功能梯度材料热弹性分析的高阶格点型有限体积法  

A high-order cell-vertex finite volume method for thermoelastic analysis of functionally graded materials

作　　者：龚京风 郑文利 宣领宽 徐宗著 Gong Jingfeng;Zheng Wenli;Xuan Lingkuan;Xu Zongzhu(College of Automobile and Traffic Engineering,Wuhan University of Science and Technology,Wuhan 430065,China)

机构地区：[1]武汉科技大学汽车与交通工程学院,湖北武汉430065

出　　处：《武汉科技大学学报》2023年第1期33-39,共7页Journal of Wuhan University of Science and Technology

基　　金：国家自然科学基金青年基金资助项目(51909197);中国舰船研究设计中心船舶振动噪声重点实验室基金资助项目(6142204200305)。

摘　　要：为提高功能梯度材料(FGMs)热弹性分析的准确性,本文发展了一种二维高阶格点型有限体积法(CV-FVM)。该方法采用八节点四边形单元(Q8)和六节点三角形单元(T6)离散控制方程,并利用交错网格技术,将材料属性定义于单元中心,将待求解的未知变量定义于单元节点。应用该方法求解FGMs的热传导、应力和热应力问题,结果与文献中的解析值吻合良好,验证了其正确性。在计算存在大温度梯度的FGMs热传导问题时,高阶CV-FVM能够有效避免数值振荡;在进行复杂FGMs热弹性分析时,高阶CV-FVM能够有效避免数值不连续问题;同时,在相同的网格数下,采用Q8单元的高阶CV-FVM比低阶CV-FVM和采用T6单元的高阶CV-FVM计算精度要高。In order to improve the accuracy of thermoelastic analysis of functionally graded materials(FGMs), a two-dimensional high-order cell-vertex finite volume method(CV-FVM) is developed. Eight-node quadrilateral element(Q8) and six-node triangular element(T6) are utilized to discretize the governing equations. By using staggered grid technique, the material properties are defined at the cell center, and the unknown variables to be solved are defined at the node. The method is applied to solve the heat conduction, stress and thermal-stress problems of FGMs, and the results are in good agreement with the analytical solutions in the literature, which verifies the correctness of the method. High-order CV-FVM can effectively avoid numerical oscillation while calculating the heat conduction problem of FGMs with large temperature gradient. In the complex thermoelastic analysis of FGMs, high-order CV-FVM can effectively avoid numerical discontinuity. Meanwhile, in the condition of the same number of grids, the high-order CV-FVM with Q8 elements is more accurate than the low-order CV-FVM and the high-order CV-FVM with T6 elements.

关 键 词：格点型有限体积法 高阶单元 功能梯度材料 热弹性分析 交错网格技术 数值振荡 

分 类 号：O343.1[理学—固体力学]