Spiral weight for modeling cracks in meshless numerical methods

Abstract

In the last decade several different approaches have been developed to study arbitrary static and dynamic cracks. Among these methods meshless techniques play an important role. These methods provide an accurate solution of a wide range of fracture mechanics problems while traditional methods such as finite element and boundary element have limitations. We wish to increase the accuracy of the meshless approximations without increasing the nodal density. This is done by an appropriate modification of the weight function near crack tips. Earlier attempts still had limitations that result in a lack of accuracy, especially in the case when a linear basis is used. In this work a new technique, the spiral weight, is introduced that minimizes the drawbacks of existing methods. Numerical examples show that the spiral weight method is more efficient than existing methods, when using a linear basis, for the solution of crack problems.