论文部分内容阅读
在正交各向异性材料V型切口理论与数值分析中,都需利用问题的特征值。本文首先根据Stroh理论给出各向异性材料的材料特征矩阵,然后通过分析V型切口近尖端领域边界条件,推导出其边界特征方程,并得到相应的简化计算公式,最后利用分区加速Müller法,给出了不同材料特性正交各向异性材料的对称与反对称平面问题前几阶特征值。引入收边法和劈因子法之后,该文采用的分区加速Müller法具有收敛快、精度高和易于实施等优点,还可以去除已得到的根的影响,提高了收敛速度。
In the orthotropic V-notch theory and numerical analysis, the eigenvalues of the problem need to be used. In this paper, firstly, the material characteristic matrix of anisotropic material is given according to Stroh theory. Then, the boundary characteristic equation of the V-notch is deduced by analyzing the boundary conditions in the near-tip region of V-notch and the corresponding simplified formulas are obtained. Finally, The first eigenvalues of the symmetric and antisymmetric plane problems of orthotropic materials with different material properties are given. After the introduction of the edge-by-beam method and the splitting factor method, the partition acceleration Müller method used in this paper has the advantages of fast convergence, high precision and easy implementation. It can also remove the influence of the root obtained and improve the convergence speed.