SUMMARYThe extended ÿnite element method (X-FEM) proposed by Belytschko et al. (International Journal for Numerical Methods in Engineering 1999; 45:602;1999; 46:131; 50:993) uses interpolation functions based on the concept of partition of unity, and considers the asymptotic solution and the discontinuity of displacement ÿelds near a crack independently of the ÿnite element mesh. This paper describes the application of X-FEM to stress analyses of structures containing interface cracks between dissimilar materials. In X-FEM, an interface crack can be modelled by locally changing an interpolation function in the element near a crack. The energy release rate should be separated into individual stress intensity factors, K 1 and K 2 , because the stress ÿeld around the interface crack has mixed modes coupled with mode-I and mode-II. For this purpose, various evaluation methods used in conjunction with numerical methods such as FEM and BEM are reviewed. These methods are examined in numerical examples of elastostatic analyses of structures containing interface cracks using X-FEM. The numerical results show that X-FEM is an e ective method for performing stress analyses and evaluating stress intensity factors in problems related to bi-material fractures.

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SUMMARYThe meshless method is expected to become an e!ective procedure for realizing a CAD/CAE seamless system for analyses ranging from modelling to computation, because time-consuming mesh generation processes are not required. In the present study, a new meshless approach, referred to as the Node-By-Node Meshless method is proposed, in which only nodal data is utilized to discretize the governing equations, which are derived using either the principle of virtual work or the Galerkin method. In this method, three key methodologies are utilized: (i) nodal integration using stabilization terms, (ii) interpolation by the Moving Least-Squares Method, and (iii) a node-by-node iterative solver. This paper presents the formulation of the proposed method along with numerical results obtained for two-dimensional elastostatic and eigenvalue problems.

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