The Explicit Finite Element Method is a powerful tool in nonlinear dynamic finite element analysis. Recent major developments in computational devices, in particular, General Purpose Graphical Processing Units (GPGPU's) now make it possible to increase the performance of the explicit FEM. This dissertation investigates existing explicit finite element method algorithms which are then redesigned for GPU's and implemented. The performance of these algorithms is assessed and a new asynchronous variational integrator spatial decomposition (AVISD) algorithm is developed which is flexible and encompasses all other methods and can be tuned based for a user-defined problem and the performance of the user's computer. The mesh-aware performance of the proposed explicit finite element algorithm is studied and verified by implementation. The current research also introduces the use of a Particle Swarm Optimization method to tune the performance of the proposed algorithm automatically given a finite element mesh and the performance characteristics of a user's computer. For this purpose, a time performance model is developed which depends on the finite element mesh and the machine performance. This time performance model is then used as an objective function to minimize the run-time cost. Also, based on the performance model provided in this research and predictions about the changes in GPU's in the near future, the performance of the AVISD method is predicted for future machines. Finally, suggestions and insights based on these results are proposed to help facilitate future explicit FEM development.

This thesis develops a finite element based dynamic modeling method for design and analysis of compliant mechanisms which transfer input force, displacement and energy through elastic deformations. Most published analyses have largely based on quasi-static and lump-parameter models neglecting the effects of damping, torsion, complex geometry, and nonlinearity of deformable contacts. For applications such as handling of objects by the robotic hands with multiple high-damped compliant fingers, there is a need for a dynamic model capable of analyzing the flexible multibody system. This research begins with the formulation of the explicit dynamic finite element method (FEM) which takes into account the effects of damping, complex geometry and contact nonlinearity. The numerical stability is considered by evaluating the critical time step in terms of material properties and mesh quality. A general framework incorporating explicit dynamic FEM, topology optimization, modal analysis, and damping identification has been developed. Unlike previous studies commonly focusing on geometry optimization, this research considers both geometric and operating parameters for evaluation where the dynamic performance and trajectory of the multibody motion are particularly interested. The dynamic response and contact behavior of the rotating fingers acting on the fixed and moving objects are validated by comparing against published experimental results. The effectiveness of the dynamic modeling method, which relaxes the quasi-static assumption, has been demonstrated in the analyses of developing an automated transfer system involved grasping and handling objects by the compliant robotic hands. This FEM based dynamic model offers a more realistic simulation and a better understanding of the multibody motion for improving future design. It is expected that the method presented here can be applied to a spectrum of engineering applications where flexible multibody dynamics plays a significant role.

The experimental investigations performed on the behaviour of reinforce concrete elements subjected to blast loading have revealed that the shear mechanisms and ductility play important roles in the overall response and failure mode of such structures. The main aim of this master thesis is to study the possibility of using finite element method as a tool for predicting the dynamic response of blast loaded reinforced concrete beams and evaluation of their shear strength. In this study, the commercial software, ABAQUS/Explicit has been used by implementing appropriate constitutive material models in order to consider the material nonlinearity, stiffness degradation and strain rate effects. The results of some blast loaded tested beams have been used for verification and calibration of the model. As a secondary objective, the calibrated model used to study the influence of some important factors on the shear strength of reinforced concrete beams and investigate their effects on the failure mode. The results used as a reference and compared with the calculations according to some design codes for blast resistance design. The results of the present research show that the implemented nonlinear finite element model successfully simulates the dynamic responses including displacement/reaction force time histories and induced damage patterns of blast tested beams with reasonable accuracy. The results of performed parametric study confirm that the ductility play important role in the failure behaviour of studied beams. The numerical simulations show that dynamic response of a soft element is more ductile than the stiffer one and the shear forces are thereby limited. Thus, although a soft element fails by large deformations in flexure, a stiff element may experience a brittle shear failure mode for the same load intensity. The comparison between the results of numerical analysis and design codes calculation show that the American approach in shear design of reinforced concrete elements subjected to blast loading is relatively conservative, similar to static design approach and do not consider the effect of ductility in the shear design procedure. On the contrary, the procedure that Swedish guideline implemented somehow considers the effect of ductility on the shear strength of reinforced concrete elements subjected to impulsive loads. Further research should involve the using the developed finite element model as a tool in order to theoretically study the dynamic response of blast loaded reinforced concrete elements and their failure modes. The results of numerical simulations can be used as a reference to derive simplified computational methods for practical design purposes.

Les stratifiés composites sont de plus en plus utilisés dans les pièces de structures des aéronefs ce qui fait émerger de nouvelles problématiques comme celle des Impacts de Faible Energie (IFE). En effet, bien qu’ils possèdent des propriétés rapportées à leur masse très intéressantes ces matériaux peuvent être vulnérables aux petits chocs. Or, compte tenu des nombreux paramètres influents lors d’un tel impact (énergie, vitesse, stratification...), les essais actuellement majoritairement privilégiés à l’échelle industrielle sont long et coûteux. Ainsi, l’apport de la simulation numérique pourrait être d’une grande aide pour les constructeurs. La pratique du « virtual testing », en particulier, permettrait d’aller dans cette direction ce qui aurait pour effet de rationaliser les campagnes d’essais et les coûts financier qui en découlent. Cependant, elle peine à être mise en place ici car le temps CPU nécessaire pour la simulation fine des ndommagements induits par les IFE est trop important avec les méthodes actuelles. Partant de ce constat, ce travail a consisté à tirer avantageusement partie de la localisation spatiale et temporelle des délaminages, fissurations matricielles et ruptures de fibres qui peuvent apparaître pendant l’impact pour diminuer le coût de calcul. Ainsi une méthode multiéchelle en espace et en temps a été mise en place. Elle consiste à découper la structure impactée en deux zones. L’une est située autour du point d’impact, elle contient l’ensemble des non-régularités du problème (contact, loi adoucissante, modèle de zone cohésive). Elle est traitée avec le code de dynamique explicite Europlexus. L’autre correspond à la partie complémentaire. Le problème mécanique y est beaucoup plus régulier et il est traité avec le code de dynamique implicite Zset/Zébulon. Un couplage peu intrusif basé sur la méthode GC est donc réalisé entre ces deux codes. Il permet d’utiliser une modélisation adaptée dans chacune des deux régions ce qui permet en particulier d’utiliser des pas de temps différents. Un rapport supérieur à 1000 peut ainsi être obtenu entre celui du code explicite fixé par la condition de stabilité et celui utilisé dans la partie complémentaire. Un gain de temps CPU significatif confirmé par la simulation d’un impact réalisé sur un panneau composite raidi est ainsi obtenu. Il est également montré que la répartition implicite/explicite peut évoluer au cours du calcul. Pour cela un mécanisme de bascule a été mis en place. Il permet ainsi de faire transiter la résolution d’une partie de la structure initialement traitée dans le code Zebulon dans Europlexus. Un gain de temps supplémentaire est alors obtenu grâce à cette méthode sur le même cas d’application. / The composite laminates are increasingly used in aircraft structural parts which lead to new issues such as the Low Energy Impacts (LEI). Indeed, although they have well mechanical properties relative to their mass, small shocks may be very harmfull for laminates. Controlling such situations is essential for manufacturers that why lot of testing campaigns are currently performed. Yet, they are time consuming and expensive considering the many influential parameters (energy, speed, layup...). Numerical simulations of this phenomenon by practicing the so called “virtual testing” process could be really helpfull to rationalize testing campaigns in order to save money. Yet, this practice remain currently hard to do at the industrial scale due to the excessive CPU time required for fine simulation of damages induced by the LEI. Based on this observation, this work has consisted in taking advantage of the spatial and temporal location of delamination, matrix cracking and fiber breakage that can occur during impact in order to reduce the computational cost. Thus, a space and time multiscale method has been put in place. The impacted structure is split into two areas. One is located around the impacted point, it contains all the non-regularities of the problem (contact, softening law, cohesive zone model). This domain is treated with the explicit dynamics code Europlexus. The other one corresponds to the complementary part. The mechanical problem is much more regular and it is treated with the implicit dynamics code Zset / Zebulon. A low intrusive coupling based on the GC method is carried out between these two codes. It allows to use an adapted model in both regions different time step are in particular used. A time step ratio upper to 1000 can be reach between the one of the explicit code set by the stability condition and the one used in the complementary part. As a results, significant CPU time is saved. This is confirmed by the simulation of a stiffened composite panel impacted. It is also shown that the implicit / explicit allocation can change over the calculation. To do that, a switch mechanism has been established. It thus makes it possible to transit the resolution of a portion of the structure initially solved in the code Zebulon to Europlexus. As a results, further gain is obtained.

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