JP Journal of Solids and Structures Volume 1, Issue 1, 2007, Pages 61-91 This paper is available online at http://www.pphmj.com  2007 Pushpa Publishing House : phrases and Keywords higher order displacement discontinuity elements, cubic elements, special crack tip elements, crack analysis, finite, infinite and semi-infinite plane problem. Received September 9, 2006 A NEW CUBIC ELEMENT FORMULATION OF THE DISPLACEMENT DISCONTINUITY METHOD USING THREE SPECIAL CRACK TIP ELEMENTS FOR CRACK ANALYSIS MOHAMMAD FATEHI MARJI 1 , HASAN HOSSEINI_NASAB 2 and AMIR HOSSEIN KOHSARY 1 1 Mining Engineering Faculty Yazd University, Yazd, Iran e-mail: mfatehi@yazduni.ac.ir; kohsary@yahoo.com 2 Industrial Engineering Faculty Yazd University, Yazd, Iran e-mail: hhn@yazduni.ac.ir Abstract Three special crack tip elements are implemented in a two dimensional displacement discontinuity method using cubic elements formulation to solve crack problems. This method uses four collocation points for each element (i.e., two sub-elements at either side of center of the element in question), and is modified so that it is able to model elastostatic and crack problems in finite, infinite and semi-infinite planes. Therefore each element has a third order (cubic) distribution of displacement discontinuity but only two degrees of freedom, which more efficiently improve the accuracy of the conventional displacement discontinuity method. A hybrid element approach is used for the analysis of crack problems by incorporating a special treatment for crack tips. A crack with any arbitrary geometry can be modeled by this technique. To verify this method and show its accuracy and effectiveness, some example