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In nuclear industry, simulating accidental transient sequences at full reactor scale is becoming an increasingly important feature of the safety demonstration towards national agencies. It thus allows limiting the number of complex and costly experiments, while simplifying and accelerating the evaluation of mitigation strategies. However, the implemented numerical models are inevitably heavy to build and maintain, with a global modelling scale making it difficult to account for local geometric details yet able to significantly influence the physical solution. To provide an answer to these problems, this PhD work is dedicated to multi-model approaches designed to integrate such details into bigger models with no modification at the global level (techniques often designated as numerical zoom techniques). Some methods are proposed for both structures and fluids, with special care given to the accuracy and stability of the coupled multi-scale solution compared to a single-scale reference solution. This work handles two very specific topics, namely its compatibility with numerical features imposed by fast transient dynamics with explicit time integration, and the general objective of simultaneously dealing with superimposed models and fluid-structure interaction., Dans l’industrie nucléaire, la simulation de transitoires accidentels à l’échelle d’un réacteur devient une composante d’importance croissante de la démonstration de sûreté à destination des agences de surveillance nationales. Elle permet ainsi de limiter le recours à des expériences complexes et coûteuses tout en facilitant l’évaluation des stratégies de mitigation. Cependant, les modèles mis en jeu sont inévitablement volumineux et construits avec une finesse de modélisation rendant difficile la prise en compte de détails géométriques locaux pourtant susceptibles d’influencer significativement la solution globale. Dans ce travail de thèse, on propose ainsi des approches multi-modèles pour l’intégration de tels détails dans un modèle global sans modification du maillage initial (on parle aussi de zoom numérique). Des techniques sont proposées aussi bien pour les structures que pour les fluides, avec un souci de démontrer la précision et la stabilité de la solution multi-modèles couplée comparée à une solution de référence à une seule échelle. Ce travail intègre deux spécificités propres, à savoir son adéquation avec les contraintes de la dynamique rapide avec intégration temporelle explicite et l’objectif de traiter simultanément la superposition de modèles et l’interaction fluide-structure.

An effective form-finding method for form-fixed spatial network structures is presented in this paper. The adaptive form-finding method is introduced along with the example of designing an ellipsoidal network dome with bar length variations being as small as possible. A typical spherical geodesic network is selected as an initial state, having bar lengths in a limit group number. Next, this network is transformed into the ellipsoidal shape as desired by applying compressions on bars according to the bar length variations caused by transformation. Afterwards, the dynamic relaxation method is employed to explicitly integrate the node positions by applying residual forces. During the form-finding process, the boundary condition of constraining nodes on the ellipsoid surface is innovatively considered as reactions on the normal direction of the surface at node positions, which are balanced with the components of the nodal forces in a reverse direction induced by compressions on bars. The node positions are also corrected according to the fixed-form condition in each explicit iteration step. In the serial results of time history, the optimal solution is found from a time history of states by properly choosing convergence criteria, and the presented form-finding procedure is proved to be applicable for form-fixed problems.

An arbitrary Lagrangian-Eulerian (ALE) approach is used to model the orthogonal metal cutting in a steady state situation. The thermomechanical model includes the effects of elasticity, plasticity, strain rate, large strains and friction with heat generated between the tool and the chip. The ALE formulation can combine the advantages of both the Eulerian and Lagrangian approaches in a single description. Particularly, problems linked to the free surface in a Eulerian description and those linked to severe mesh distortions in a Lagrangian one can be solved by this formulation. The ALE governing equations are briefly reviewed in this paper; finite element and finite volume methods are used for the discretization of the conservation equations and an explicit time integration is adopted. Only the steady state solution is required; the ALE formulation is exploited to update the free and the contact surfaces. The model predicts the thermomechanical quantities, the chip geometry and the cutting forces from the cutting data and the material and friction parameters. Cutting experiments were performed with 42CD4 steel and comparisons of experimental tool forces and chip geometry with the numerical results are presented.

Constitutive models of unsaturated soils, and in particular those based on constitutive variables which include both degree of saturation and suction, are characterised by strong non linearities due to hydromechanical coupling. In this paper, a refined Runge–Kutta–Dormand–Prince explicit algorithm and a fully implicit Euler scheme are compared for the integration of the latter class of models. The explicit and implicit procedures have been tested along different hydromechanical paths, involving various hydraulic and mechanical external control conditions. Accuracy and efficiency of the algorithms have been investigated. The results confirm that substepping is mandatory for the explicit algorithm to converge regardless the initial step size and to remain sufficiently accurate. The value of the incremental hydromechanical work per unit volume was calculated during the explicit integration procedure. The numerical results show that the maximum size of the substep which can be adopted to meet a given tolerance depends on the gradient of the incremental work per unit volume. Therefore, the latter appears a good candidate to identify problematic integration steps in terms of convergence. Accuracy of the implicit algorithm also depends on the chosen step size, although the algorithm proved to be convergent in all the paths analysed.

This is the post-print version of the final paper published in Engineering Structures. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2011 Elsevier B.V. In this paper a robust static-dynamic procedure has been developed. The development extends the capability of the Vulcan software to model the dynamic and static behaviour of steel buildings during both local and global progressive collapse of the structures under fire conditions. The explicit integration method was adopted in the dynamic procedure. This model can be utilized to allow a structural analysis to continue beyond the temporary instabilities which would cause singularities in the full static analyses. The automatic switch between static and dynamic analysis makes the Vulcan a powerful tool to investigate the mechanism of the progressive collapse of the structures generated by the local failure of components. The procedure was validated against several practical cases. Some preliminary studies of the collapse mechanism of steel frame due to columns’ failure under fire conditions are also presented. It is concluded that for un-braced frame the lower loading ratio and bigger beam section can give higher failure temperature in which the global structural collapse happens. However, the localised collapse of the frame with the higher loading ratio and smaller beam section can more easily be generated. The bracing system is helpful to prevent the frame from progressive collapse. The higher lateral stiffness of the frame can generate the smaller vertical deformation of the failed column at the re-stable position. However, the global failure temperature of the frame is not sensitive to the lateral stiffness of the frame.

In a traditional finite element method for the simulation of deformable objects, the stiffness matrix depends on the shape of the tetrahedral elements. Ill-shaped elements containing large or small dihedral angles lead to an arbitrary large condition number of the stiffness matrix, thus slowing down the simulation. In addition, high modal frequencies cannot be simulated stably if an explicit numerical time-integration scheme is considered. We propose an approach consisting of two components to address this problem: First, we isolate the ill-shaped tetrahedra by performing an eigenvalue decomposition, and then remove their high modal frequencies by directly altering their element stiffness matrices. This makes the elements softer in some directions. To prevent element inversion, we define constraints that rigidify the object along those directions. The fast projection method, implemented as a velocity filter, is employed to enforce the constraints after the temporal evolution. With our approach, a significantly larger time step can be chosen in explicit integration methods, resulting in a faster simulation.

In this paper we will present meshless Adaptive Fup Collocation Method (AFCM) based on Fup basis functions and collocation approach for spatial approximation [2] and explicit stabilized Runge-Kutta temporal integration especially well suited for stiff parabolic problems [3]. The basic scheme of MOL methodology was described in [2], but now we improve efficiency of the spatial approximation, introduce a novel explicit time integration scheme and therefore significantly increase capabilities of the methodology for a real demanding 2-D and 3-D stiff parabolic problems. On the other side, we implement stabilized Runge–Kutta methods (they have also been called Chebyshev–Runge–Kutta methods) which are explicit methods with extended stability domains, usually along the negative real axis. Due to demonstrative purposes, we present the efficiency of the AFCM to the Henry saltwater benchmark example of groundwater density driven flow.

Numerical analyses of bird impact damage in complex aircraft structures have been performed using ABAQUS/Explicit. A Lagrangian formulation was used for the bird model in combination with various material models. Several failure and damage modes have been considered for different material models used in the inboard flap of a typical large transport aircraft. A submodeling approach has been used to reduce computational time. Parametric analyses have been performed using different bird sizes, impact locations and velocity vectors.

Robustness and stability of the Continuum Strong Discontinuity Approach (CSDA) to material failure are addressed. After identification of lack of symmetry of the finite element formulation and material softening in the constitutive model as possible causes of loss of robustness, two remedies are proposed: (1) the use of an specific symmetric version of the elementary enriched (E-FEM) finite element with embedded discontinuities and (2) a new implicit–explicit integration of the internal variable, in the constitutive model, which renders the tangent constitutive algorithmic operator positive definite and constant. The combination of both developments leads to finite element formulations with constant, in the time step, and non-singular tangent structural stiffness, allowing dramatic improvements in terms of robustness and computational costs. After assessing the convergence and stability properties of the new strategies, three-dimensional numerical simulations of failure problems illustrate the performance of the proposed procedures Fil: Oliver, J.. Technical University of Catalonia; España Fil: Huespe, Alfredo Edmundo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina Fil: Blanco, S.. Technical University of Catalonia; España Fil: Linero, D.L.. Technical University of Catalonia; España

During the last fifty years, the development of better numerical methods and more powerful computers has been a major enterprise for the scientific community. Recent advances in computational softwares have lead to the possibility of solving more physical and complex problems (coupled problems, nonlinearities, high strain and high strain rate problems, etc.). The development of object-oriented programming leads to better structured codes for the finite element method and facilitates the development, the maintainability and the expandability of such codes. This paper presents an implementation in C++ of an explicit finite element program dedicated to the simulation of impacts. We first present a brief overview of the kinematics, the conservative and constitutive laws related to large deformation inelasticity. Then we present the design and the numerical implementation of some aspects developed with an emphasis on the object-oriented programming adopted. Finally, the efficiency and accuracy of the program are investigated through some benchmark tests.

Cette étude s'intéresse à l'analyse non linéaire géométrique statique des coques par éléments finis tridimensionnels dégénérés, avec intégration explicite dans l'épaisseur. Les formulations lagrangiennes totale et actualisée sont présentées. L'élément fini développé est prévu pour modéliser des coques minces ou modérément épaisses et le matériau peut être isotrope ou composite orthotrope. Cet élément fini donne de bons résultats mais demande un temps de calcul élevé des opérateurs non-linéaires si l'intégration numérique dans l'épaisseur est utilisée pour les multicouches. Pour cela le problème tridimensionnel du calcul des matrices de rigidité tangente et des efforts intérieurs est ici ramené a un problème bidimensionnel, l'intégration suivant l'épaisseur étant effectuée explicitement et non numériquement. Ceci nécessite d'écrire préalablement les développements limités des différents opérateurs en fonction de la variable épaisseur. L'intégration suivant les deux directions du plan tangent reste numérique et réduite, de manière à atténuer les problèmes de verrouillage dans le cas des coques minces. Les applications numériques comparent cet élément à d'autres éléments de coques ou plaques ainsi qu'au même élément utilisant l’intégration numérique dans l'épaisseur de chaque couche. Les temps de calcul sont examinés dans le cas de l'analyse non-linéaire des structures composites multicouches. Cet élément fini a été implanté dans le code de calcul de l'Aérospatiale, ASELF (AéroSpatiale ELéments Finis), et permet les calculs de type flambement critique et l'analyse non linéaire complète avec les techniques de pilotage en charge imposée, déplacement imposé, longueur d'arc imposée. The object of this study is the geometrical nonlinear static analysis using a three dimensional degenerated shell finite element, with explicit thickness integration. Total and updated lagrangian formulations are presented. This element can be used to calculate thin or moderately thick shells and the material of the element can be isotropic or orthotropic. This element gives accurate results even for moderately thick composite panels, but requires an important non-linear generation time in the case of multilayered structures. So the three-dimensional problem of tangent stiffness and internal forces computing is reduced to a bi-dimensional one, the thickness integration being obtained explicitly. So an expansion into power series of the thickness variable is performed for various matrices appearing in the formulation. The reduced numerical integration is performed in each direction of the middle-surface, so the locking phenomenon is considerably reduced for thin shells. The numerical applications have been conducted in the case of isotropic and multilayered composite structures. The results have been compared with those given by other shell or plate finite elements and with those given by the same element using numerical thickness integration in each layer. Computational time is investigated to show the interest of explicit thickness integration in nonlinear analysis when using multilayered composite structures. This finite element has been introduced in the Aerospatiale Finite Element code ASELF (AéroSpatiale ELéments Finis) for buckling and post-buckling analyse. Load / displacement curves are obtained by using different numerical strategies and control techniques such as load increment, displacement increment or arc length method.

Une étude des éléments finis tridimensionnels dégénérés de coques avec intégration explicite suivant l'épaisseur est réalisée dans le cas général des coques multicouches pour l'analyse linéaire-statique. Le problème tridimensionnel du calcul des matrices de rigidité et de masse se réduit à un problème bidimensionnel, l'intégration suivant l'épaisseur étant effectuée explicitement. La formulation proposée permet de définir différentes approximations en comparant les puissances du rapport épaisseur-rayon de courbure principal minimal de la surface moyenne à l'unité. Le phénomène de "verrouillage" est expliqué grâce à la présente formulation. La dégradation de la précision due à la position des noeuds intermédiaires est évitée à l'aide des fonctions de forme modifiées, proposées dans le présent travail. Les coefficients correctifs de cisaillement transversal ont été étudiés et leurs expressions analytiques pour un sandwich symétrique ont été obtenues. Les applications numériques effectuées testent l'élément fini quadrilatère à 8 nœuds dans les cas de structures multicouches et sandwiches en comparant les résultats par éléments finis avec ceux donnés par différentes théories. Une comparaison a été faite entre les résultats obtenus en utilisant l'élément fini avec intégration explicite-première approximation avec ceux obtenus en utilisant l'élément avec intégration numérique. L'élément fini avec intégration explicite a été implanté dans le code ASELF (AéroSpatiale ELéments Finis). A study of three-dimensional degenerated shell finite elements with explicit thickness integration is realized in the general case of multilayered shells for linear static analysis. The three-dimensional problem of stiffness and mass matrices computing is reduced to a bi-dimensional one, the thickness integration being obtained explicitly. The proposed formulation allows the definition of several approximations to be carried out by comparing the powers of the thickness-principal minimum radius of curvature ratio to unity. The "locking" phenomenon is explained thanks to the present formulation. The loss of precision due to the midside nodes position is avoided owing to the modified shape functions proposed in the present work. The transverse shear correction factors have been studied and their analytical expressions for a symmetrical sandwich have been obtained. The numerical applications test the quadrilateral 8-node finite element in the cases of multilayered and sandwich structures by comparing the finite element results with those given by several theories. The results obtained using the explicit integration-first approximation finite element and those obtained using the numerical integration one are compared. The finite element with explicit integration has been introduced in the AéroSpatiale Finite Element code ASELF (AéroSpatiale ELéments Finis).