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| Analysis of crack problems by Williams generalized parametric element |
| Received:March 03, 2007 |
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| DOI：10.7511/jslx20091006 |
| KeyWord:stress intensity factor Williams element transition element finite element with generalized parametric finite element |
| Author | Institution |
| 杨绿峰 |
广西大学 土木建筑工程学院 工程防灾与结构安全重点实验室,南宁 |
| 徐华 |
广西大学 土木建筑工程学院 工程防灾与结构安全重点实验室,南宁 |
| 彭俚 |
广西大学 土木建筑工程学院 工程防灾与结构安全重点实验室,南宁 |
| 李冉 |
广西大学 土木建筑工程学院 工程防灾与结构安全重点实验室,南宁 |
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| Abstract: |
| The Williams generalized parametric element and the transition element are developed for mode Ⅱ crack problems. The relationship between the leading coefficients of the Williams series and the stress intensity factor is obtained. The finite self-similar elements are generated in the singular domain around the crack tip. Based on the Williams series and the method of finite element with generalized degrees of freedom, the global and local displacement fields near the tip are described by Williams expansion series and the conventional shape function of the FEM, respectively. The Williams element and the transition element are proposed, respectively. The influence of the radial discretizing ratio, radial partition number in singular domain and the number of the terms of the Williams expansions on computing precision are illustrated, their design values are presented. The influence of the plate’s dimensions on the stress intensity factor is analyzed. Several examples are used to demonstrate the accurate and convenient determination of the stress intensity factor by the proposed element. |
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