钝形和锐形切口尖端应力场边界元法分析

发布时间：2019-03-21 11:19

【摘要】：工程结构中经常会遇到含切口构件,切口端部严重的应力集中或应力奇异会影响构件的安全,对切口根部的应力场展开研究具有重要的理论意义和很强的工程应用价值。本文利用边界元法计算钝形切口端部的热弹应力集中系数和锐形切口的热弹奇异应力场以及应力强度因子,分析切口端部应力集中以及奇异应力场与切口深度、切口角度的关系。本文主要研究内容如下:首先梳理了弹性力学边界元法基本理论和实施过程,利用边界元法计算平面钝形切口端部的弹性应力场。选取切口开口角度为30°、60°、90°、135°,切口端部圆孔半径为0.05mm、0.5mm、1.0mm、2.5mm的钝形切口模型,计算钝形切口角平分线上内点的应力值。研究发现最大周向应力出现在切口根部圆弧边界上,周向应力随着距切口端部距离的增加而减小,并最终趋于角平分线上的平均应力,而角平分线上的径向应力值由零增加到极值后再逐渐减小。另外,当切口开角为锐角时,周向应力、径向应力随切口张角的增大有微弱减小,但切向应力随切口张角的增大而明显减小。当切口开角为钝角时,不同圆孔半径内点的周向应力值与该切口周向应力极值的比值不随圆孔半径的变化而变化。其次引入自然热应力边界积分方程,分析了单、双材料平面钝形切口端部的热应力场,发现钝形切口端部的热应力变化规律与弹性应力场相似。又计算了平面锐形切口的奇性次数和热应力强度因子,发现对称锐形切口只有I型热应力强度因子K1,且其值随着开口角度的增加而减小,而锐形斜切口同时有I型和II型应力强度因子,且热应力强度因子K1随着斜切口倾角的增加而减少,而热应力强度因子K2却随切口倾角的增加而增加。文章同时利有限元法对结构模型进行了计算,通过和有限元结果对比,验证了边界元结果的准确性。边界元法只需沿区域的边界划分单元,可用较少的单元获得较高的计算精度,大大减轻了工程结构分析的计算量。
[Abstract]:The severe stress concentration or stress singularity at the end of the notch will affect the safety of the component. It has important theoretical significance and strong engineering application value for the study of the stress field at the root of the notch. The research on the stress field at the root of the notch has important theoretical significance and strong engineering application value. In this paper, the thermal elastic stress concentration coefficient at the end of the blunt notch, the thermal elastic singular stress field and the stress intensity factor of the sharp notch are calculated by the boundary element method, and the stress concentration at the end of the notch, the singular stress field and the depth of the notch are analyzed. The relationship between the angle of the incision. The main contents of this paper are as follows: firstly, the basic theory and implementation process of boundary element method (BEM) for elastic mechanics are combed, and the elastic stress field at the end of a plane blunt notch is calculated by using BEM. The open angle of the incision is 30 掳, 60 掳, 90 掳, 135 掳, and the radius of the round hole at the end of the incision is 0.05mm, 0.5mm, 1.0mm, 2.5mm. The stress value of the internal point on the bisection line of the obtuse notch angle is calculated. It is found that the maximum circumferential stress appears on the arc boundary at the root of the notch, and the circumferential stress decreases with the increase of the distance from the end of the notch, and finally tends to the average stress on the equalizing line of the angle. On the other hand, the radial stress value increases from zero to extreme value and then decreases gradually. In addition, when the opening angle of the notch is sharp, the circumferential stress and radial stress decrease slightly with the increase of the notch tension angle, but the tangential stress decreases obviously with the increase of the notch tension angle. When the opening angle of the notch is obtuse angle, the ratio of the circumferential stress value to the circumferential stress extremum of different circular hole radius does not change with the change of the circular hole radius. Secondly, the natural thermal stress boundary integral equation is introduced to analyze the thermal stress field at the end of blunt notch of single and double materials. It is found that the variation of thermal stress at the end of blunt notch is similar to that of elastic stress field. The singularity number and thermal stress intensity factor of plane sharp notch are calculated. It is found that there is only I type thermal stress intensity factor K _ 1 in symmetrical sharp notch, and its value decreases with the increase of opening angle. There are both I and II stress intensity factors in sharp oblique notch, and the thermal stress intensity factor K _ 1 decreases with the increase of inclined notch angle, while the thermal stress intensity factor K _ 2 increases with the increase of notch inclination angle. At the same time, the finite element method is used to calculate the structural model. By comparing with the finite element results, the accuracy of the boundary element results is verified. The boundary element method (BEM) only needs to divide the elements along the boundary of the region, and can obtain a higher calculation precision with less elements, which greatly reduces the computational complexity of the engineering structure analysis.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU31

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