孔隙热弹性轴对称薄板的静态分析

上海大学学报(自然科学版) ›› 2009, Vol. 15 ›› Issue (3): 276-283.

孔隙热弹性轴对称薄板的静态分析

李莹程昌钧

1.上海大学上海市应用数学和力学研究所，上海 200072; 2.上海大学理学院,上海 200444

出版日期:2009-06-30 发布日期:2009-06-30
通讯作者: 程昌钧(1937～)，女，教授，博士生导师,研究方向为非线性固体力学的理论、方法及应用. E-mail:chjcheng@mail.shu.edu.cn

Static Analysis of Axisymmetric Thermoelastic Thin Plate with Voids

LI Ying, CHENG Chang-Jun

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2. College of Sciences, Shanghai University, Shanghai 200444, China

Online:2009-06-30 Published:2009-06-30

摘要/Abstract

摘要：

根据孔隙热弹性材料线性理论，建立任意形状的有孔隙热弹性薄板的数学模型.作为应用，得到了圆薄板轴对称静力学问题的解析解，在边界固支和简支情况下，给出了解的具体表达式.并进行了数值计算，对比了有孔隙和无孔隙存在时热弹性板的挠度变化情况.研究了板的厚宽比、温度和基体材料体积百分比等参数对薄板挠度的影响.

关键词: 孔隙;热弹性;薄板;轴对称问题;解析解

Abstract:

In this paper, a model of thermoelastic thin plate with voids is established based on the theory of thermoelastic materials with voids. An analytic solution of the axisymmetric problem under static state is presented, and expressions of the deflection and voids are obtained with both fixed and simply supported boundary conditions. Numerical computation is carried out. Effects of voids and temperature on the deflection are considered. Influence of thickradius ratio of plate and temperature on deflection and the change in volume fraction are investigated.

Key words: voids; thermoelastic; thin plate; axisymmetric problem; analytic solution

中图分类号:

O343

李莹程昌钧. 孔隙热弹性轴对称薄板的静态分析[J]. 上海大学学报(自然科学版), 2009, 15(3): 276-283.

LI Ying, CHENG Chang-Jun. Static Analysis of Axisymmetric Thermoelastic Thin Plate with Voids[J]. Journal of Shanghai University（Natural Science Edition）, 2009, 15(3): 276-283.