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.

Uncertain eigenvalue problem of linear vibration is analyzed by means of the stochastic finite element method, the basis of which utilizes mean-centered second order perturbation technique. Attention is paid to the fluctuation of the stacking sequence, that is, fiber orientation and layer thickness of FRP laminated plates. The stacking sequence is expressed in terms of probabilistic variables. The eigenvalue problem is formulated based on the Kirchhoff-Love’s theory of thin plate, the stretching, coupled and bending stiffnesses of which are uncertain due to the stacking sequence. The numerical analyses deal with the vibration of simply-supported graphite/epoxy plates. The sensitivity of the input stacking sequence and the correlation coefficients of the probabilistic variables are evaluated quantitatively.

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