Les structures sandwichs sont largement utilisées dans le domaine de l’aéronautique et de l’espace du fait de leur bon rapport rigidité sur masse. Cependant, leur amortissement doit être amélioré pour le confort des utilisateurs et la durabilité des structures. L’objectif de cette thèse est d’étudier l’amortissement apporté à une structure sandwich par l’utilisation d’un matériau d’âme récemment développé. Ce matériau est fabriqué à base de fibres de carbone enchevêtrées, réticulées avec de la résine époxy. Le matériau enchevêtré-Réticulé est d’abord étudié seul. Les mesures expérimentales montrent un comportement dépendant de l’amplitude et de l’historique de sollicitation, et indépendant de la fréquence. Un modèle d’hystérésis est développé pour décrire les boucles contrainte-Déformation mesurées. L’étude théorique d’une structure à un degré de liberté permet de détailler l’effet des différentes composantes de ces boucles sur la réponse dynamique. Le matériau est ensuite inclus dans une poutre sandwich. Un modèle de vibrations de poutres sandwichs en flexion est proposé pour inclure un comportement non-Linéaire dissipatif du matériau d’âme. Une étude expérimentale est menée sur des poutres sandwichs, montrant un amortissement très supérieur à celui apporté par un matériau d’âme classique comme le nid d’abeille. Les simulations réalisées avec le modèle de poutre sandwich et le modèle d’hystérésis permettent de bien capturer les phénomènes non-Linéaires observés. A la fin de l’étude, une utilisation mixte d’un matériau d’âme en nid d’abeille et d’un matériau d’âme enchevêtré-Réticulé est proposée afin d’obtenir un bon amortissement pour un faible ajout de masse. / Sandwich structures are widely used in aerospace applications for their very good stiffness to weight properties. However, the damping properties of these structures have to be improved for user comfort and structural durability. The aim of this thesis is to study how the use of a recently developped core material can increase damping in sandwich structures. This material is made with entangled carbon fibres cross-Linked with epoxy resin. The entangled-Cross-Linked material is first studied separately. Experimental measurements show that the behavior depends strongly on strain amplitude and excitation history, while it depends weakly on frequency. A hysteresis model is developed to describe measured stress-Strain loops. A single-Degree-Of-Freedom structure containing the material is studied theoretically to show the effect of the different parts of the hysteresis loops on the steadystateand transient responses. The material is then included in a sandwich beam. A model for the bending vibrations of a sandwich beam is developped to include any nonlinear nonconservative behavior of the core material. Sandwich beams are then studied experimentally, showing a much higher damping than for classical core materials such as honeycomb. Simulations made with the sandwich beam model and the hysteresis loop model capture well the observed nonlinear phenomena. At the end of the study, a mixed use of honeycomb and entangled-Cross-Linked core materials is proposed, in order to obtain a high level of damping without adding much weight to the structure.

La conception sur-mesure de matériaux architecturés à l'échelle du milli/centimètre est une stratégie pour développer des matériaux de structure plus performants vis-à-vis de cahiers des charges multifonctionels. Ce travail de thèse s'intéresse en particulier à la conception optimale de panneaux architecturés périodiques, dans le but de combiner des exigences mécaniques de flexion et de cisaillement, ainsi que de conductivité thermique. Le comportement élastique peut être prédit grâce à l'identification sur la cellule périodique des coefficients de la matrice des souplesses équivalente. Ces calculs d'homogénéisation ont été mis en oeuvre par éléments finis pour estimer en particulier les souplesses en flexion et en cisaillement transverse. Après validation expérimentale, cette méthode de calcul constitue un outil d'évaluation des performances mécaniques pour chaque géométrie de cellule périodique (2D ou 3D). À titre d'exemple, et dans un contexte de développement de solutions matériaux architecturés pour l'automobile, la conception de tôles "texturées" est proposée en menant une étude paramétrique à l'aide de cet outil. L'implémentation d'un algorithme d'optimisation topologique couplé à la procédure d'homogénéisation permet d'enrichir les méthodes de conception sur-mesure en élargissant l'espace de recherche des "architectures". Après l'étude modèle du compromis entre flexion et cisaillement, le cas industriel d'un panneau sandwich isolant est traité. Dans ce cas, l'optimisation fournit plusieurs compromis prometteurs entre rigidité en cisaillement et isolation thermique. Ces géométries ont été réalisées et testées, et une nouvelle version améliorée du panneau sandwich a été sélectionnée. / The "material by design" strategy consists in tailoring architectured materials in order to fulfill multi-functional specifications. This PhD study focuses more specifically on designing architectured panels in regards with mechanical compliances (bending and transverse shear), as well as thermal conductivity. Recent advances on periodic homogenization of plates are integrated into a finite elements tool that enables to identify the Reissner-Mindlin effective compliance from the unit cell geometry. The comparison with four-point bending tests illustrates a discussion on the shear loading for homogenization, and its contribution to the global bending stiffness. In a context of architectured steel solutions for automotive, a parametric study is treated on "embossed" steel sheets using this homogenization tool. As a try to enlarge the space of available "architectures", a topological optimization algorithm (using the level-set method) is coupled to the homogenization procedure. The influence of each parameters of the method are studied on the optimization problem of compromising flexural and shear compliances. Finally, the industrial case of an insulation sandwich panel is treated. Few optimized geometries, with a high combination of shear stiffness and thermal insulation, are built, produced and tested. An improved design is highlighted and proposed as next version of this product.

This master thesis focuses on a scaled fuselage design made from composite material. The first part deals with a description of composite materials and used material models in an explicit FEM simulation. Two types of scaled structures were designed that were subjected to drop test. Test results were compared with FEM simulation. Finally the calibration of models was carried out.

Em engenharia, a quantidade de problemas geométricos complexos que precisam ser resolvidos empregando teorias de placas ou cascas é notável. Esta é a razão por que há tantas teorias que buscam simplificar os problemas tridimensionais em outros menos custosos computacionalmente. Além disso, o aumento atual do uso de estruturas sanduíche requer que as formulações bidimensionais sejam mais precisas. Esta tese, num primeiro momento, compila a maioria das teorias de placa, comentando as principais diferenças, vantagens e desvantagens de cada uma. As formulações bidimensionais de placas laminadas são classificadas principalmente de acordo com o tratamento da coordenada na direção normal a superfície da mesma: Camada Única Equivalente (ESL), ESL refinada (teorias Zig-Zag) e Teorias Discretas ou de Camada (LW). Cada uma destas teorias é revista juntamente com as hipóteses de placas que são feitas para cada uma das camadas ou para o laminado como um todo. Para resolver tais problemas estruturais em engenharia, métodos numéricos são normalmente utilizados. Portanto, num segundo momento, alguns métodos de solução são citados e revisados, mas o foco é dado ao Método dos Elementos Finitos (MEF). A contribuição deste trabalho consiste na implementação de um novo método de solução de compósitos laminados e estruturas sanduíche com base em um sistema unificado de Formulação Generalizada (GUF) via MEF. Um elemento quadrilátero de 4 nós foi desenvolvido e avaliado com um código de Elementos Finitos desenvolvido pelo presente autor. Os requisitos para continuidade do tipo C-1 são respeitados para a variável de deflexão da placa. Esse método é nomeado de Formulação Generalizada do Caliri (CGF). Resultados para placas isotrópicas, placas de laminado compósito e estruturas sanduíche consideradas finas ou espessas são comparados com dados da literatura e soluções via Abaqus. Os resultados obtidos ao longo da espessura reforçam a necessidade de soluções de placa não-lineares para placas espessas (laminadas ou não). Mostrou-se que as soluções estáticas e dinâmicas empregando o método proposto fornecem resultados coerentes quando comparados com outros métodos de solução. Dentre os diversos estudos de caso investigados, verificou-se que é possível se obter resultados com alta concordância. Para uma estrutura sanduíche com núcleo macio, o resultado de deslocamento previsto para um carregamento estático chega a 99.8% de concordância e o resultado de uma análise modal da mesma estrutura mostra uma concordância de 99.5% com os resultados de um modelo feito com elementos 3D em um programa comercial de elementos finitos. / In engineering, the amount of complex geometrical problems, which need to be solved by using plates and shells theories, is remarkable. This is the reason why there are so many plate and shell theories which attempt to simplify three dimensional problems into ones with low computational cost. Additionally, the current increasing use of sandwich structures requires that the two dimensional formulations be accurate enough. First, this thesis compiles most of the plate theories from the literature and quotes the main differences, advantages and weaknesses of each one. The bi-dimensional laminated plate formulations are mainly classified according to the treatment of the variable in the normal direction of the plate surface: Equivalent Single Layer (ESL), Refined ESL (Zig-Zag theories) and Layer-Wise (LW) theories. Each one of these theories is reviewed along with the plate hypotheses which are made for each ply and/or laminate. To solve such complex structural engineering problems, numerical methods are normally used. Second, few solution methods are reviewed and quoted, but focus is given to the Finite Element Method (FEM). The contribution of this work is the implementation of a new solution method for laminated composites and sandwich structures based on a Generalized Unified Formulation (GUF) via FEM. A quadrilateral 4-node element was developed and evaluated using in-house Finite Element program. The C-1 continuity requirements is fulfilled for the transversal displacement field variable. This method is tagged as Caliri\'s Generalized Formulation (CGF). Results for isotropic plates, laminated composite plates and sandwich structures for thin and thick laminates are compared with literature data and solutions via Abaqus. The through-the-thickness profile results reinforce the need for non-linear plate (laminated or not) solutions. It was shown that the static and dynamic solutions employing the proposed solution method yield coherent results when compared with other solution methods. Among the different case studies investigated, it was verified that it is possible to obtain results with high agreement. For a soft-core sandwich structure, the displacement result for a static loading is reported as high as 99.8% and the result of a modal analysis of the same structure shows an accuracy of 99.5%, comparing to the results from a 3D finite element model built with a commercial software.

Em engenharia, a quantidade de problemas geométricos complexos que precisam ser resolvidos empregando teorias de placas ou cascas é notável. Esta é a razão por que há tantas teorias que buscam simplificar os problemas tridimensionais em outros menos custosos computacionalmente. Além disso, o aumento atual do uso de estruturas sanduíche requer que as formulações bidimensionais sejam mais precisas. Esta tese, num primeiro momento, compila a maioria das teorias de placa, comentando as principais diferenças, vantagens e desvantagens de cada uma. As formulações bidimensionais de placas laminadas são classificadas principalmente de acordo com o tratamento da coordenada na direção normal a superfície da mesma: Camada Única Equivalente (ESL), ESL refinada (teorias Zig-Zag) e Teorias Discretas ou de Camada (LW). Cada uma destas teorias é revista juntamente com as hipóteses de placas que são feitas para cada uma das camadas ou para o laminado como um todo. Para resolver tais problemas estruturais em engenharia, métodos numéricos são normalmente utilizados. Portanto, num segundo momento, alguns métodos de solução são citados e revisados, mas o foco é dado ao Método dos Elementos Finitos (MEF). A contribuição deste trabalho consiste na implementação de um novo método de solução de compósitos laminados e estruturas sanduíche com base em um sistema unificado de Formulação Generalizada (GUF) via MEF. Um elemento quadrilátero de 4 nós foi desenvolvido e avaliado com um código de Elementos Finitos desenvolvido pelo presente autor. Os requisitos para continuidade do tipo C-1 são respeitados para a variável de deflexão da placa. Esse método é nomeado de Formulação Generalizada do Caliri (CGF). Resultados para placas isotrópicas, placas de laminado compósito e estruturas sanduíche consideradas finas ou espessas são comparados com dados da literatura e soluções via Abaqus. Os resultados obtidos ao longo da espessura reforçam a necessidade de soluções de placa não-lineares para placas espessas (laminadas ou não). Mostrou-se que as soluções estáticas e dinâmicas empregando o método proposto fornecem resultados coerentes quando comparados com outros métodos de solução. Dentre os diversos estudos de caso investigados, verificou-se que é possível se obter resultados com alta concordância. Para uma estrutura sanduíche com núcleo macio, o resultado de deslocamento previsto para um carregamento estático chega a 99.8% de concordância e o resultado de uma análise modal da mesma estrutura mostra uma concordância de 99.5% com os resultados de um modelo feito com elementos 3D em um programa comercial de elementos finitos. / In engineering, the amount of complex geometrical problems, which need to be solved by using plates and shells theories, is remarkable. This is the reason why there are so many plate and shell theories which attempt to simplify three dimensional problems into ones with low computational cost. Additionally, the current increasing use of sandwich structures requires that the two dimensional formulations be accurate enough. First, this thesis compiles most of the plate theories from the literature and quotes the main differences, advantages and weaknesses of each one. The bi-dimensional laminated plate formulations are mainly classified according to the treatment of the variable in the normal direction of the plate surface: Equivalent Single Layer (ESL), Refined ESL (Zig-Zag theories) and Layer-Wise (LW) theories. Each one of these theories is reviewed along with the plate hypotheses which are made for each ply and/or laminate. To solve such complex structural engineering problems, numerical methods are normally used. Second, few solution methods are reviewed and quoted, but focus is given to the Finite Element Method (FEM). The contribution of this work is the implementation of a new solution method for laminated composites and sandwich structures based on a Generalized Unified Formulation (GUF) via FEM. A quadrilateral 4-node element was developed and evaluated using in-house Finite Element program. The C-1 continuity requirements is fulfilled for the transversal displacement field variable. This method is tagged as Caliri\'s Generalized Formulation (CGF). Results for isotropic plates, laminated composite plates and sandwich structures for thin and thick laminates are compared with literature data and solutions via Abaqus. The through-the-thickness profile results reinforce the need for non-linear plate (laminated or not) solutions. It was shown that the static and dynamic solutions employing the proposed solution method yield coherent results when compared with other solution methods. Among the different case studies investigated, it was verified that it is possible to obtain results with high agreement. For a soft-core sandwich structure, the displacement result for a static loading is reported as high as 99.8% and the result of a modal analysis of the same structure shows an accuracy of 99.5%, comparing to the results from a 3D finite element model built with a commercial software.

The present document covers the studies over Structural Health Monitoring systems via vibration based methods. The topic is organized in two parallel studies. The first one analyzes the integrity of metal-composite single lap bonded joints. The second one approaches similar analyses for sandwich structures. The monitoring was made by investigating the dynamic response both computationally and experimentally to verify the reliability of applying vibration based SHM procedures, specifically with the objective of identifying the presence of debonding damage. The dynamic responses were obtained via accelerometers and piezoelectric sensors placed on top of the investigated structures (on the outward surface). The purpose for the accelerometers is to provide reference data for the analyses involving the piezoelectric sensors. Different metrics of damage identification were investigated, all working over a determined frequency range. They quantify the damage by analyzing either the magnitudes or phase angles of the dynamic responses among the undamaged and damage structures. This present work proposed modifications to some methodologies of damage quantification found in the literature and compared the results. The new metrics offered more reliable values for the damage quantification on several of the analyses. It was verified that the metrics are valid for the scenarios observed in the present study. The experimental analyses showed also the influence on the dynamic response due to the position of small elastomeric elements. In regards to the finite element analyses, the computational models showed similar results to the experimental data, the more accurate ones being the models for the bonded joints. For the computational models, improvements can be applied into the piezoelectric sensor (e.g. by using new finite element formulations), as well as the region of debonding (e.g. by using contact algorithms). It is important to highlight that the elastic properties of the skins for the sandwich structure were obtained by the literature, so the model can be improved in the future by applying properties obtained experimentally. / Esta dissertação aborda os estudos realizados no campo de Sistemas de Monitoramento da Integridade Estrutural por meio de métodos baseados em vibrações. O tópico abordado é organizado em dois estudos paralelos. O primeiro é relativo ao monitoramento da integridade de juntas coladas metal-compósito. O segundo versa sobre análises semelhantes em estruturas sanduíche. O monitoramento foi executado através das análises das assinaturas dinâmicas das estruturas, tanto computacionalmente quanto experimentalmente, visando avaliar a capacidade de metodologias vibracionais de SHM em detectar dano de descolamento. As respostas dinâmicas foram obtidas por meio de acelerômetros e sensores piezelétricos dispostos sobre a superfície das estruturas avaliadas. Os acelerômetros fornecem dados de referência para as análises realizadas com base nas respostas do sensor piezelétrico. Diferentes métricas de identificação de dano são abordadas, sendo que todas estão baseadas em análise no domínio da frequência, utilizando parâmetros de magnitude ou ângulo de fase das estruturas danificadas e intactas. O presente trabalho propôs alterações em algumas das metodologias encontradas na literatura e comparou os resultados das métricas originais com as modificadas. As métricas modificadas apresentaram resultados mais consistentes em vários cenários de análise. Constatou-se também que as métricas abordadas mostram-se válidas para os casos observados no presente estudo. As análises experimentais também evidenciaram a influência na assinatura dinâmica da estrutura sanduíche causada pelo posicionamento de pequenos elementos elastoméricos. Com relação às análises via elementos finitos, os modelos computacionais apresentaram resultados similares aos obtidos experimentalmente, sendo os da junta colada os mais precisos. Tais modelos computacionais podem ser melhorados no futuro por meio de uma modelagem mais detalhada dos elementos piezelétricos (por exemplo: por meio de novas formulações), como também da região de descolamento (por exemplo: por meio da implementação de algoritmos de contato). Deve-se ressaltar também que as propriedades elásticas das lâminas externas da estrutura sanduíche foram obtidas da literatura, assim sendo, o modelo poderá ser melhorado em estudos futuros por meio do emprego de propriedades obtidas experimentalmente.

The present document covers the studies over Structural Health Monitoring systems via vibration based methods. The topic is organized in two parallel studies. The first one analyzes the integrity of metal-composite single lap bonded joints. The second one approaches similar analyses for sandwich structures. The monitoring was made by investigating the dynamic response both computationally and experimentally to verify the reliability of applying vibration based SHM procedures, specifically with the objective of identifying the presence of debonding damage. The dynamic responses were obtained via accelerometers and piezoelectric sensors placed on top of the investigated structures (on the outward surface). The purpose for the accelerometers is to provide reference data for the analyses involving the piezoelectric sensors. Different metrics of damage identification were investigated, all working over a determined frequency range. They quantify the damage by analyzing either the magnitudes or phase angles of the dynamic responses among the undamaged and damage structures. This present work proposed modifications to some methodologies of damage quantification found in the literature and compared the results. The new metrics offered more reliable values for the damage quantification on several of the analyses. It was verified that the metrics are valid for the scenarios observed in the present study. The experimental analyses showed also the influence on the dynamic response due to the position of small elastomeric elements. In regards to the finite element analyses, the computational models showed similar results to the experimental data, the more accurate ones being the models for the bonded joints. For the computational models, improvements can be applied into the piezoelectric sensor (e.g. by using new finite element formulations), as well as the region of debonding (e.g. by using contact algorithms). It is important to highlight that the elastic properties of the skins for the sandwich structure were obtained by the literature, so the model can be improved in the future by applying properties obtained experimentally. / Esta dissertação aborda os estudos realizados no campo de Sistemas de Monitoramento da Integridade Estrutural por meio de métodos baseados em vibrações. O tópico abordado é organizado em dois estudos paralelos. O primeiro é relativo ao monitoramento da integridade de juntas coladas metal-compósito. O segundo versa sobre análises semelhantes em estruturas sanduíche. O monitoramento foi executado através das análises das assinaturas dinâmicas das estruturas, tanto computacionalmente quanto experimentalmente, visando avaliar a capacidade de metodologias vibracionais de SHM em detectar dano de descolamento. As respostas dinâmicas foram obtidas por meio de acelerômetros e sensores piezelétricos dispostos sobre a superfície das estruturas avaliadas. Os acelerômetros fornecem dados de referência para as análises realizadas com base nas respostas do sensor piezelétrico. Diferentes métricas de identificação de dano são abordadas, sendo que todas estão baseadas em análise no domínio da frequência, utilizando parâmetros de magnitude ou ângulo de fase das estruturas danificadas e intactas. O presente trabalho propôs alterações em algumas das metodologias encontradas na literatura e comparou os resultados das métricas originais com as modificadas. As métricas modificadas apresentaram resultados mais consistentes em vários cenários de análise. Constatou-se também que as métricas abordadas mostram-se válidas para os casos observados no presente estudo. As análises experimentais também evidenciaram a influência na assinatura dinâmica da estrutura sanduíche causada pelo posicionamento de pequenos elementos elastoméricos. Com relação às análises via elementos finitos, os modelos computacionais apresentaram resultados similares aos obtidos experimentalmente, sendo os da junta colada os mais precisos. Tais modelos computacionais podem ser melhorados no futuro por meio de uma modelagem mais detalhada dos elementos piezelétricos (por exemplo: por meio de novas formulações), como também da região de descolamento (por exemplo: por meio da implementação de algoritmos de contato). Deve-se ressaltar também que as propriedades elásticas das lâminas externas da estrutura sanduíche foram obtidas da literatura, assim sendo, o modelo poderá ser melhorado em estudos futuros por meio do emprego de propriedades obtidas experimentalmente.

Ces travaux de thèse proposent utiliser les polymères à mémoire de forme comme moyen de contrôle desvibrations des structures. Outre hystérésis de mémoire qui est classiquement mis en avant, ces matériauxpossèdent des propriétés amortissantes intrinsèques qui sont d'autant plus intéressantes lorsque l’effetmémoire de forme est important. Dans un premier temps une caractérisation des propriétés mécaniques dutBA/PEGDMA, polymère à mémoire de forme de l'étude, est effectuée par analyse dynamique mécanique.Un modèle rhéologique basé sur lʹéquivalence temps-température, le 2S2P1D, est utilisé pour rendre comptedu comportement viscoélastique du polymère. Dans un deuxième temps, une campagne expérimentale estmenée, sur une large bande de fréquences et de températures, grâce à divers moyens expérimentaux(statiques, modaux, nano-indentations, ultrasons, dynamiques hautes fréquences, microscopie acoustique)afin de définir le domaine de validité, fréquentiel et thermique, du modèle rhéologique. Dans un troisièmetemps, le polymère à mémoire de forme est intégré à une structure composite de type sandwich pour mettreen évidence le pouvoir amortissant impressionnant du matériau. Enfin, une méthodologie de contrôle delʹamortissement par la température est proposée. En effet, la dissipation d’énergie dans le sandwich sʹavèrecontrôlable, la température permettant d’ajuster la rigidité et le facteur de perte du tBA/PEGDMA pour unamortissement optimal sur une large bande de fréquences. / This work proposes to use shape memory polymers to control structural vibrations. These materials exhibit amemory hysteresis which is practically associated with intrinsic damping properties which are very highwhen the memory effect is strong. First, a thermomechanical characterization of the shape memory polymerof interest (tBA/PEGDMA) is performed by dynamic mechanical analysis. A rheological model based on timetemperaturesuperposition is used to represent the viscoelastic behavior of the polymer. Secondly, anexperimental campaign is performed over a wide frequency and temperature range, through variousexperimental techniques (static, modal, nanoindentation, ultrasounds, high frequency dynamic analysis,acoustic microscopy) to define the area of validity, in frequency and temperature, of the rheological model.Third, the shape memory polymer is integrated into a composite sandwich structure to highlight the awesomedamping capabilities of the material. Finally, a damping tuning methodology by temperature control isproposed. Indeed, the power dissipation in the sandwich is related to physical properties of the tBA/PEGDMA core which are temperature-controlled to optimize the damping over a given frequency range.

Failure modes for sandwich beams of GFRP laminate skins and Nomex honeycomb core are investigated. Theoretical models using honeycomb mechanics and classical beam theory are described. A failure mode map for loading under 3-point bending, is constructed, showing the dependence of failure mode and load on the ratio of skin thickness to span length and honeycomb relative density. Beam specimens are tested in 3-point bending. The effect of honeycomb direction is also examined. The experimental data agree satisfactorily with the theoretical predictions. The results reveal the important role of core shear in a sandwich beam's bending behaviour and the need for a better understanding of indentation failure mechanism. High order sandwich beam theory (HOSBT) is implemented to extract useful information about the way that sandwich beams respond to localised loads under 3-point bending. 'High-order' or localised effects relate to the non-linear patterns of the in-plane and vertical displacements fields of the core through its height resulting from the unequal deformations in the loaded and unloaded skins. The localised effects are examined experimentally by Surface Displacement Analysis of video images recorded during 3-point bending tests. A new parameter based on the intrinsic material and geometric properties of a sandwich beam is introduced to characterise its susceptibility to localised effects. Skin flexural rigidity is shown to play a key role in determining the way that the top skin allows the external load to pass over the core. Furthermore, the contact stress distribution in the interface between the central roller and the top skin, and its importance to an indentation stress analysis, are investigated. To better model the failure in the core under the vicinity of localised loads, an Arcan- type test rig is used to test honeycomb cores under simultaneous compression and shear loading. The experimental measurements show a linear relationship between the out-of-plane compression and shear in honeycomb cores. This is used to derive a failure criterion for applied shear and compression, which is combined with the high order sandwich beam theory to predict failure caused by localised loads in sandwich beams made of GFRP laminate skins and Nomex honeycomb under 3-point bending loading. Short beam tests with three different indenter's size are performed on appropriately prepared specimens. Experiments validate the theoretical approach and reveal the nature of pre- and post-failure behaviour of these sandwich beams. HOSBT is used as a compact computational tool to reconstruct failure mode maps for sandwich panels. Superposition of weight and stiffness contours on these failure maps provide carpet plots for design optimisation procedures.

Dans le cadre du développement d’un outil semi-analytique de pré-dimensionnement de structures sandwich soumises à des impacts à vitesse intermédiaire (<20m.s-1), nous proposons la détermination d’une solution efficace, basée sur les séries de Fourier avec des conditions aux limites générales. Les équations gouvernantes qui permettent de décrire la réponse transitoire élastique de plaques stratifiées orthotropes avec prise en compte d’une loi non linéaire de contact hertzien sont développées en utilisant un schéma de discrétisation temporelle explicite. Pour les conditions aux limites générales, la solution en séries de Fourier est complétée par une série mixte de polynômes-cosinus, qui permet d’aboutir à la solution, tout en permettant à la série de satisfaire les équations d’équilibres ainsi que les conditions limites, de façon exacte en augmentant le nombre de termes de la série. Afin de tenir compte des phénomènes physiques locaux lors de l’impact de structure sandwich, la plasticité et la rupture locale de la plaque anti-perforation sont introduites dans une formulation modifiée du contact de Hertz et l’écrasement de l’âme du sandwich est ajouté dans l’équation d’équilibre du projectile. Les solutions obtenues par cette méthode sont en accord avec les résultats par modélisation éléments finis de plaques composites multicouches impactées par un projectile. Une campagne expérimentale d’impact de type « box corner » sur des plaques sandwich de 1m², a servi de référence expérimentale et permis la validation de ce modèle complet. Finalement, le couplage de ce modèle à un optimiseur basé sur les techniques de plans d’expériences et de surfaces de réponses (métamodèles), nous a permis de choisir la meilleure structure d’absorption d’énergie (matériaux et géométrie) pour des structures plaques soumises à des impacts de 7kJ. Un test sur un véhicule réel avec la configuration structurelle choisie, nous a permis de valider l’outil final de pré-dimensionnement et de confirmer la qualité des résultats numériques obtenus par ce modèle semi-analytique. / A semi-analytical tool for the design of sandwich structures under intermediate speed loadings impact (<20m.s-1) is proposed by using an efficient solution based on the Fourier series with general boundary conditions. The governing equations, which describe dynamic elastic response of orthotropic laminates and include the non linear Hertzian contact law, are derived by means of explicit time discretization. For the general boundary conditions, the Fourier series solution is supplemented with mixed polynomial-cosine series, which allows derivation of the classical solution by letting the series satisfy exactly the governing differential equation and the boundary conditions with increased values of terms series. To take local physical behavior during sandwich structure impact into account, local plasticity and failure of the protection plate are introduced in a modified form of the Hertzian contact and the compression of the foam is added in the equilibrium equation of the projectile. The solutions obtained with this new method are close to those found by finite element simulations for impact on multilayers composite structures. An experimental campaign with one square meter sandwich structures impacted by corner box projectile is then used to validate the whole model. Finally, the best sandwich structure for energy absorption under a 7kJ impact (material and geometry) is chosen by coupling the model with an optimizer based on the metamodel approach. This solution is applied to a real vehicle and the results confirm the quality of the design of the structure.