摘 要

工程结构中经常会遇到含切口构件，而切口端部严重的应力集中会对结构的安全造成严重的影响，所以研究切口端部应力场不仅有着很强的经济价值，也存在着重要的意义，本文基于切口强度理论和有限元方法分析研究钝形切口和V形切口端部的应力集中现象及其相应的应力变化规律，分析切口端部应力集中现象与圆孔半径、开口角度的关系。主要研究内容如下：

本文首先介绍了本文的研究背景和意义以及国内外研究现状，表明了本文的研究对工程具有很大的意义；其次引入了计算平面钝形和V形切口应力场的方程，并通过理论公式计算了钝形切口构件应力场大小以及应力集中系数。

本文的核心内容在于通过有限元数值计算研究不同切口端部的应力集中现象和变化规律；选取钝形切口和V形切口的模型，控制钝形切口的开口角度和圆孔半径以及V形切口的圆孔半径进行分析，并与理论公式所计算的应力值进行比较，可以得出：所有构件的切口端部附近都存在应力集中现象；对于钝形构件，其径向应力值都是一开始随距切口前端距离的增加而增大，增加到最大值后再逐渐减小，但其周向应力值是逐渐减小的，并且可以得出应力值变化与开口角度大小关系不明显，但与圆孔半径的大小有着明显的关系，圆孔半径越大，其应力值越小；对于V形构件，其应力值变化均随距切口前端距离的增加而减小；对比于理论公式，有限元计算结果与理论公式求解结果一致，且在一定范围内，双材料弹性模量比值越大，其应力值也越大。

关键词：有限元；切口应力；应力场；异种材料

Abstract

Engineering structures often encounter members with incisions, and severe stress concentration at the ends of the incision will have a serious impact on the safety of the structure. Therefore, studying the stress field at the end of the incision not only has strong economic value, but also has important significance. Based on the notch strength theory and the finite element method, this paper analyzes the stress concentration phenomena at the ends of blunt and V-shaped incisions and their corresponding stress changes, and analyzes the relationship between the stress concentration phenomena at the ends of the incision and the radius of the circular hole and the opening angle. The main research contents are as follows:

This paper first introduces the research background and significance of this paper and the current research status at home and abroad, showing that the research of this paper has great significance for engineering; secondly, the equations for calculating the stress field of plane blunt and V-shaped cuts are introduced and calculated by theoretical formulas The stress field size and stress concentration factor of blunt-shaped notch members are given.

The core content of this paper is to study the stress concentration phenomenon and change law of different cut ends by finite element numerical calculation; select the model of blunt cut and V-shaped cut, control the opening angle and radius of round hole of blunt cut and the V-shaped cut The radius of the circular hole is analyzed and compared with the stress value calculated by the theoretical formula. It can be concluded that all members have stress concentration near the cut end; for blunt members, the radial stress value is initially The distance from the front end of the incision increases and increases, and then gradually decreases after increasing to the maximum value, but its circumferential stress value gradually decreases, and it can be concluded that the relationship between the change in stress value and the opening angle is not obvious, but it is not The size of the hole radius has an obvious relationship. The larger the radius of the round hole, the smaller the stress value. For the V-shaped member, the change in stress value decreases with the increase of the distance from the front end of the cut; compared with the theoretical formula, finite element calculation The result is consistent with the solution of the theoretical formula, and the greater the ratio of the bi-material elastic modulus, the greater the stress value.

Keywords: finite element; notch stress; stress field; dissimilar materials目 录

第一章 绪论 1

1.1 引言 1

1.2 异种材料破坏及其应力奇异效应 4

1.3 异种材料应力场和疲劳评估方法 5

1.3.1 异种材料应力场 6

1.3.1 疲劳评估方法 6

1.4 本文的主要研究内容 8

第二章 平面切口弹性应力场理论分析 10

2.1 平面构件切口 10

2.2 平面V形切口应力场 10

2.3 平面钝形切口应力场 12

第三章 平面切口计算模型的建模与计算 15

3.1 单材料平面切口计算分析 15

3.1.1 单材料平面切口几何模型 15

3.1.2 收敛性分析 16

3.1.3 平面V形切口计算结果 18

3.1.4 平面钝形切口计算结果 20

3.2 双材料平面切口计算分析 24

3.2.1 双材料平面切口几何模型 24

3.2.2 平面V形切口计算结果 25

3.2.3 平面钝形切口计算结果 27

3.3 本章小结 29

第四章 结论与展望 31

4.1 结论 31

4.2 展望 32

参考文献 33

致谢 36

第一章 绪论

1.1 引言

通常来说，在结构中使用异种材料（钢-铝；土木工程材料；复合材料等）的优点就是满足结构的发展要求，例如的就是结构轻量化、功能一体化或者低成本设计与制造的这些功能。所以，在如今这个时代，人们越来越重视异种材料的使用，例如，钢-铝材料就是异种材料的一种运用。目前，对于异种材料的使用，已经广泛应用于汽车、飞机、微结构以及焊接接头等各个方面，并且具有良好的经济收益，如下图1.1就是异种材料应用于汽车行业。