三维切口板应力奇异性分析

发布时间：2018-11-09 12:12

【摘要】：含切口构件广泛存在于各种实际工程结构中,切口尖端的应力奇异严重影响含切口构件的使用安全。本文总结了近年来理论和数值研究切口的成果,在此基础上,基于有限元法对三维切口根部区域的奇异应力场展开详细研究。主要分析了荷载模式、切口样式、尺寸效应和泊松比等因素对面外奇异性的影响。全文的工作内容及主要结论如下:(1)研究了V形切口板在平面剪切荷载作用下的面外奇异性。结果表明,在远场剪切荷载作用下,切口根部区域会产生一个耦合的面外奇异应力场,该场在靠近外表面的区域内有剧烈的变化。随着切口开角的增大,II型应力场的奇异性逐渐消失,O型应力场始终保持着奇异性。由于奇性指数的不同,面外奇异模式随着切口板尺寸的增大而越发重要。(2)分别对受平面剪切荷载作用的含钝化V形切口、圆形切口和椭圆形切口板的应力场进行了分析,并研究了泊松比对这种面外应力集中的影响。结果表明,增大切口的根半径可显著减小面外应力集中的强度。由于泊松效应导致的侧向收缩是引发面外奇异性的主要因素,面外应力场的强度随泊松比的增大而增大。二维分析得到的理论应力集中系数和三维分析所得结果之间存在一定的差距,这个差距也随着泊松比的增大而越来越大。(3)研究了V形切口板在反平面荷载作用下的耦合奇异应力场。结果表明,在厚度方向上,II型应力场关于中平面反对称分布,III型应力场关于中平面对称分布。III型应力场的强度随泊松比的增大而减小,II型应力场的强度受泊松比的影响较小。(4)对含中心切口板的三维奇性应力场进行了分析。结果表明,三维切口板厚度方向各平面内的切口奇性特征规律均遵循经典平面理论,不因外部荷载形式的改变而改变,但在板厚度方向上应力强度因子的变化规律却受荷载形式的影响。
[Abstract]:Notched members are widely used in various practical engineering structures. The stress singularity at the notch tip seriously affects the safety of the notched members. In this paper, the theoretical and numerical results of notch research in recent years are summarized. On this basis, the singular stress field in the root region of a three-dimensional notch is studied in detail based on the finite element method. The effects of load mode, notch pattern, size effect and Poisson's ratio on the external singularity are analyzed. The main conclusions are as follows: (1) the out-of-plane singularity of V-notched plate under plane shear load is studied. The results show that a coupled out-of-plane singular stress field is produced in the root region of the notch under the far-field shear load, and the field changes dramatically in the region near the outer surface. With the increase of the notch opening angle, the singularity of the II stress field gradually disappears, and the O-type stress field always maintains singularity. Because of the difference of singularity exponent, the out-of-plane singularity mode becomes more and more important with the increase of notch size. (2) the stress fields of V-shaped notch, circular notch and elliptical notch with plane shear load are analyzed, respectively. The influence of Poisson's ratio on the stress concentration is studied. The results show that the strength of stress concentration can be significantly reduced by increasing the root radius of the notch. The lateral contraction caused by Poisson effect is the main factor to trigger the out-of-plane singularity. The strength of the out-of-plane stress field increases with the increase of Poisson's ratio. There is a certain gap between the theoretical stress concentration factor obtained by two-dimensional analysis and the result obtained by three-dimensional analysis. The gap also increases with the increase of Poisson's ratio. (3) the coupled singular stress field of V-notched plate under anti-plane load is studied. The results show that, in the thickness direction, the stress field of the II type is the antisymmetric distribution of the middle plane, and the stress field of the III type is the symmetrical distribution of the plane in the middle plane. The strength of the stress field of the III type decreases with the increase of Poisson's ratio. The strength of the II stress field is less affected by Poisson's ratio. (4) the three-dimensional singular stress field of the plate with central notch is analyzed. The results show that the singularities of the notches in each plane in the thickness direction of the three dimensional notched plates follow the classical plane theory and do not change with the change of the external load form. However, the variation of the stress intensity factor in the direction of plate thickness is affected by the load form.
【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】：TU311

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