有限块体法在功能梯度材料上的研究与应用

发布时间：2018-01-27 22:33

本文关键词： 反问题热传导问题有限块体法功能梯度材料移动边界边界型有限块体法摩擦分析　出处：《太原理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：功能梯度材料是一类物理性质与位置坐标有关的特殊的复合材料。该材料广泛应用于航空器材的热障涂层、生物医学的骨科植入材料、固体氧化物燃料电极等高科技领域。一般地,很难找到功能梯度材料上力学问题的基本解,而且传统数值算法如有限元法求解该类问题时网格划分繁琐,精度略低。基于无网格法提出的有限块体法(FBM)在建立系统代数方程时不需要基本解,具有配点灵活、精度较高的特点。本文通过有限块体法求解功能梯度材料的移动反边界问题、二维热传导问题以及一致接触类摩擦问题。本文考虑炼钢炉上的移动反边界问题并对其内层腐蚀边界进行探测与动态识别,炼钢炉的复合结构通过多层功能梯度材料模拟,借助于适度大小的虚拟矩形域可求得腐蚀点位置信息。此外边界修正的Chebyshev零点的引入进一步提升了有限块体法的收敛性。本文还研究了功能梯度圆环上的二维热传导问题。由于功能梯度圆环的物理属性与圆环半径相关,本文采用基于极坐标的有限块体法进行求解,并给出极坐标下有限块体法的热传导方程和边界条件的矩阵形式。最后本文研究了压缩载荷下弹性地基上的平冲头模型并提出边界型有限块体法。通过理论推导可以看出,采用边界型有限块体法分析一致接触类摩擦问题,可以减少平衡方程中未知量的个数、提高求解效率。本文列举了五个数值算例,并通过与有限元法(FEM)和径向基函数(RBF)的比较来展现有限块体法的优势。数值结果表明:有限块体法有高稳定性、高效率、高精度的特点。
[Abstract]:Functionally graded material (FGM) is a kind of special composite material whose physical properties are related to position coordinates. It is widely used in thermal barrier coating of aeronautical equipment and orthopedic implant material in biomedicine. In general, it is difficult to find the basic solution of mechanical problems on functionally graded materials in high-tech fields such as solid oxide fuel electrodes, and the traditional numerical algorithms such as finite element method are tedious to solve such problems. The finite block method (FBM) based on meshless method does not need the basic solution when establishing the algebraic equation of the system, and it is flexible in collocation. The finite block method is used to solve the moving inverse boundary problem of functionally graded materials. In this paper, the problem of moving inverse boundary on steelmaking furnace is considered, and the inner layer corrosion boundary is detected and dynamically identified. The composite structure of steelmaking furnace is simulated by multi-layer functionally gradient material. In addition, the introduction of Chebyshev 00:00 with boundary correction further improves the convergence of the finite block method. The functional ladder is also studied in this paper. Two-dimensional heat conduction problem on a circular ring. The physical properties of the functionally gradient ring are related to the radius of the ring. In this paper, a finite block method based on polar coordinates is used to solve the problem. The heat conduction equation and the matrix form of boundary conditions of finite block method in polar coordinates are given. Finally, the flat punch model of elastic foundation under compression load is studied and the boundary finite block method is presented. You can see. The boundary finite block method can reduce the number of unknowns in the equilibrium equation and improve the efficiency of solving the uniform contact friction problems. Five numerical examples are given in this paper. Compared with the finite element method (FEMM) and the radial basis function (RBF), the advantages of the finite block method are demonstrated. The numerical results show that the finite block method has the characteristics of high stability, high efficiency and high accuracy.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB34

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