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SUMMARYA new method for the simulation of particulate ows, based on the extended ÿnite element method (X-FEM), is described. In this method, the particle surfaces need not conform to the ÿnite element boundaries, so that moving particles can be simulated without remeshing. The near ÿeld form of the uid ow about each particle is built into the ÿnite element basis using a partition of unity enrichment, allowing the simple enforcement of boundary conditions and improved accuracy over other methods on a coarse mesh. We present a weak form of the equations of motion useful for the simulation of freely moving particles, and solve example problems for particles with prescribed and unknown velocities.

In this paper, meshfree simulations of large deformation of thin shell structures is presented. It has been shown that the window function based meshfree interpolants can be used to construct highly smoothed (high order``manifold'') shape functions for three-dimensional (3-D) meshfree discretization/interpolation, which can be used to simulate large deformation of thin shell structures while avoiding ill-conditioning as well as stiffening in numerical computations.The main advantage of such 3-D meshfree continuum approach is its simplicity in both formulation and implementation as compared to shell theory approach, or degenerated continuum approach. Moreover, it is believed that the accuracy of the computation may increase because of using 3-D exact formulation. Possible mechanism to relieve shear/volumetric locking due to the meshfree interpolation is discussed. Several examples have been computed by using a meshfree, explicit, total Lagrangian formulation. Towards to developing a self-contact algorithm, a novel meshfree contact algorithm is proposed in the end.

This paper presents a continuum-based sheardeformable ®nite element formulation for geometrically nonlinear analysis of thick layered composite shells. The proposed variational formulation is based on an assumed strain method. From a kinematical viewpoint displacements and rotations are assumed ®nite while strains are in®nitesimal. The model is then cast in a co-rotational framework which is derived consistently from the updated Lagrangian method. Close relationship between the co-rotational procedure and the underlying updated Lagrangian procedure is presented to highlight the ef®ciency of the method for application to composite shell analysis. Numerical examples are presented to demonstrate the accuracy and the range of applicability of the proposed formulation. IntroductionLaminated structures made of advanced ®lamentary composite materials continue to be of great interest for engineering applications. Their high strength to weight ratio and the¯exibility to tailor make various components with strength far exceeding that of the parent constituent materials are their main attributes. These engineered materials are generally orthotropic in nature and quite often show very unique response even under simple loading conditions and geometric con®gurations. For a detailed account on nonlinear response of composite materials and structures see, e.g., Brank et al.

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