正交各向异性材料含切口平面问题特征值研究  

RESEARCH ON CHARACTERISTIC VALUES OF NOTCHED PLANE PROBLEM OF ORTHOTROPIC MATERIALS

作　　者：傅向荣[1] 岑松[2] 田歌[1] 邓娇[1] 周明珏[2] 宋孟燕[1] 

机构地区：[1]中国农业大学土木工程系,北京100083 [2]清华大学航天航空学院,北京100084

出　　处：《工程力学》2013年第B06期1-5,18,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(11272340;11272181);国家重点基础研究发展计划项目(2010CB731503)

摘　　要：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。The V-notch analysis of orthotropic materials requires the eigenvalues of a problem. Firstly, the material characteristic matrixes of the orthotropic materials and the boundary characteristic equations based on the boundary conditions are derived. Then simplified Stroh formula for orthotropic materials is given. Finally, the eigenvalues of symmetric and antisymmetric plane problems of different materials are studied using the sub-region accelerated M/iller method. With the introduction of the boundary-withdraw and split-factor methods, the sub-region accelerated M/Jller method shows the advantages of fast convergence, high precision and easy to implement. It is also an effective method to avoid the calculation of the previous roots. Thusly, the convergence speed can be increased.

关 键 词：Stroh理论 分区加速Müller法 特征值 含切口平面问题 收边法 

分 类 号：O302[理学—力学]