应用最小二乘法求解平面P波在孔洞上的散射  

Application of least square method to solve the scattering of plane P-wave on a cavity

作　　者：陈志刚 CHEN Zhigang(School of Mechanics and Construction Engineering,Jinan University,Guangzhou 510632,China;MOE Key Lab of Disaster Forecast and Control in Engineering,Jinan University,Guangzhou 510632,China)

机构地区：[1]暨南大学力学与建筑工程学院 [2]暨南大学重大工程灾害与控制教育部重点实验室

出　　处：《地震工程与工程振动》2019年第6期106-112,共7页Earthquake Engineering and Engineering Dynamics

基　　金：暨南大学“重大工程灾害与控制”教育部重点实验室项目~~

摘　　要：弹性波在孔洞上的散射问题可采用复变函数方法求解,用含有待定系数的“域函数”表示散射波的位移势函数,如何准确地求解该待定系数是获得问题解答的关键。本文根据孔洞边缘的径向和切向应力为零的边界条件用最小二乘法建立求解待定系数的线性方程组,得到有限项系数的近似解。通过圆孔、椭圆孔和方孔的数值算例,分析了P波作用下不同形状孔洞边缘的动应力集中系数的特征,讨论了孔边的径向和切向应力计算误差与待定系数项数的关系。计算结果表明,采用最小二乘法求解散射波的待定系数,能够获得满足一定精度要求的孔附近动应力集中系数的解答。The scattering problem ofelastic waves on a cavity can be solved by complex function method. The 11 do­main function" containing the undetermined coefficient is used to represent the displacement potential function ofthe scattered wave. How to solve the undetermined coefficientaccurately is the key to obtain the solution. In this pa­per ,based on the boundary condition of the radial stress at the boundary of the cavity is zero , a set of linear equa­tions for solving the undetermined coefficients are established by the least squares method , and the approximate so­lution of the finite term coefficients is obtained. Through numerical examples of circular , eiiptical and square cavi­ties ,the characteristics of dynamic stress concentration factorsat the boundary of cavities with different shapes underP-wave are analyzed. The relationship between the accuracy of radial and tangential stress calculation at the cavityboundary and the number of undetermined coefficients is discussed. The calculation results show that the leastsquare method can be introduced to solve the undetermined coefficients of the scattered wave , and the solution ofthe dynamic stress concentration factors near the cavity that meets certain accuracy requirements can be obtained.

关 键 词：平面P波 动应力集中系数 孔洞 最小二乘法 复变函数法 

分 类 号：O347.4[理学—固体力学] P315.3[理学—力学]