点力作用在各向同性板表面的格林函数

The Green’s Function for Isotropic Infinite Plate with a Point Force on the Surface

基于点力作用在各向同性半无限平面表面的格林函数,得到点力作用在各向同性板表面的二维格林函数。首先,根据文献,得到各向同性材料二维通解和边界条件。第二,假设出2组级数表示的调和函数,将调和函数代入到通解和界面条件中,得到4个递推关系的方程组。在给出满足表面条件的各向同性半无限平面的格林函数,就可以求解出任意的递推调和函数,进而求出整个位移场和应力场。最后,通过数值计算,将本文的计算结果与有限元方法(FEM)对比,验证本文算法的正确性。通过计算全场应力等值线,分析全场应力分布。利用叠加原理,计算出法向分布力作用在平板表面的位移场和应力场。本文方法收敛性快,计算简单。为此类问题的工程计算提供有效的方法。

Based on the Green’s function for isotropic half-infinite plane with a point force on the surface,the Two-dimensional Green’s function for isotropic infinite plate with a point force on the surface is solved.Firstly,the two-dimensional general solutions of isotropic materials and boundary conditions are received according to the literature.Second,two series harmonic functions are assumed,and the harmonic functions are substituted into the general solution and boundary conditions.Four recursive equations are deduced.In view of the Green’s function of an isotropic semi-infinite plane satisfied the surface condition,the recursive harmonic function can be solved,and then the displacement field and stress field can be obtained.Finally,through numerical calculation,the results of this paper are compared with the finite element method(EFM)to verify the correctness of the algorithm.By contour of stress components,the whole stress field distribution is analyzed.By using the superposition principle,the displacement field and stress field for the plate surface under the action on any direction load can be calculated.Our method has fast convergence and simple calculation.So that,it provides an effective method for such problems in engineering.