JP Journal of Solids and Structures
Volume 1, Issue 1, Pages 61 - 91
(March 2007)
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A NEW CUBIC ELEMENT FORMULATION OF THE DISPLACEMENT DISCONTINUITY METHOD USING THREE SPECIAL CRACK TIP ELEMENTS FOR CRACK ANALYSIS
Mohammad Fatehi Marji (Iran), Hasan Hosseini Nasab (Iran) and Amir Hossein Kohsary (Iran)
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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 problems in finite, infinite and semi-infinite planes are solved numerically. Then the numerical results (e.g., Mode I and Mode II stress intensity factors) computed by the proposed method are compared with those cited in the literature. The solved examples demonstrate that this method is comparable, but more efficient than, the conventional displacement discontinuity method. Although, this method can be hybridized with other numerical methods, but because of its high accuracy, in many cases, there may be no need to use the more complicated hybridized forms, especially when two or more special crack tip elements are also added to increase the accuracy of its numerical results near the crack ends. In this study the formulation of three special crack tip elements for obtaining their displacement discontinuities is derived and coded carefully. Although using three special elements for the treatment of each crack tip is somewhat complicated but it will highly increase the accuracy of the displacement discontinuity variations near these singular ends. |
| Keywords and phrases: higher order displacement discontinuity elements, cubic elements, special crack tip elements, crack analysis, finite, infinite and semi-infinite plane problem. |
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