基于多边形流形元法的均质材料热弹性问题研究

发布时间：2018-06-02 14:42

本文选题：数值流形方法 + 多边形单元　；参考：《南昌航空大学》2017年硕士论文

【摘要】：热弹性问题是科学和工程领域中的重要问题。数值求解凭借其适用性强、效率高、成本低等优势成为研究此类问题的主要工具之一。近年来,数值流形方法(Numerical Manifold Method,简称NMM,又称流形元法)因其特有的两套覆盖系统而备受关注。与常用的三角形和四边形单元相比,多边形单元具有网格划分更灵活、不易发生体积自锁等优势。本文发展了用于分析二维均质材料热弹性问题的多边形NMM,并结合典型算例对方法的可行性与精度进行了验证,完成的主要工作与相关成果如下:(1)对热弹性问题、NMM以及多边形单元的国内外研究现状进行了简要的综述。(2)给出NMM的基本概念和近似函数,简述了多边形单元的常用权(形)函数形式,对NMM与其他常用数值方法进行了比较。(3)发展了用于分析均质材料二维稳态热传导问题的多边形NMM。列出了相应的控制方程和边界条件,给出了多边形NMM温度场近似函数,基于变分原理导出了多边形NMM离散方程,探讨了积分策略,采用C++语言编制了仿真程序,通过对典型算例的分析验证了方法的可行性和精度。(4)发展了用于分析均质材料二维热弹性问题的多边形NMM。列出了相应的控制方程和边界条件,给出了多边形NMM位移场近似函数,基于变分原理导出了多边形NMM离散方程,采用C++语言编制了仿真程序,通过对典型算例的模拟验证了方法的可行性和精度。
[Abstract]:Thermoelasticity is an important problem in the field of science and engineering. Numerical solution has become one of the main tools to study this kind of problems by virtue of its strong applicability, high efficiency and low cost. In recent years, numerical Manifold methods (NMMs) have attracted much attention because of their unique covering systems. Compared with the common triangular and quadrilateral elements, the polygonal element has the advantages of more flexible meshing and less easy to occur volume self-locking. In this paper, polygonal NMMs are developed for the analysis of thermoelastic problems of two-dimensional homogeneous materials, and the feasibility and accuracy of the method are verified by a typical example. The main work and related results are as follows: (1) A brief review of the domestic and international research status of thermoelastic problems and polygonal elements is given. (2) the basic concepts and approximate functions of NMM are given. The weight (shape) function forms of polygonal elements are briefly described. The NMM is compared with other numerical methods to develop the polygonal NMMs for the analysis of two-dimensional steady-state heat conduction problems of homogeneous materials. The corresponding governing equations and boundary conditions are listed, and the approximate function of polygon NMM temperature field is given. Based on the variational principle, the polygon NMM discrete equation is derived, the integration strategy is discussed, and the simulation program is developed by using C language. The feasibility and accuracy of the method are verified by the analysis of typical examples. The polygonal NMMMs used to analyze the two-dimensional thermoelastic problems of homogeneous materials are developed. The corresponding governing equations and boundary conditions are listed, and the approximate function of the polygon NMM displacement field is given. Based on the variational principle, the polygon NMM discrete equation is derived, and the simulation program is compiled with C language. The feasibility and accuracy of the method are verified by simulation of typical examples.
【学位授予单位】：南昌航空大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O343.6;O302

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