各向异性材料平面问题基本解析解的特征方程解法  

A STRATEGY FOR FORMULATING THE FUNDAMENTAL ANALYTICAL SOLUTIONS BY SOLVING THE CHARACTERISTIC EQUATIONS OF PLANE PROBLEMS WITH ANISOTROPIC MATERIALS

作　　者：王文婕[1] 田歌[2] 傅向荣[2] 赵阳[2] 

机构地区：[1]中国矿业大学(北京)力学与建筑工程学院,北京100083 [2]中国农业大学水利与土木工程学院,北京100083

出　　处：《工程力学》2012年第9期11-16,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(10872108);国家重点基础研究发展计划项目(2010CB731503)

摘　　要：该文提出了一种利用特征方程解法构造基本解析解的新方法,并将其应用到各向异性材料平面问题,成功构造了完备且独立的系列基本解析解。构造各向异性材料平面问题控制微分方程的算子矩阵,通过其行列式计算可得到问题特征通解所需满足的特征方程,将所求得特征通解代入到微分方程算子矩阵所对应的伴随矩阵,可推导得出各向异性材料平面问题的基本解析解。根据基本解析解独立性的论证,可得到系列独立且完备各向异性材料平面问题基本解析解。利用特征方程解法求解基本解析解思路简单、并且容易找到独立且完备的解析解,其结果可以成为相关数值计算方法的基础。A new strategy for formulating the fundamental analytical solutions by solving the characteristic equations of plane problems with anisotropic materials was proposed in this paper. And as a result, a series of independent and complete fundamental analytical solutions were successfully formulated. Firstly, the general characteristic solutions of the plane problem with anisotropic materials were obtained by calculating the determinant of the characteristic equations of the differential operator matrix. Then, the fundamental analytical solutions were formulated by substituting these general characteristics solutions into the adjoint matrix of the differential operator matrix. Finally, according to the argumentation for the independence of the fundamental analytical solutions, the series of the independent and complete fundamental analytical solutions could be simply given. The proposed strategy is quite simple and effective developing many numerical high-performance methods. And the resulting analytical solutions can be used for

关 键 词：各向异性 平面问题 基本解析解 特征方程 独立性 

分 类 号：O343[理学—固体力学]