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   Strain smoothing in FEM and XFEMBordas, Stéphane  ; ; et alin Computers and Structures (2010), 88(23-24), 1419-1443 We present in this paper recent achievements realised on the application of strain smoothing in finite elements and propose suitable extensions to problems with discontinuities and singularities. The ... [more ▼] We present in this paper recent achievements realised on the application of strain smoothing in finite elements and propose suitable extensions to problems with discontinuities and singularities. The numerical results indicate that for 2D and 3D continuum, locking can be avoided. New plate and shell formulations that avoid both shear and membrane locking are also briefly reviewed. The principle is then extended to partition of unity enrichment to simplify numerical integration of discontinuous approximations in the extended finite element method. Examples are presented to test the new elements for problems involving cracks in linear elastic continua and cracked plates. In the latter case, the proposed formulation suppresses locking and yields elements which behave very well, even in the thin plate limit. Two important features of the set of elements presented are their insensitivity to mesh distortion and a lower computational cost than standard finite elements for the same accuracy. These elements are easily implemented in existing codes since they only require the modification of the discretized gradient operator, B. © 2008 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 224 (1 UL) Meshless methods: A review and computer implementation aspects; ; Bordas, Stéphane et alin Mathematics and Computers in Simulation (2008), 79(3), 763-813 The aim of this manuscript is to give a practical overview of meshless methods (for solid mechanics) based on global weak forms through a simple and well-structured MATLAB code, to illustrate our ... [more ▼] The aim of this manuscript is to give a practical overview of meshless methods (for solid mechanics) based on global weak forms through a simple and well-structured MATLAB code, to illustrate our discourse. The source code is available for download on our website and should help students and researchers get started with some of the basic meshless methods; it includes intrinsic and extrinsic enrichment, point collocation methods, several boundary condition enforcement schemes and corresponding test cases. Several one and two-dimensional examples in elastostatics are given including weak and strong discontinuities and testing different ways of enforcing essential boundary conditions. © 2008 IMACS. [less ▲] Detailed reference viewed: 1236 (5 UL)Architecture tradeoffs of integrating a mesh generator to partition of unity enriched object-oriented finite element software; ; et al in European Journal of Computational Mechanics (2007), 16(2), 237-258 We explore the tradeoffs of using an internal mesher in a XFEM code. We show that it allows an efficient enrichement detection scheme, while retaining the ability to have welladapted meshes. We provide ... [more ▼] We explore the tradeoffs of using an internal mesher in a XFEM code. We show that it allows an efficient enrichement detection scheme, while retaining the ability to have welladapted meshes. We provide benchmarks highlighting the considerable gains which can be expected from a well designed architecture. The efficiency of the proposed algorithm is shown by solving fracture mechanics problems of densely micro-cracked bodies including adaptive mesh refinement. [less ▲] Detailed reference viewed: 125 (0 UL) |
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