高精度求解应力强度因子的数值外插法  

NUMERICAL EXTRAPOLATED METHOD FOR CALCULATING SIF ACCURATELY

作　　者：李和平[1] 巫绪涛[1] 杨伯源[1] 

机构地区：[1]合肥工业大学土建学院,合肥230009

出　　处：《机械强度》2001年第2期209-212,共4页Journal of Mechanical Strength

摘　　要：首先介绍求解应力强度因子的传统蜕化奇异等参元法和一种新型的数值外插法 ,两种方法均在裂尖使用精度较高的蜕化奇异二次等参元。考虑到传统方法受裂尖单元尺寸大小、结构物类型、材料泊松比影响较大等缺陷 ,新方法使用了不同的插值手段。其次 ,讨论了两种方法插值基础的显著区别 ,结合空间Ⅰ型裂纹问题论证了新型数值外插法的插值基础 ,研究了两种方法的理论插值误差 ,发现本文提出的数值外插法比传统的蜕化奇异等参元法的理论精度高一阶。最后 ,对两种方法的计算误差进行了探讨。数值外插法考虑到有限元计算断裂问题的误差 ,能以一定的方式决定不同裂纹问题的优化裂尖单元尺寸。The collapsed singular isoparametric element's method and a numerical extrapolated new method for calculating the stress intensity factor are introduced at first. Both methods use the collapsed singular quadratic isoparametric elements. The crack tip element size, type of structure and material's Poission ratio have a pronounced influence on accuracy of the tradition method. These defects are taken into account. So the different extrapolated technique is used in the new method. The marked difference between the extrapolated basis of both methods are discussed secondly. The theoretical basis of the numerical extrapolated method are proved with 3D crack problem. The theoretical error of both methods are evaluated. Better accuracy has been found for the numerical extrapolated method. The calculative error of both methods are discussed at last. The calculative error of FEM is considered by the numerical extrapolated method. The optimum size of crack tip element for different crack problems can be obtained fr om the new method.

关 键 词：数值外插法 蜕化奇异等参元 应力强度因子 平面应力 平面应变 

分 类 号：O346[理学—固体力学]