工程力学 ›› 2017, Vol. 34 ›› Issue (6): 1-8.doi: 10.6052/j.issn.1000-4750.2015.10.0868

• 基本方法 •    下一篇

非均匀热载荷作用下功能梯度梁的非线性静态响应

毛丽娟1,2, 马连生1,2   

  1. 1. 兰州理工大学理学院, 兰州 730050;
    2. 西安交通大学机械结构强度与振动国家重点实验室, 西安 710049
  • 收稿日期:2015-10-27 修回日期:2017-05-13 出版日期:2017-06-25 发布日期:2017-06-25
  • 通讯作者: 马连生(1963―),男,山东临朐人,教授,博士,从事新型材料结构的力学行为研究(E-mail:lsma@lut.cn) E-mail:lsma@lut.cn
  • 作者简介:毛丽娟(1991―),女,甘肃酒泉人,硕士生,从事新型材料结构的力学行为研究(E-mail:maolijuan917@163.com)
  • 基金资助:
    国家自然科学基金项目(11472123);西安交通大学机械结构强度与振动国家重点实验室开放课题项目(SV2014-KF-04)

NONLINEAR STATIC RESPONSES OF FGM BEAMS UNDER NON-UNIFORM THERMAL LOADING

MAO Li-juan1,2, MA Lian-sheng1,2   

  1. 1. School of Science, Lanzhou University of Technology, Lanzhou 730050, China;
    2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China
  • Received:2015-10-27 Revised:2017-05-13 Online:2017-06-25 Published:2017-06-25

摘要: 由于功能梯度材料结构沿厚度方向的非均匀材料特性,使得夹紧和简支条件的功能梯度梁有着相当不同的行为特征。该文给出了热载荷作用下,功能梯度梁非线性静态响应的精确解。基于非线性经典梁理论和物理中面的概念导出了功能梯度梁的非线性控制方程。将两个方程化简为一个四阶积分-微分方程。对于两端夹紧的功能梯度梁,其方程和相应的边界条件构成微分特征值问题;但对于两端简支的功能梯度梁,由于非齐次边界条件,将不会得到一个特征值问题。导致了夹紧与简支的功能梯度梁有着完全不同的行为特征。直接求解该积分-微分方程,得到了梁过屈曲和弯曲变形的闭合形式解。利用这个解可以分析梁的屈曲、过屈曲和非线性弯曲等非线性变形现象。最后,利用数值结果研究了材料梯度性质和热载荷对功能梯度梁非线性静态响应的影响。

关键词: 精确解, 静态响应, 热载荷, 功能梯度梁, 多解支

Abstract: Due to the variation in material properties through the thickness of functionally graded material (FGM) structures, an FGM beam simply supported at both ends exhibits characteristics quite different from those of a FGM beam clamped at both ends. An exact, closed form solution is obtained for nonlinear static responses of FGM beams subjected to non-uniform in-plane thermal loadings. The equations governing the axial and transverse deformations of FGM beams are derived based on the nonlinear classical beam theory and the physical neutral surface concept. The two equations are reduced to a single nonlinear fourth-order integral-differential equation governing the transverse deformation. For an FGM beam clamped at both ends, the equation and the corresponding boundary conditions lead to a differential eigenvalue problem, whereas for an FGM beam simply supported at both ends, an eigenvalue problem does not arise due to the inhomogeneous boundary conditions. This consequently results in quite different behavior between a clamped and a simply supported FGM beams. The nonlinear equation is directly solved without any use of approximation and a closed-form solution for thermal bending deformation is obtained as a function of the applied thermal load. By using the exact solutions, the nonlinear deformation problems for buckling, postbuckling and nonlinear bending of the beam can be investigated. Finally, the numerical analyses are carried out to investigate the effects of material gradient properties and thermal loads on the nonlinear static responses of FGM beams.

Key words: exact solution, static response, thermal loading, functionally graded material beam, multi-solution branch

中图分类号: 

  • TB34
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