Shanghai 202100, China;
    2. Department of Ships Engineering, Naval University of Engineering, Wuhan 430033, China
  • Received:2014-04-24 Revised:2014-07-16 Online:2015-02-15 Published:2015-02-14

摘要:

基于双参数弹性基础模型,研究了梯度弹性基础上正交异性薄板的屈曲问题. 首先,基于能量法与变分原理,给出了梯度弹性基础上正交异性薄板的屈曲控制方程,并得到了梯度弹性基础刚度系数K1K2的计算式;进而,通过将位移函数采用三角函数展开的方法,给出了单向压缩载荷作用下、四边简支正交异性弹性基础板屈曲载荷的计算式;在算例中,通过将该文的解退化到单纯的正交异性板,并与经典弹性解比较,证明了理论的正确性;最后,求解了弹性模量在厚度方向上呈幂律分布的梯度基础上的薄板屈曲问题,分析了基础上下表层材料弹性模量比与体积分数指数对屈曲载荷的影响.

关键词:

正交异性板|双参数弹性基础|屈曲|功能梯度材料|变分原理

Abstract:

Based on the two-parameter foundation model, the buckling of orthotropic thin plates on graded elastic foundations is studied. Firstly, the buckling governing differential equation of orthotropic thin plates on graded elastic foundations and the expressions of two elastic parameters of the elastic foundation are obtained by using the energy method and the variational principle. Then, by expanding the displacement into trigonometric functions, the calculation formula of the uniaxial compression buckling load for orthotropic thin plates on graded elastic foundations with simply supported edges is obtained. In the example, the proposed solution is validated by comparing the degenerated results for an orthotropic thin plate with the classical elasticity solution. Finally, this paper studies the buckling load of the orthotropic thin plate on a graded elastic foundation, whose Young's modulus obeys a power law against the thickness. The effects of the top-bottom surfaces' Young's modulus ratio and the volume fraction exponent are also discussed.

Key words:

orthotropic plate|two-parameter foundation model|buckling|functionally graded materials|variation principle

中图分类号: