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Imposing Dirichlet boundary conditions in the extended finite element method ; Béchet, Eric ; in International Journal for Numerical Methods in Engineering (2006), 67(12), 1641-1669 This paper is devoted to the imposition of Dirichlet-type conditions within the extended finite element method (X-FEM). This method allows one to easily model surfaces of discontinuity or domain ... [more ▼] This paper is devoted to the imposition of Dirichlet-type conditions within the extended finite element method (X-FEM). This method allows one to easily model surfaces of discontinuity or domain boundaries on a mesh not necessarily conforming to these surfaces. Imposing Neumann boundary conditions on boundaries running through the elements is straightforward and does preserve the optimal rate of convergence of the background mesh (observed numerically in earlier papers). On the contrary, much less work has been devoted to Difichlet boundary conditions for the X-FEM (or the limiting case of stiff boundary conditions). In this paper, we introduce a strategy to impose Dirichlet boundary conditions while preserving the optimal rate of convergence. The key aspect is the construction of the correct Lagrange multiplier space on the boundary. As an application, we suggest to use this new approach to impose precisely zero pressure on the moving resin front in resin transfer moulding (RTM) process while avoiding remeshing. The case of inner conditions is also discussed as well as two important practical cases: material interfaces and phase-transformation front capturing. Copyright (c) 2006 John Wiley & Sons, Ltd. [less ▲] Detailed reference viewed: 149 (11 ULg)A general discontinuous Galerkin method for finite hyperelasticity. Formulation and numerical applications Noels, Ludovic ; in International Journal for Numerical Methods in Engineering (2006), 68(1), 6497 A discontinuous Galerkin formulation of the boundary value problem of finite-deformation elasticity is presented. The primary purpose is to establish a discontinuous Galerkin framework for large ... [more ▼] A discontinuous Galerkin formulation of the boundary value problem of finite-deformation elasticity is presented. The primary purpose is to establish a discontinuous Galerkin framework for large deformations of solids in the context of statics and simple material behaviour with a view toward further developments involving behaviour or models where the DG concept can show its superiority compared to the continuous formulation. The method is based on a general Hu-Washizu-de Veubeke functional allowing for displacement and stress discontinuities in the domain interior. It is shown that this approach naturally leads to the formulation of average stress fluxes at interelement boundaries in a finite element implementation. The consistency and linearized stability of the method in the non-linear range as well as its convergence rate are proven. An implementation in three dimensions is developed, showing that the proposed method can be integrated into conventional finite element codes in a straightforward manner. In order to demonstrate the versatility, accuracy and robustness of the method examples of application and convergence studies in three dimensions are provided. Copyright (c) 2006 John Wiley [less ▲] Detailed reference viewed: 79 (12 ULg)An energy momentum conserving algorithm using the variational formulation of visco-plastic updates Noels, Ludovic ; Stainier, Laurent ; Ponthot, Jean-Philippe in International Journal for Numerical Methods in Engineering (2006), 65(6), 904942 In this paper we use the variational formulation of elasto-plastic updates proposed by Ortiz and Stainier (Comput. Methods Appl. Mech. Eng. 1999; 171:419-444) in the context of consistent time integration ... [more ▼] In this paper we use the variational formulation of elasto-plastic updates proposed by Ortiz and Stainier (Comput. Methods Appl. Mech. Eng. 1999; 171:419-444) in the context of consistent time integration schemes. We show that such a formulation is well suited to obtain a general expression Of energy momentum conserving algorithms. Moreover, we present numerical examples that illustrate the efficiency of our developments. Copyright (c) 2005 John Wiley [less ▲] Detailed reference viewed: 32 (7 ULg)Improved implementation and robustness study of the X-FEM for stress analysis around cracks Béchet, Eric ; ; et al in International Journal for Numerical Methods in Engineering (2005), 64(8), 1033-1056 Numerical crack propagation schemes were augmented in an elegant manner by the X-FEM method. The use of special tip enrichment functions, as well as a discontinuous function along the sides of the crack ... [more ▼] Numerical crack propagation schemes were augmented in an elegant manner by the X-FEM method. The use of special tip enrichment functions, as well as a discontinuous function along the sides of the crack allows one to do a complete crack analysis virtually without modifying the underlying mesh, which is of industrial interest, especially when a numerical model for crack propagation is desired. This paper improves the implementation of the X-FEM method for stress analysis around cracks in three ways. First, the enrichment strategy is revisited. The conventional approach uses a 'topological' enrichment (only the elements touching the front are enriched). We suggest a 'geometrical' enrichment in which a given domain size is enriched. The improvements obtained with this enrichment are discussed. Second, the conditioning of the X-FEM both for topological and geometrical enrichments is studied. A preconditioner is introduced so that 'off the shelf' iterative solver packages can be used and perform as well on X-FEM matrices as on standard FEM matrices. The preconditioner uses a local (nodal) Cholesky based decomposition. Third, the numerical integration scheme to build the X-FEM stiffness matrix is dramatically improved for tip enrichment functions by the use of an ad hoc integration scheme. A 2D benchmark problem is designed to show the improvements and the robustness. Copyright (c) 2005 John Wiley & Sons, Ltd. [less ▲] Detailed reference viewed: 71 (8 ULg)A model updating strategy of non-linear vibrating structures Kerschen, Gaëtan ; Golinval, Jean-Claude in International Journal for Numerical Methods in Engineering (2004), 60(13), 2147-2164 The objective of this paper is to present a model updating strategy of non-linear vibrating structures. Because modal analysis is no longer helpful in non-linear structural dynamics, a special attention ... [more ▼] The objective of this paper is to present a model updating strategy of non-linear vibrating structures. Because modal analysis is no longer helpful in non-linear structural dynamics, a special attention is devoted to the features extracted from the proper orthogonal decomposition and one of its non-linear generalizations based on auto-associative neural networks. The efficiency of the proposed procedure is illustrated using simulated data from a three-dimensional portal frame. Copyright (C) 2004 John Wiley Sons, Ltd. [less ▲] Detailed reference viewed: 11 (2 ULg)An energy-momentum conserving algorithm for non-linear hypoelastic constitutive models Noels, Ludovic ; Stainier, Laurent ; Ponthot, Jean-Philippe in International Journal for Numerical Methods in Engineering (2004), 59(1), 83-114 This paper presents an extension of the energy momentum conserving algorithm, usually developed for hyperelastic constitutive models, to the hypoelastic constitutive models. For such a material no ... [more ▼] This paper presents an extension of the energy momentum conserving algorithm, usually developed for hyperelastic constitutive models, to the hypoelastic constitutive models. For such a material no potential can be defined, and thus the conservation of the energy is ensured only if the elastic work of the deformation can be restored by the scheme. We propose a new expression of internal forces at the element level which is shown to verify this property. We also demonstrate that the work of plastic deformation is positive and consistent with the material model. Finally several numerical applications are presented. Copyright (C) 2003 John Wiley Sons, Ltd. [less ▲] Detailed reference viewed: 37 (5 ULg)Simulating sedimentation of liquid drops ; ; Pfennig, Andreas in International Journal for Numerical Methods in Engineering (2004), 59(14), 1821-1837 Detailed reference viewed: 2 (0 ULg)An improved weighting method with multibounds formulation and convex programming for multicriteria structural optimization ; ; Fleury, Claude in International Journal for Numerical Methods in Engineering (2001), 52(9), 889-902 This paper presents an improved weighting method for multicriteria structural optimization. By introducing artificial design variables, here called as multibounds formulation (MBF), we demonstrate ... [more ▼] This paper presents an improved weighting method for multicriteria structural optimization. By introducing artificial design variables, here called as multibounds formulation (MBF), we demonstrate mathematically that the weighting combination of criteria can be transformed into a simplified problem with a linear objective function. This is a unified formulation for one criterion and multicriteria problems. Due to the uncoupling of involved criteria after the transformation, the extension and the adaptation of monotonic approximation-based convex programming methods such as the convex linearization (CONLIN) or the method of moving asymptotes (MMA)are made possible to solve multicriteria problems as efficiently as for one criterion problems. In this work, a multicriteria optimization tool is developed by integrating the multibounds formulation with the CONLIN optimizer and the ABAQUS finite element analysis system. Some numerical examples are taken into account to show the efficiency of this approach. [less ▲] Detailed reference viewed: 32 (0 ULg)An algorithm and a method to search bifurcation points in non-linear problems ; ; Charlier, Robert in International Journal for Numerical Methods in Engineering (2001), 51(3), 315-332 This paper is devoted to a numerical method able to help the determination of the bifurcation threshold in non-linear time-independent continuum mechanic problems. First, some theoretical results about ... [more ▼] This paper is devoted to a numerical method able to help the determination of the bifurcation threshold in non-linear time-independent continuum mechanic problems. First, some theoretical results about uniqueness are recalled. In the framework of the large-strain assumption, the differences between the classical finite-step problem and the rate problem are presented. An iterative algorithm able to solve the rate problem is given. Using different initializations, it is seen in some numerical experiments that it is possible with this algorithm to get different solutions when the underlying mathematical problem solved does not enjoy a uniqueness property. The constitutive equations used have been chosen to be simple enough to deduce some theoretical knowledge about the corresponding uniqueness problems. Finally, a method is given which is able in some case to give an upper bound of the bifurcation threshold. Copyright (C) 2001 John Wiley & Sons, Ltd. [less ▲] Detailed reference viewed: 168 (5 ULg)An Original integration scheme. Application to a simple shear test of anisotropic material ; Habraken, Anne in International Journal for Numerical Methods in Engineering (2000) Finite element simulations involving large deformations and large displacements imply the setting up of a precise kinematic for the integration scheme. Moreover, anisotropic mechanical behaviors have to ... [more ▼] Finite element simulations involving large deformations and large displacements imply the setting up of a precise kinematic for the integration scheme. Moreover, anisotropic mechanical behaviors have to be expressed in an appropriate local reference frame. In the present paper, a computational procedure is derived from a particular velocity gradient de¯nition. The implementation in the ¯nite element code Lagamine developed in the M&S department is described. An application to a simple shear test is proposed. A sinusoidal behavior of the shear component stress is emphasized. It is due to the anisotropic yield locus and appears in the case of a saturated isotropic hardening law. [less ▲] Detailed reference viewed: 27 (3 ULg)Topology Optimization of Continuum Structures with Local Stress Constraints Duysinx, Pierre ; in International Journal for Numerical Methods in Engineering (1998), 43 We introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria. We rst consider relevant stress criteria for porous ... [more ▼] We introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria. We rst consider relevant stress criteria for porous composite materials, initially by studying the stress states of the so-called rank 2 layered materials. Then, on the basis of the theoretical study of the rank 2 microstructures, we propose an empirical model which extends the power penalized sti ness model (also called SIMP for Solid Isotropic Microstructure with Penalization for intermediate densities). In a second part, solution aspects of topology problems are considered. To deal with the so-called 'singularity' phenomenon of stress constraints in topology design, an -constraint relaxation of the stress constraints is used. We describe the mathematical programming approach that is used to solve the numerical optimization problems, and show results for a number of example applications. [less ▲] Detailed reference viewed: 93 (5 ULg)FRICTIONAL CONTACT FINITE-ELEMENTS BASED ON MIXED VARIATIONAL-PRINCIPLES Cescotto, Serge ; Charlier, Robert in International Journal for Numerical Methods in Engineering (1993), 36(10), 1681- This paper presents an original approach to the numerical modelling of unilateral contact by the finite element method. The main point is the development of mixed contact finite elements in which the ... [more ▼] This paper presents an original approach to the numerical modelling of unilateral contact by the finite element method. The main point is the development of mixed contact finite elements in which the displacement field and the contact stress field (pressure and friction shear) are discretized independently. The theory, based on variational principles, is first presented in the framework of infinitesimal deformations and, subsequently, is extended to large inelastic strains. [less ▲] Detailed reference viewed: 97 (23 ULg)An automatic remeshing technique for finite element simulation of forming processes Habraken, Anne ; Cescotto, Serge in International Journal for Numerical Methods in Engineering (1990), 30(8), 1503-1525 Detailed reference viewed: 51 (10 ULg)Validation of Structural Computation Codes in Elastoviscoplasticity ; ; et al in International Journal for Numerical Methods in Engineering (1990), 29 This paper discusses various procedures for the implementation of viscoplastic constitutive equations in Finite Element Codes. The set of constitutive equations that has been used is described. Several ... [more ▼] This paper discusses various procedures for the implementation of viscoplastic constitutive equations in Finite Element Codes. The set of constitutive equations that has been used is described. Several kinds of implementation, using various numerical techniques, are proposed. Validations of these implementations and comparisons between them are investigated by means of a set of simple but comprehensive examples [less ▲] Detailed reference viewed: 29 (3 ULg)Modelling coastal/shelf systems with emphasis on long term trends Nihoul, Jacques ; Djenidi, Salim ; Hecq, Jean-Henri in International Journal for Numerical Methods in Engineering (1989), 27(1), 113-127 Hydrodynamic studies of continental seas have been primarily concerned with tides and storm surges and the associated currents which can have velocities as high as several metres per second. However, the ... [more ▼] Hydrodynamic studies of continental seas have been primarily concerned with tides and storm surges and the associated currents which can have velocities as high as several metres per second. However, the period of the dominant tide is only about half a day and the characteristic life time of a synoptic weather pattern is of the order of a few days. The very strong currents which are produced by the tides and the atmospheric forcing are thus relatively transitory and, over time scales of biological interest, they change and reverse so many times that they more or less cancel out, leaving only a small residual contribution to the net water circulation. Mathematical modelling appears at present as the most reliable approach to the determination of the residual circulation and of the long term transport of nutrients and pollutants in the sea. The residual circulation model developed at the GeoHydrodynamics and Environment Research Laboratory of Liège University (GHER) is described and illustrated by its application to the West-European Continental Shelf. Residual flow patterns on the shelf, and in particular in the Irish Sea and the North Sea, are presented and shown to be in excellent agreement with the observations. The results are exploited to estimate the typical routes and times of residence of nutrients and pollutants and the subsequent long term changes in shelf ecosystems and in the Belgian coastal zone. [less ▲] Detailed reference viewed: 6 (3 ULg)On the approximation of incompressible materials in the displacement method Debongnie, Jean-François in International Journal for Numerical Methods in Engineering (1979), 14(7), 1095-1099 A mathematical description of the numerical approximation to incompressibility with nearly incompressible displacement finite elements is presented. By the way of functional analysis, it leads to a ... [more ▼] A mathematical description of the numerical approximation to incompressibility with nearly incompressible displacement finite elements is presented. By the way of functional analysis, it leads to a condition of convergence to the incompressible problem when v is increased up to 0.5, which can be identified with Fried's K1 criterion. [less ▲] Detailed reference viewed: 12 (1 ULg)Variational Principles and the patch test Fraeijs de veubeke, Baudouin in International Journal for Numerical Methods in Engineering (1974), 8 The patch test is shown to be contained in the variational formulations of the finite element methods at the assembling level, all of which require the vanishing of the virtual work of interface connexion ... [more ▼] The patch test is shown to be contained in the variational formulations of the finite element methods at the assembling level, all of which require the vanishing of the virtual work of interface connexion loads. By a systematic introduction of stress generating functions, attention is drawn to the fact that any given finite element model can be assembled in two different ways: either by identiification of a set of boundary displacements (leading to the direct stiffness method), or by identification of a set of local stress function values (leading to the dual direct flexibility method). Looking at any conjugate couple (generalized displacement - generalized surface traction) at an interface, one is strongly transmitted, the other weakly. Discretization of the zero virtual work condition at an interface of plate bending models, by means of Legendre polynomials expansions, allows q systematic construction of so-called "non-conforming" elements that pass the patch test. They are in fact identified with weakly conforming, but strongly diffusive , htbrids, and the lowest degree element (quadratic) is in fact the Morley constant-moment element. Examples are given for higher displacement fields. The case of plate stretching elements can be handles by duality, the difficulties being here associated with the requirements for diffusivity. Non diffusive elements that pass the zero interface virtual worktest can be constructed systematically and are identifiable with weakly diffusive, but strongly conforming, hybrids, of the type first proposed by T.H.H. Pian. [less ▲] Detailed reference viewed: 78 (9 ULg) |
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