No / In this paper, a new three-dimensional spline finite strip method (spline FSM) is introduced. This is done by combining the classical spline finite strip method [1] and the state space approach. According to the traditional spline FSM, a laminated plate is divided into strips. Within each strip, the spline FSM calls for the use of simple polynomials and a continuously differentiable spline function, respectively, in the transverse and in-plane directions. In the through-thickness direction, the state space method is used to compute the distribution of displacements and stresses. The combination of the in-plane spline FSM and the out-of-plane state space formulations results in a global state space equation that is solved numerically by the precise time step integration method [2,3]. Apart from obtaining a three-dimensional solution, the new method has a unique feature that the final algebra equation system is independent of the number of material layers of a laminate. The main aim of this work is to establish the new solution procedure and validate the method. To this end, the work reported in the paper focus on laminated plates with arbitrary boundary conditions. Thus, the spline FSM is more flexible than the FSM in imposing boundary conditions. Future development is expected to extend the solution to more practical applications. From the numerical validation included, it can be seen clearly that the newly developed method can provide accurate three dimensional solutions for laminated composites, particularly, with continuous transverse stress distributions across material interfaces. This is normally difficult to obtain if a traditional three dimensional finite element is used, where only continuity of displacements across material boundaries are guaranteed. Apart from the above new feature, the new three-dimensional formulation always ends up with a global matrix whose dimension depends only on the number of strips and knots that a plate has been divided into, and is completely independent of the number of material layers of the plate.

Les modes de déformation des systèmes de rift hyper-étirés pauvres en magma évoluent dans le temps et dans l’espace. Ainsi les structures et architectures observées varient le long d’une section en profondeur ainsi que sur une carte. Cette étude vise à caractériser les modes de déformation des systèmes hyper-étirés et leur propagation en utilisant les exemples du sud de l’Atlantique Nord. L’architecture de la terminaison de la croûte continentale a été comparée à la théorie du prisme critique de Coulomb car sa forme est prismatique, la déformation finale est cassante/frictionnelle et ce prisme glisse sur un décollement basal. Cette théorie met en évidence le comportement distinct des deux marges conjuguées. De plus, elle contraint l’architecture crustale, permet l’intégration des failles contre-régionales et explique la formation des blocs allochtones dans un modèle de failles en séquence. L’intégration des modes de déformation dans un modèle évolutif 3D impose un contexte cinématique fiable, ce qui n’est pas le cas de l’ouverture océanique du sud de l’Atlantique Nord. Ceci est dû à l’interprétation de l’anomalie J comme un isochrone. L’investigation de cette anomalie indique une formation polygénique et polyphasée incohérente avec un isochrone ou une limite de domaine. Ainsi l’anomalie J est inutilisable pour les reconstructions cinématiques. L’évolution de la déformation de rift a été analysée grâce à une nouvelle reconstruction cinématique du sud de l’Atlantique Nord. Il apparait alors que la déformation de la croûte continentale est segmentée alors que la propagation de la croûte océanique forme un V. L’approche développée dans cette thèse pose également de nouvelles questions géodynamiques quant à l’influence de l’héritage et l’effet des points triple. / Deformation modes of magma-poor hyper-extended rift systems evolve through time and space. Hence the observed structures and architectures vary along a depth section as well as on a map. This study aims to characterize the deformation modes of hyper-extended systems and their propagation using the examples of the southern North Atlantic. The architecture of the continental crust termination has been compared to the critical Coulomb wedge theory because it has a wedge shape, the final deformation is brittle/frictional and this wedge is gliding over a basal detachment. This theory highlights the distinct behavior of the two conjugate margins. Moreover it constrains crustal architecture of the continental crust termination, integrates continentward dipping faults and explains the formation of extensional allochthons in a sequential faulting model. The integration of deformation modes in an evolving 3D model necessitates a reliable kinematic context, which is not the case for the opening of the southern North Atlantic Ocean. This is linked to the interpretation of the J-magnetic anomaly as an oceanic isochron. Re-investigations of this anomaly revealed its polygenic and polyphased formation, which is inconsistent for an oceanic isochrons or a domain boundary making it unusable for plate reconstruction. The evolution of rift deformation has been analyzed with a new plate reconstruction of the southern North Atlantic. It appears that the continental crust deformation is segmented whereas oceanic crust propagates in a V-shape. The approach developed in this thesis also asks new geodynamical questions on the influence of inheritance and the effect of triple junction.