功能梯度与均匀圆板弯曲解的线性转换关系

李世荣 张靖华 徐华

doi:10.6052/0459-1879-2011-5-lxxb2010-810

功能梯度与均匀圆板弯曲解的线性转换关系

doi: 10.6052/0459-1879-2011-5-lxxb2010-810

李世荣张靖华徐华

1.
扬州大学建筑科学与工程学院
2.
兰州理工大学理学院

基金项目: 功能梯度材料介质中广义热弹性波的传播研究

详细信息

中图分类号: O343.7
计量
- 文章访问数: 2362
- HTML全文浏览量: 94
- PDF下载量: 1041
- 被引次数: 0
出版历程
- 收稿日期: 2010-12-09
- 修回日期: 2011-03-19
- 刊出日期: 2011-09-18

Linear transformation between the bending solutions of functionally graded and homogenous circular plats

Shirong Li Jinghua Zhang Hua Xu

1.
College of Civil Science and Engineering, Yangzhou University, Yangzhou 225127, China
2.
School of Science, Lanzhou University of Technology, Lanzhou 730050, China

Funds: Study of generalized thermoelastic waves in functionally graded materials

摘要

摘要: 基于一阶剪切理论, 研究了功能梯度材料圆板与均匀圆板轴对称弯曲解之间的线性转换关系. 通过理论分析和比较功能梯度材料圆板和均匀圆板在一阶剪切理论下的位移形式的轴对称弯曲控制方程, 发现了功能梯度材料圆板的转角与均匀圆板的转角之间的相似转换关系. 在假设材料性质沿板厚连续变化的情况下, 给出了相似转换系数的解析表达式. 在此基础上, 进一步导出了一阶剪切理论下功能梯度圆板的挠度与经典理论下, 均匀圆板的挠度之间的线性关系. 从而, 可将功能梯度材料圆板在一阶剪切理论下的弯曲问题求解, 转化为相应均匀薄圆板在经典理论下的弯曲问题求解, 以及转换系数的计算问题. 这一方法为功能梯度非均匀中厚度圆板的求解提供了简捷途径, 而且更便于工程应用. 作为例子, 采用上述方法分别求得了周边简支和夹紧条件下, 梯度圆板在均布横向载荷作用下的弯曲解析解, 该解答与Reddy得到的结果完全吻合.
- 线性转换
Abstract: Based on the first-order shear deformation theory (FSDT),linear transformation relationship between bending solutions of functionallygraded material (FGM) and homogenous circular plates was studied. Firstly,through theoretically analyzing and comparing the displacement-typegoverning equations for axially symmetrically bending of FGM and homogenouscircular plates based on the first-order shear deformation theory, linearlydependent relationship between the rotational angles of FGM circular plateand those of homogenous one was found. By giving the material properties ofFGM circular plates changing as continuous functions in the thicknessdirection, the corresponding transition factor between the solutions of thetwo kind plates were derived in analytical forms. Furthermore, a linearrelationship between the deflections of FGM circular plate based on FSDT andthose of homogenous one based on the classical plate theory were derived. Asa result, solutions for static bending based on the first-order sheardeformation plate theory of a non-homogenous circular plate can be reducedto that based on classical plate theory of a homogenous one and thecalculation of the transformation factors. This approach provides a simpleand facile procedure for solutions of the non-homogenous moderately thickFGM circular plates, which can be very easily and conveniently used inengineering. By using the above mentioned approach, analytical bendingsolutions of FGM circular plates with simply supported as well as clampedboundary conditions under uniformly distributed lateral force werepresented, which show a very good agreement with the results given by Reddy.
- linear transformation.