SUMMARYThis paper presents and exercises a general structure for an object-oriented enriched finite element code. The programming environment provides a robust tool for extended finite element (XFEM) computations and a modular and extensible system. The program structure has been designed to meet all natural requirements for modularity, extensibility, and robustness. To facilitate meshgeometry interactions with hundreds of enrichment items, a mesh generator and mesh database are included. The salient features of the program are: flexibility in the integration schemes (subtriangles, subquadrilaterals, independent near-tip and discontinuous quadrature rules); domain integral methods for homogeneous and bi-material interface cracks arbitrarily oriented with respect to the mesh; geometry is described and updated by level sets, vector level sets or a standard method; standard and enriched approximations are independent; enrichment detection schemes: topological, geometrical, narrow-band, etc.; multi-material problem with an arbitrary number of interfaces and slip-interfaces; non-linear material models such as J2 plasticity with linear, isotropic and kinematic hardening. To illustrate the possible applications of our paradigm, we present two-dimensional linear elastic fracture mechanics for hundreds of cracks with local near-tip refinement, and crack propagation in two dimensions as well as complex three-dimensional industrial problems.

SUMMARYA stabilized conforming nodal integration finite element method based on strain smoothing stabilization is presented. The integration of the stiffness matrix is performed on the boundaries of the finite elements. A rigorous variational framework based on the Hu-Washizu assumed strain variational form is developed.We prove that solutions yielded by the proposed method are in a space bounded by the standard, finite element solution (infinite number of subcells) and a quasi-equilibrium finite element solution (a single subcell). We show elsewhere the equivalence of the one-subcell element with a quasi-equilibrium finite element, leading to a global a posteriori error estimate.We apply the method to compressible and incompressible linear elasticity problems. The method can always achieve higher accuracy and convergence rates than the standard finite element method, especially in the presence of incompressibility, singularities or distorted meshes, for a slightly smaller computational cost.It is shown numerically that the one-cell smoothed four-noded quadrilateral finite element has a convergence rate of 2.0 in the energy norm for problems with smooth solutions, which is remarkable. For problems with rough solutions, this element always converges faster than the standard finite element and is free of volumetric locking without any modification of integration scheme.

SUMMARYThe meshless method is particularly appropriate to solve crack propagation problems. In this paper, the fatigue growth of cracks in two-dimensional bodies is considered. The analysis is based upon Paris' equation. New enriched weight functions are introduced in the meshless method formulation to capture the singularity at the crack tip. Simple problems show the accuracy and efficiency of this method. Then, it is applied to fatigue analysis of single-and multi-cracked bodies under mixed-mode conditions.

Published paperLe, C.V., Nguyen-Xuan, H. and Nguyen-Dang, H. (2010) in which the pressure is equilibrated by corner loads only, ensuring that exact equilibrium relations associated with a uniform pressure can be obtained. Once the displacement or moment fields are approximated and the bound theorems applied, limit analysis becomes a problem of optimization. In this paper, the optimization problems are formulated in the form of a standard second-order cone programming which can be solved using highly efficient interior point solvers.The procedures are tested by applying it to several benchmark plate problems and are found good agreement between the present upper and lower bound solutions and results in the literature.Key words: Limit analysis, upper and lower bounds, displacement and equilibrium models, criterion of mean, second order cone programming

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