导　　师： 杨晓春

学科专业： G0105

授予学位： 硕士

作　　者： ;

机构地区： 大连海事大学

摘　　要： 近几年来,断裂力学方面的研究十分活跃,并在该领域取得了卓越的成就。传统的裂纹模型往往是建立在线裂纹的基础上,但20世纪70年代著名物理学家陈篪先生在他的论文中提出了关于钝裂纹的观点,即从真实裂纹出发讨论相关因子对材料的影响,钝裂纹的研究开始发展起来。 本论文正是基于此背景,讨论了一弹性半无限平面体中含一钝裂纹的静力学问题。文章的第一部分为绪论,介绍了断裂力学的研究背景,线弹性断裂力学理论,以及对钝裂纹的认识和发展现状；第二章简单介绍了线弹性力学中一些相关的基本知识,为模型的建立奠定了理论基础；论文的第三章提出半无限平面边界钝裂纹问题,给出边界条件,在此基础上利用D.I.Sherman方法建立边界裂纹L0+L1上的积分方程,通过反演变换将原问题化简为只在裂纹L1上的奇异积分方程问题；为了求解方程的数值解,第四章介绍了求解此奇异积分方程的相关理论和求解方法,通过使用Gauss求积公式对方程进行离散化简；第五章中给出了数值算例,通过Matlab绘制复Airy函数、正应力以及剪应力在裂纹尖端的变化趋势,更加直观的反映了应力集中等现象的变化特点,揭示了这些参量与真实模型的内在联系；本文的最后一章总结了所提出模型的物理参量所反映的力学特征和变化特点,并对此课题的发展进行了展望。 Recently, some scholars have studied the subject on fracture mechanics actively, and made remarkable achievements in this field. They always explored the crack model without width. But the famous physicist, Mr. Chen Chi, found the crack with width in the experiment, and published viewpoint about the crack with width in the 1970s in his paper. The paper is based on this background. The static problem in elastic semi-infinite plane with a width edgecrack has been discussed. The first part of the article is the introduction. It describes the fracture mechanics research background, the linear elastic fracture mechanics theory and the developments about the width cracks.The second part briefly introduces the basic knowledge on linear elasticity mechanics. It makes preparations for the following model building. The third chapter in this paper points out the model boundary condition, and establishs the edgecrack model equation by the D. I. Sherman Methods. Then it is to simplify the model into singular integral equation question on a crack. To obtain the numerical solution of equations, the fourth chapter introduces the relevant basic theory and methods. The equation is dispersed by using the Gauss quadrature formula. In chapter five, a numerical example is given. The Complex Airy functions, the normal stress and shear stress trends are drawn by Matlab. These trends reflect intuitively the changes of the crack tip. Finally, the last part summarizes the mechanical characteristics that the physical parameters of the model reflects, and introduces the prospect.

关 键 词： 半无限平面 钝裂纹 弹性材料 奇异积分方程

分 类 号： [V21 TM2]

领　　域： [航空宇航科学与技术] [航空宇航科学技术] [电气工程] [一般工业技术]