应力强度因子分析的三角形Williams单元  

Triangular Williams element for stress intensity factor analysis

作　　者：杨绿峰[1,2] 徐华[1] 汪梅兰[1] 

机构地区：[1]广西大学土木建筑工程学院工程防灾与结构安全教育部重点实验室,南宁530004 [2]广西壮族自治区住房与城乡建设厅,南宁530028

出　　处：《应用力学学报》2011年第6期570-575,670,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(50768001;51168003);广西科学基金项目(桂科自0991020Z;2010GXNSFD169008);广西教育厅博士创新基金项目(T31040);工程防灾与结构安全教育部重点实验室主任基金项目(2009TMZR004);广西大学科研基金项目(XGL090004)

摘　　要：弹性断裂分析的Williams广义参数单元计算模型中忽略了紧邻裂尖的微区域,为了进一步完善该计算模型,本文提出并建立了三角形Williams单元。首先围绕裂尖将奇异区均匀分割为有限个三角形单元,利用改进的Williams级数建立该单元的整体位移场计算模型;其次沿径向将该三角形单元进一步离散为多个相似四边形微单元和裂尖三角形微单元,并利用经典有限元理论建立微单元的局部位移场计算模型;然后利用整体位移场控制各微单元结点位移,并在此基础上研究建立裂尖奇异区三角形Williams单元及其控制方程。该单元模型中含有与裂尖应力强度因子相关的参数,能够直接计算裂尖处的应力强度因子。最后结合算例详细分析了三角形Williams单元计算模型中径向离散因子、离散数、Williams级数项对计算结果的影响。算例分析表明,三角形Williams单元所得的应力强度因子具有对奇异区尺寸不敏感的优点,且收敛快,计算精度高。The micro domain neighboring to the crack tip is neglected in the model of Williams element with generalized degrees of freedom(DOFs) in elastic fracture mechanics.A new triangular Williams element is proposed to perfect the model.The singular region around the crack tip is evenly divided alone the tangent direction into several triangular elements,which can be approximated by the modified Williams series.This element is further refined along the radial direction by a number of quadrilateral micro-elements as well as a triangular micro-element neighboring to the crack tip,whose displacement fields can be developed according to the conventional finite element method.The nodal displacements of the micro-element should be governed by the global displacement field of the triangular element,so that the triangular Williams element with generalized DOFs is presented for discretizing the singular region around the crack tip and can be used to evaluate directly the stress intensity factor at the crack tip.The influence of the radial scale factor,the number of discretized elements and the terms of Williams series on the results is discussed.Examples provided demonstrate that the triangular Williams element is insensitive to the size of singular region with satisfied convergency and accuracy.

关 键 词：Williams单元 三角形 应力强度因子 广义参数 

分 类 号：TU318[建筑科学—结构工程]