基于微分求积单元法的层合梁热弹性分析  

Thermoelastic Analysis of Layered Beams by Differential Quadrature Element Method

作　　者：孙益星 陈继业 SUN Yixing;CHEN Jiye(Chongqing Vocational Institute of Safety&Technology,Chongqing 404020,China;School of Civil Engineering and Architecture,Jiangsu University of Science and Technology,Zhenjiang 212100,Jiangsu,China)

机构地区：[1]重庆安全技术职业学院,重庆404020 [2]江苏科技大学土木工程与建筑学院,江苏镇江212100

出　　处：《力学季刊》2023年第4期881-890,共10页Chinese Quarterly of Mechanics

基　　金：江苏省自然科学基金青年项目(BK20220655)。

摘　　要：基于微分求积单元法,开展了非均匀温度场中层合梁的热弹性分析.首先基于Fourier导热定律,分析一般热边界条件下层合梁的二维稳态温度场;然后基于二维热弹性力学理论,分析层合梁的热应力和变形.为求解热传导和热应力问题,将层合梁沿各层界面划分为若干空间子域,采用微分求积法对每一子域的控制方程和边界条件进行离散并求解.数值算例验证了本方法的收敛性,与已有文献结果的对比验证了本方法的正确性.最后,算例分析了非均匀热边界条件对夹层梁温度分布的影响,以及端部支承条件和长厚比对梁内位移和应力分布的影响.Based on the differential quadrature element method,the thermoelastic analysis of layered beams in nonuniform temperature field is conducted.First,the two-dimensional steady temperature distributions within the beam under general thermal boundary conditions are studied based on Fourier's law of heat transfer.Then,the thermal stresses and deformations of the beam are studied based on the two-dimensional thermoelasticity theory.To solve the heat transfer problem and thermal stress problem,the layered beam is divided into several subdomains along the layer interfaces.The governing equations and boundary conditions of each subdomain are discretized and solved using the differential quadrature method.The convergence of the present method is verified through numerical examples.The correctness of the present method is verified by comparing with available literature results.Finally,numerical examples are carried out to study the effects of nonuniform thermal boundary conditions on the temperature distributions of a sandwich beam,as well as the effects of end support conditions and length-to-thickness ratio on the displacement and stress distributions within the beam.

关 键 词：微分求积单元法 层合梁 热传导 热弹性力学 

分 类 号：O343.6[理学—固体力学]