Meshless numerical manifold method based on unit partition

In this paper the meshless numerical manifold method ispresented based on the numerical manifold method and the partition of unitymethod. In meshless numerical manifold method, two cover systems areemployed. The mathematical cover system provides the nodes for formingfinite covers of the solution domain and the partition of unityfunctions, and the physical cover system describes geometry of the domain of theproblem and the discontinuous surfaces in the domain. The shape function inthis method is formed by the partition of unity and the finite covertechnology, so the shape functions cannot be affected by discontinuousdomain, and crack problems can be treated better. To local problems, theshape functions are more effective than other method. So the method canavoid the disadvantages in other meshless methods in which the tip of thediscontinuous crack is not considered. Comparing with the conventionalnumerical manifold method, the shape of the finite cover can be selectedeasily. And the finite covers and the partition of unity functions areformed with the influence domains of a series of nodes. So the meshlessmanifold method has some advantages of the meshless and gets rid of thedisadvantage of the mesh in the numerical manifold method. Comparing withthe conventional meshless method, finite cover technology is used in themethod, and then the test functions cannot be influenced by thediscontinuity in the solving domain. And this method can conquer somedifficulties in the conventional meshless methods for the problems with adiscontinuous domain. The test function and the equations of the meshlessnumerical manifold method are obtained in detail. And a numerical example isgiven and it shows the method in this paper is correct.