带裂纹的弹性半平面接触问题

平面弹性基本问题中的接触问题与断裂问题是工程实际中的重要问题。研究工程实际中一类带任意裂纹的弹性半平面接触问题。根据平面弹性复变方法，将问题归结为求解一类解析函数边值问题。通过适当的函数分解和消元方法，将问题减化为一类有求解程序的一般Ｒｉｅｍａｎｎ边值问题，从而得到弹性体应力函数封闭形式的解，并导出了裂纹端点的应力强度因子与压头下方边界压力分布情况。

Contact Problem of Elastic Half-Plane with Cracks

On the fundamental problems in elstic plane,both contact problem and fracture problem are important problems in engineering practice. In this paper,one kind of contacting problem in engineering practice for the elastic half-plane with arbitrarily cracks is studied. According to the method of plane elstic complex variable, the problem is sumed to solve one kind boundary value problem for analytic functions. By using proper functions decomposition and elimination,the problem is reduced to one Rieminn's boundary value problem,solution of which is existent. Thus, the stress functions of elastic body is obtained in close form. The formulas for the stress intensity factors and the stress distribution under the punch are also derived.