航空学报 > 1981, Vol. 2 Issue (3): 31-41

用杂交应力元及等参元计算应力强度因子

何积范1, 常亮明1, 高占民1, 李洲圣2, 孙笃信2   

  1. 1. 清华大学2. 红安飞机公司研究所
  • 收稿日期:1980-08-15 修回日期:1900-01-01 出版日期:1981-09-25 发布日期:1981-09-25

CALCULATION OF STRESS INTENSITY FACTORS WITH HYBRID STRESS ELEMENTS AND ISOPARAMETRIC ELEMENTS

He Jifan1, Chang Liangming1, Gao Zhanmin1, Li Zhousheng2, Sun Duxin2   

  1. 1. Qinghua Universiiy;2. Institute of Hongan Aircraft Company
  • Received:1980-08-15 Revised:1900-01-01 Online:1981-09-25 Published:1981-09-25

摘要: 本文介绍一种用奇异性杂交应力元及等参元计算平面裂纹的应力强度因子和J积分的方法。实际计算表明,此种方法的优点是精度高,计算时间短,便于实际应用。文中给出三个算例。各例分别采用216~256个自由度。计算结果同解析解及其他奇异元的解进行了比较。各例算得的应力强度因子值,均同解析解相差仅1~2%。每例中由4~6条路径求得的J积分值,其分散度均在±O.7%以内。 计算在TQ-16机上进行,程序编译约6~7分钟,每例的计算时间约6~8分钟。

Abstract: Hybrid stress elements and isoparametric elements are adopted to calculate stress intensity factors and J-integral of plane cracks in this paper. At every crack tip, an array of singular hybrid stress elements as sectors with parabolical arcs is arranged. Each sector is connected to a quadrilateral isoparametric element with eight Nodal points. The principle how to use the two types of elements mixedly is interpreted in this paper. The advantages of the method are the following.( 1 ) The singular elements adopted as sectors can give a better description of the hoop stress distribution in the vicinity of a crack tip;( 2 ) The isoparametric elements are adaptable to every kind of curve boundary, and simple and convenient to calculate;( 3 )J-integral can be calculated quite accurately in the isoparametric element region, so that it can be extended to elasto-plasticity calculation of plane cracks.Three numerical examples are given as follows:( 1 ) a rectangular sheet with equal length edge cracks in both sides;( 2 ) a rectangular sheet with a long crack in single side; ( 3 ) a rectangular sheet with a oblique crack.Every sheet is stressed under single uniform tensile load. 216-256 degrees of freedom are adopted in every example respectively. Comparison o f the obtained results with those of analytical and other singular element solutions shows that the values of the stress intensity factors obtained in every example, whether those were solved from the linear equations or came from J-integral values, are all in good agreement. The errors are only within 1 - 2 %. The scatter degrees of J-integrals from 4 - 6 integral pathes in each example are only within±0.7%.By carrying out practical calculations it is shown that the advantages of the method are high accuracy, reduced computer run time, and adaptability to practical application.