A higher order displacement discontinuity method for analysis of crack problems

A new formulation of a higher order displacement discontinuity method is developed to model two-dimensional elastostatics problems. The new method uses three collocation points for each element, one at the center of the element in question and the others at the centers of the adjacent elements. Each element therefore has a second-order (quadratic) distribution of displacement discontinuity but only two degrees of freedom, which contributes to the efficiency of the approach. By incorporating a special treatment for crack tips, a crack with arbitrary geometry can be modeled. The accuracy of the method is demonstrated by example problems; the results are in good agreement with the analytical solutions and show that the new method is comparable to, but more efficient than, the conventional higher order displacement discontinuity method.