用切口尖端单元分析各向异性材料中多边形孔奇异性应力场

ANALYSIS OF SINGULAR STRESS FIELDS OF POLYGONAL HOLES IN AN ANISOTROPIC MATERIAL WITH A CORNER TIP ELEMENT

该文提出了一种基于全数值方法的新型杂交元方法,用于研究各向异性复合材料中多边形孔奇异性应力场干涉问题。该方法的建立分3个步骤:首先,用一维有限元方法求解各向异性材料切口尖端奇异性应力场数值特征解;然后,采用杂交有限元列式构造一种超级切口尖端单元,其中,假设应力场和位移场是利用上述奇异性场数值特征解推导出来的;最后,将上述超级切口尖端单元与传统4结点杂交应力元组装,得到新型杂交元方法。算例中,将裂纹问题作为考核例,并进一步考察双菱形孔和双矩形孔的奇异性应力干涉问题。算例表明:当前模型能降低单元数,且精度好;与传统有限元法和积分方程方法相比,该模型更具有通用性和高效性,为各向异性材料的细观力学分析打下了基础。

A novel hybrid finite element method based on a full numerical procedure is proposed to compute the singular field in the interaction of double polygonal holes in anisotropic material.The novel hybrid finite element method is established by the following three steps： 1） an ad hoc one-dimensional finite formulation is employed to determined the numerical eigensolution of the singular field near an angular corner;2） a super corner element is constructed to determine the strength of the singular field,in which the independent assumed stress fields are extracted from the numerical eigensolution obtained from previous ad hoc one-dimensional finite element formulation;3） a novel hybrid finite element equation is obtained by coupling the super corner element with conventional hybrid stress elements.In numerical examples,a central crack problem is firstly considered to validate the present method,and then singular stress fields for interacting double diamond holes and double rectangular holes are investigated.The numerical results show that present method yields satisfactory results with fewer elements.Compared with conventional finite element methods and integral equation methods,the present method is more suitable to deal with micromechanics of anisotropic materials.