A new formulation of internal forces for non-linear hypoelastic constitutive models verifying conservation laws

in Bathe, K. J. (Ed.) Second MIT Conference on Fluid and Solid Mechanics (2003)

This paper proposes a new formulation of the internal forces for hypoelastic constitutive models ensuring that the elastic work of deformation can be restored by the scheme. Moreover, we demonstrate that ... [more ▼]

This paper proposes a new formulation of the internal forces for hypoelastic constitutive models ensuring that the elastic work of deformation can be restored by the scheme. Moreover, we demonstrate that the work of the plastic deformation is positive and consistent with the material model. [less ▲]

Détermination automatique de la taille du pas de temps pour les schémas implicites en dynamique non-linéaire

in Mécanique & Industries (2002), 3(1), 63-77

Pour les problèmes caractérisés par de fortes non-linéarités, ainsi que des phénomènes d'impacts et de contacts, une stratégie d'intégration à pas de temps variables est particulièrement intéressante. Ces ... [more ▼]

Pour les problèmes caractérisés par de fortes non-linéarités, ainsi que des phénomènes d'impacts et de contacts, une stratégie d'intégration à pas de temps variables est particulièrement intéressante. Ces phénomènes sont par exemple rencontrés lors de l'étude dynamique d'une interaction aube-carter d'un moteur d'avion, le cas le plus critique étant la perte de l'aube. Une stratégie d'intégration implicite à pas de temps constant donne rarement satisfaction du fait qu'il est pratiquement impossible de déterminer une durée de pas qui ne conduise pas à la divergence ou à un coût de calcul prohibitif. Une gestion automatique du pas de temps, qui tient compte de l'histoire récente des accélérations dans le corps considéré, est proposée. En fait, l'algorithme est basé sur la mesure de l'erreur d'intégration des équations d'équilibre. Cela permet d'intégrer correctement les phénomènes transitoires avec un pas de temps très long (en régime) ou très petit (lors de la perte d'aube), en garantissant une bonne précision en un temps de calcul raisonnable. De plus, un algorithme qui décide automatiquement de recalculer ou non, la matrice hessienne est proposé. Cet algorithme permet d'éviter un nombre important de remises à jour de cette matrice, ce qui permet de réduire le coût de calcul tout en assurant la convergence. Enfin, un critère de divergence des itérations est proposé. Afin d'illustrer l'efficacité des algorithmes développés, des simulations numériques sont présentées. Il s'agit aussi bien de problèmes académiques que de problèmes industriels (contacts aubes carter). [less ▲]

Self-adapting time integration management in crash-worthiness and sheet metal forming computations

in International Journal of Vehicle Design (2002), 30(1-2), 67-114

Variable step strategies are especially well suited to deal with problems characterized by high non-linearity and contact/impact, and resolved with an implicit scheme. Both phenomena are typical of ... [more ▼]

Variable step strategies are especially well suited to deal with problems characterized by high non-linearity and contact/impact, and resolved with an implicit scheme. Both phenomena are typical of dynamic simulations of contact-impact problems, as well as sheet metal forming. Constant step size strategies do not give a satisfactory answer for this kind of problem, since it is very difficult, if not impossible, for the user to find an appropriate time step that does not lead to divergence nor generate extremely costly computations. An automatic time stepping algorithm is proposed, which takes into account the recent history of accelerations in the deformable bodies under consideration. More precisely, the adaptation algorithm is based on estimators of the integration error of the differential dynamic balance equations. This allows for adaptation of the step size to capture correctly the transient phenomena, with characteristic times which can range from relatively long (after contact, or during sheet metal forming) to very short (during contact-impact). thus ensuring precision while keeping the computation cost to a minimum. Furthermore, we will see that this strategy can be used in explicit schemes. Additionally, the proposed algorithm automatically takes decisions regarding the necessity of updating the tangent matrix or stopping the iterations, further reducing the computational costs especially, when the Augmented Lagrangian method is used. As an illustration of the capabilities of this algorithm, several numerical simulations (shock absorber devices for vehicle crash-worthiness or sheet metal forming) problems will be presented. Other simulations pertaining to the sheet metal forming for vehicle structures will also be investigated, thus demonstrating the versatility, the capabilities and the efficiency of the proposed strategy. [less ▲]

Implicit-explicit time integration algorithms for the numerical simulation of blade-casing interactions

in Rajendran, A. M.; Jones, B. N.; Brebbia, C. A. (Eds.) Structures under Shock and Impact VII (2002)

In order to solve fast dynamic problems, an explicit method is the most adapted. But for slower dynamics, an implicit method is more stable. Typical industrial problems are governed by high frequency, e.g ... [more ▼]

In order to solve fast dynamic problems, an explicit method is the most adapted. But for slower dynamics, an implicit method is more stable. Typical industrial problems are governed by high frequency, e.g. impact, during short time intervals and slower dynamics, e.g. spring-back, during other time intervals. The optimal solution is then to have both implicit algorithm and explicit methods readily available in the same code and to be able to switch automatically from one to the other. Criteria that decide when to shift from a method to another have been developed here. Implicit balanced restarting conditions that annihilate numerical oscillations resulting for an explicit calculation are also proposed. [less ▲]

Automatic time stepping algorithms for implicit numerical simulations of blade/casing interactions

in International Journal of Crashworthiness (2001), 6(3), 351-362

An automatic time stepping algorithm for non-linear problems, solved by implicit schemes, is presented. The time step computation is based on the estimation of an integration error calculated from the ... [more ▼]

An automatic time stepping algorithm for non-linear problems, solved by implicit schemes, is presented. The time step computation is based on the estimation of an integration error calculated from the acceleration difference. It is normalised according to the size of the problem and the integration parameters. This time step control algorithm modifies the time step size only if the problem has a long time physical change. Additionally, the Hessian matrix can be kept constant for several iterations, even though the problem is non-linear. A criterion selecting if the Hessian matrix must be calculated or not is developed. Finally, a criterion of iterations divergence is also proposed. It avoids the determination, by the user, of a maximal iteration number. This minimises the total number of iterations, and thus the computation cost. Industrial numerical examples are presented that demonstrate the performances (precision and computational cost) of the algorithms. [less ▲]

Determination automatique de la taille du pas de temps pour les schémas implicites en dynamique non-linéaire

Master's dissertation (2000)

Ce travail propose une gestion du choix de la durée du pas de temps. Pour ce faire nous choisissons d’utiliser un indicateur de l’erreur d’intégration numérique. La gestion développée s’adapte aux ... [more ▼]

Ce travail propose une gestion du choix de la durée du pas de temps. Pour ce faire nous choisissons d’utiliser un indicateur de l’erreur d’intégration numérique. La gestion développée s’adapte aux différents schémas d’intégration implicites étudiés. Elle garantit une précision sur les résultats obtenus tout en assurant un coût de calcul réduit. Cette stratégie est d’abord validée sur des cas généraux de grandes déformations afin de mettre en évidence son large domaine d’application. Ensuite, elle est validée sur des cas industriels. Pour l’étude de ces cas industriels, la nouvelle gestion du pas de temps est associée à un nouveau critère de convergence ainsi qu’à un nouveau schéma de décision de remise à jour de la matrice d’itération. L’intérêt principal de l’étude de cas industriels est leur nombre important de degrés de liberté ainsi que la variation des phénomènes physiques qui apparaissent au cours du temps. Les intérêts pratiques (gain de temps de calcul, garantie de précision et diminution du nombre de paramètres utilisateur) des nouveaux schémas sont alors clairement mis en évidence. Nous sommes ainsi parvenus à réduire fortement les temps de calcul de ces cas. [less ▲]

Automatic time stepping algorithms for implicit numerical simulations of non-linear dynamics

in Topping, B. H. V.; Motas Soares, C. A. (Eds.) FINITE ELEMENTS: TECHNIQUES AND DEVELOPMENTS (2000)

Variable step strategies are specially well suited to deal with problems characterized by high non-linearity and contact/impact. Both phenomena are typical of dynamic simulations of the interactions ... [more ▼]

Variable step strategies are specially well suited to deal with problems characterized by high non-linearity and contact/impact. Both phenomena are typical of dynamic simulations of the interactions between a turbine blade and its casing, the most dramatic example being blade loss. Constant step size strategies do not give satisfactory answer for this kind of problems, since it is very difficult, if not impossible, for the user to find an appropriate time step that does not lead to divergence nor generate extremely costly computations. An automatic time stepping algorithm is proposed, which takes into account the recent history of accelerations in the bodies under consideration. More precisely, the adaptation algorithm is based on estimators of the integration error of the differential dynamic balance equations. This allows for adaptation of the time step to capture correctly the transient phenomena, with characteristic times which can range from relatively long (in regime) to very short (blade loss), thus ensuring precision while keeping the computation cost to a minimum. Additionally, the proposed algorithm automatically takes decisions regarding the necessity of updating the tangent matrix or stopping the iterations, further reducing the computational cost. As an illustration of the capabilities of this algorithm, several numerical simulations of both academic and industrial (the contact/impact between a turbine blade and the casing) problems will be presented. [less ▲]