Three dimensional singular element

Abstract

The finite element method has become a powerful tool for computation of stress intensity factors in fracture mechanics. The simulation of singular behavior in the stress field is accomplished using “quarter points,” following the methods of Barsoum[1] and Henshell-Shaw[2]. The analysis has also been extended to cubic elements [3] and transition elements [4]. However, these concepts cannot be easily extended to three dimensional cases without additional conditions. Progress has been hampered firstly due to a variety of possible shapes the element may possess near the singular edge of the crack, and secondly due to the complexity of algebraic expressions that have to be manipulated. In the present investigation we extensively used MACSYMA[5], a large symbolic manipulation program at MIT, thereby alleviating some of these difficulties. A simple condition between mid-side nodes has been derived which simulates the proper singular behavior along the crack. In the investigation we first study a simple collapsed brick element. This is then generalized to a curved crack front. A few results are derived which can be used to compute the stress intensity factors. The concept of the transitional element has also been outlined. The stability of singular element has been discussed. Some of these ideas have been applied to a specific problem with unusual crack geometry. The analysis was carried out using ADINA on VAX machine. ADINA was implemented on VAX by W. E. Lorensen.