基于梁的弯曲变形问题理解格林函数法  

UNDERSTANDING GREEN FUNCTION METHOD BASED ON BENDING DEFORMATION PROBLEM OF BEAM

作　　者：雍华东 YONG Huadong(College of Civil Engineering and Mechanics,Lanzhou University,Lanzhou 730000,China)

机构地区：[1]兰州大学土木工程与力学学院,兰州730000

出　　处：《力学与实践》2024年第5期1045-1050,共6页Mechanics in Engineering

基　　金：兰州大学研究生课程思政示范课程项目资助。

摘　　要：格林函数法作为求解偏微分方程的主要方法之一,是数学物理方程课的重点教学内容。格林函数在求解泊松方程及热传导方程等问题时得到了广泛的应用,但由于格林函数满足特定的定解问题并具有对称的性质,其主要内容的掌握一直是教学的难点。本文结合梁的弯曲问题和功的互等定理,阐述了格林函数及其对称性的力学意义,并对第一类和第二类边值问题的解中不同项的贡献进行了解释。相比于传统的格林函数教学方式,采用梁的弯曲问题进行讲解更为简单并易于理解。As one of the main methods to solve the partial differential equations,Green function method is the key teaching content of mathematical physics equation.Green function has been widely used in solving Poisson equation and heat conduction equation.Since Green function satisfies the specific problem of definite solution and has the property of symmetry,it is always difficult to master the main content of Green function in teaching.In this paper,the mechanical meaning of Green function and its symmetry are elaborated by combining the bending problem of beam and the reciprocal theorem of work.The contributions of different terms in the solutions of the first and second kinds of boundary value problems are explained.Compared with the traditional teaching of Green function,it is simpler and easier to understand to explain with the bending problem of beam.

关 键 词：格林函数 梁的弯曲 功的互等定理 对称性 边值问题 

分 类 号：O302[理学—力学]