拉伸载荷作用下无限大板中三角孔-裂纹问题

刘宝良, 闫相桥

哈尔滨工业大学航天学院



摘要:

针对Bueckner原理普遍化,提出了一种求解远方载荷作用下无限大板中孔边裂纹问题的数值方法.通过把适于单一裂纹的Bueckner原理扩充到远方载荷作用下无限大板中孔边裂纹问题,将原问题分解为承受远方载荷不含孔边裂纹的均匀问题和在远方不承受载荷但在裂纹面上和孔的表面上承受面力的问题.算例说明本数值方法对分析无限大板中孔边裂纹问题既简单又非常有效,进而利用这种数值方法研究了拉伸载荷作用下无限大板中三角孔-裂纹问题.通过改变孔的几何参数与无限大板中心裂纹问题的应力强度因子比较,揭示了孔的几何参数对应力强度因子的影响,发现孔对源于它的裂纹的应力强度因子具有屏蔽效应和放大效应,这种屏蔽效应和放大效应随着孔的几何参数而变化.

关键词:  孔,裂纹  应力强度因子  边界元  裂尖单元  位移不连续

DOI：10.11918/j.issn.0367-6234.2011.07.011

分类号:O346.1

基金项目:国家自然科学基金资助项目(10672046)



Triangle hole-crack problem in infinite plate in tension

LIU Bao-liang, YAN Xiang-qiao

School of Astronautics,Harbin Institute of Technology,150001 Harbin,China

Abstract:

By extending Bueckner’s principle suited for a crack to a hole crack problem in infinite plate in tension,here,the original problem(the hole crack problem in infinite plate in tension) is divided into a homogeneous problem(the one without hole crack) subjected to remote loads and a hole crack problem in an unloaded body with applied tractions on the surfaces of hole and crack. Numerical results illustrate that the approach is very simple and effective for analyzing the hole crack problem in infinite plate in tension and by which a crack emanating from a triangle hole in infinite elastic plate in tension is analyzed in detail.The effect of hole geometry parameters on the stress intensity factors is revealed.It is found that a hole has a shielding and an amplifying effect on the stress intensity factors of crack emanating from the hole,and the shielding and amplifying effects varied with hole geometry parameters.

Key words:  hole  crack  stress intensity factor  boundary element  crack-tip element  displacement discontinuity