A new formulated method of a quasi-compatible finite-element and its application in fracture-mechanics

Abstract Based on the local properties of a singular field, the displacement pattern of an isoparametric element is improved and a new formulated method of a quasi-compatible finite element is proposed in this paper. This method can be used to solve various engineering problems containing singular distribution, especially, the singular field existing at the tip of cracks. The singular quasi-compatible element (SQCE) is constructed. The characteristics of the element are analysed from various angles and many examples of calculations are performed. The results show that this method has many significant advantages, by which, the numerical analysis of brittle fracture problems can be solved.