各向异性两相材料尖劈奇性场的非协调元分析  

A NON-CONFIRMING FINITE ELEMENT ANALYSIS OF SINGULAR FIELDS IN PRISMATIC ANISOTROPIC BIMATERIAL WEDGES

作　　者：平学成[1] 谢基龙[1] 陈梦成[2] 李强[1] 

机构地区：[1]北京交通大学机械与电子控制工程学院,北京100044 [2]华东交通大学土木建筑学院,南昌330013

出　　处：《力学学报》2005年第1期24-31,共8页Chinese Journal of Theoretical and Applied Mechanics

基　　金：江西省自然科学基金(0112001).~~

摘　　要：提出了一个基于位移的、分析柱状各向异性两相材料尖劈端部邻域的奇性位移场和应力场问题的非协调元特征分析法．该方法从柱状扇区的散度定理出发，将柱状扇区控制方程的弱式化为一个与虚功原理相同形式的方程，采用一种新的非协调元技术把所导出的“虚功原理”转化为标准一阶特征方程的求解问题．非协调元法中，尖劈端部邻域的位移场假定没有采用奇异变换技术，有限元的单元形式是一维的．将柱状各向异性两相材料尖劈视为“广义平面应变”问题，位移场与坐标 z 无关，只关注界面端的幂奇异性而不考虑对数奇异性．运用该方法给出了柱状各向异性两相材料尖劈端部奇性应力指数、奇性位移角分布和应力角分布的算例．所有的计算结果表明，该方法使用的单元少而且精度较高．A non-confirming finite element eigenanalysis method(NFEEM)based on displacement is developedin this paper to study the singular displacement and stress fields surrounding the tips of prismatic anisotropicbimaterial wedges.This method starts from the Divergence Theorems for prismatic sectorial domains,basedon which the weak form of governing equations composed of stress equilibriums conditions and wedge boundaryconditions are transformed into that with the same form of Virtual Work Principal.In order to solve thesingular displacement and stress fields,a kind of non-confirming finite element method is used to discretizethe“Virtual Work Principal”.Finally,a standard first order characteristic equation is deduced.From thecharacteristic equation a certain number of eigenvalues and eigenvecters can be solved correspondingly.Thenumerical solutions of stress singularities and angular variations of singular displacement and stress fields onnodes can be obtained.If the generalized stress factors are known,the NFEEM can be used to solve the exactsingular displacement and stress fields surrounding the tips of prismatic anisotropic bimaterial wedges,so thework of this paper provides a new numerical method for singular field solutions.Compared with the existingfinite element eigenanalysis methods(Pageau SS et al 1996),current method has a novel jump-off,the formof the element is a kind of one-dimensional non-confirming element,and the singular transformation techniqueis not used in the assumption of displacement fields surrounding the wedges tips.Therefore,although thedisplacement fields of prismatic sectorial domains are also asymptotic in the radial direction measured fromthe singular point,it is a(n+1)-degree polynomial in the angular coordinate direction,in which n is thenumber of imaginary interpolation points because of additive displacement items in an element.In the currentpaper,the three-dimensional prismatic sectorial domains have been considered as“generalized plane strain”problems,the displacement assumpti

关 键 词：线弹性断裂 奇性应力指数 两相材料尖劈 非协调元法 广义平面应变 

分 类 号：O346.1[理学—固体力学]