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

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.