In the thesis explicit dual parabolic-elliptic models are constructed for the Konenkov flexural edge wave and the Stoneley-type flexural interfacial wave in case of thin linearly elastic plates. These waves do not appear in an explicit form in the original equations of motion within the framework of the classical Kirchhoff plate theory. The thesis is aimed to highlight the contribution of the edge and interfacial waves into the overall displacement field by deriving specialised equations oriented to aforementioned waves only. The proposed models consist of a parabolic equation governing the wave propagation along a plate edge or plate junction along with an elliptic equation over the interior describing decay in depth. In this case the parabolicity of the one-dimensional edge and interfacial equations supports flexural wave dispersion. The methodology presented in the thesis reveals a dual nature of edge and interfacial plate waves contrasting them to bulk-type wave propagating in thin elastic structures. The thesis tackles a number of important examples of the edge and interfacial wave propagation. First, it addresses the propagation of Konenkov flexural wave in an elastic isotropic plate under prescribed edge loading. For the latter, parabolic-elliptic explicit models were constructed and thoroughly investigated. A similar problem for a semi-infinite orthotropic plate resulted in a more general dual parabolic-elliptic model. Finally, an anal- ogous model was derived and analysed for two isotropic semi-infinite Kirchhoff plates under perfect contact conditions.

Les panneaux sandwichs sont des éléments de structure omniprésents au quotidien. Leur efficacité structurelle n'est plus à démontrer. Elle est même un élément déterminant dans le marché qui leur est associé. Ce mémoire de doctorat s'intéresse à un nouveau type d 'âme de panneau sandwich qui pourrait être amené à supplanter le nid d'abeilles dans certaines applications, le module à chevrons. L'objectif est donc de pouvoir faire une estimation précise du comportement de ces nouvelles âmes. Cependant le gain en efficacité structurelle des panneaux sandwichs se paye par une augmentation considérable de la complexité de leur comportement mécanique. C'est en particulier le cas de la raideur à l'effort tranchant qui est déterminante pour estimer l'efficacité d'une âme de panneau sandwich. Ainsi, ce travail nous a amené à reconsidérer en profondeur les méthodes pour calculer le comportement à l'effort tranchant des plaques en général. Il nous a conduit à proposer une nouvelle théorie des plaques ainsi qu'une méthode d'homogénéisation associée dans le cas périodique. Cette théorie peut être considérée comme l'extension de la théorie bien connue de Reissner-Mindlin au cas des plaques hétérogènes. Elle ne peut cependant pas être réduite au mod èle de Reissner-Mindlin dans le cas général. Dans le cas particulier des panneaux sandwichs incluant le module à chevrons, l'application de cette méthode d'homogénéisation permet de mettre en évidence un phénomène de distorsion des peaux qui affecte de façon notable la raideur à l'effort tranchant de ces panneaux / Sandwich panels are widespread in everyday life. Their structural efficiency is well-known and is a central criterion in possible applications. This Ph.D. thesis is dedicated to the study of a new sandwich panel core which might replace honeycomb in some applications: the chevron pattern. In order to compare this new core to other ones, an accurate knowledge of its mechanical behavior is necessary. However, the price for structural efficiency is a more complex mechanical behavior. This is the case for the shear forces stiffness which is critical when comparing sandwich panels cores. Thus, in this work we reconsider in details and in the general case how to derive plates behavior under shear forces. A new plate theory is suggested as well as the related homogenization scheme for periodic plates. This plate theory is the extension of the well-known Reissner-Mindlin plate theory in the case of heterogeneous plates. However, it cannot be reduced to a Reissner-Mindlin plate theory in the general case. In the special case of sandwich panels including the chevron pattern, applying the homogenization scheme brings out a skins distorsion phenomenon which affects a lot their shear forces stiffness

The complicated process may cause the internal defects of multi-layered ceramic capacitors (MLCCs) and result in the malfunctions. This work aims to investigate the deformations of MLCCs that composed of nearly a hundred of BaTiO3 and Ni electrode films interleaved and stacked due to high pressure at elevated temperature. This study focuses on theoretical and numerical analyses. Classical laminated plate theory, linear elastic assumptions and equilibrium equations were adopted. Associated with the texts by Timoshenko and practical manufacturing process, three types of boundary conditions were considered, such as all edges simple-supported, two opposite edges simple-supported and the other two free, and four edges free. Also, two more conditions need be added, including four fixed points at corners and the elastic foundation at bottom. The numerical simulation by finite element method (FEM) incorporated with software ANSYS was used to obtain the displacement field of MLCCs due to high pressure at elevated temperature. The MLCCs were divided into nine regions with suitably different boundary conditions. Compared with the numerical results the analytical solutions of nine regions were found satisfactorily acceptable, i.e., the errors were about 0.1% - 6.2% for the boundary conditions of four edges free and four corners fixed. The errors about 0.13% - 6.15% were also acceptable for the boundary conditions of two opposite edges simple-supported and the others free. However, the analytical solutions did not agree with the numerical results for the case of all the boundary conditions simple-supported. Finally the proposed theoretical methodology provides an analytical method alternatively, instead of FEM and ANSYS, to analyze a nearly hundred layered MLCCs.

abstract: Stress-related failure such as cracking are an important photovoltaic (PV) reliability issue since it accounts for a high percentage of power losses in the midlife-failure and wear-out failure regimes. Cell cracking can only be correlated with module degradation when cracks are of detectable size and detrimental to the performance. Several techniques have been explored to access the deflection and stress status on solar cell, but they have disadvantages such as high surface sensitivity. This dissertation presents a new and non-destructive method for mapping the deflection on encapsulated solar cells using X-ray topography (XRT). This method is based on Bragg diffraction imaging, where only the areas that meet diffraction conditions will present contrast. By taking XRT images of the solar cell at various sample positions and applying an in-house developed algorithm framework, the cell‘s deflection map is obtained. Error analysis has demonstrated that the errors from the experiment and the data processing are below 4.4 and 3.3%. Von Karman plate theory has been applied to access the stress state of the solar cells. Under the assumptions that the samples experience pure bending and plain stress conditions, the principal stresses are obtained from the cell deflection data. Results from a statistical analysis using a Weibull distribution suggest that 0.1% of the data points can contribute to critical failure. Both the soldering and lamination processes put large amounts of stress on solar cells. Even though glass/glass packaging symmetry is preferred over glass/backsheet, the solar cells inside the glass/glass packaging experience significantly more stress. Through a series of in-situ four-point bending test, the assumptions behind Von Karman theory are validated for cases where the neutral plane is displaced by the tensile and compressive stresses. The deflection and stress mapping method is applied to two next generation PV concepts named Flex-circuit and PVMirror. The Flex-circuit module concept replaces traditional metal ribbons with Al foils for electrical contact and PVMirror concept utilizes a curved PV module design with a dichroic film for thermal storage and electrical output. The XRT framework proposed in this dissertation successfully characterized the impact of various novel interconnection and packaging solutions. / Dissertation/Thesis / Doctoral Dissertation Materials Science and Engineering 2019

The aerospace industry is increasingly coming to the conclusion that physics-based high-fidelity models need to be used as early as possible in the design of its products. At the preliminary design stage of wing structures, though highly desirable for its high accuracy, a detailed finite element analysis(FEA) is often not feasible due to the prohibitive preparation time for the FE model data and high computation cost caused by large degrees of freedom. In view of this situation, often equivalent beam models are used for the purpose of obtaining global solutions. However, for wings with low aspect ratio, the use of equivalent beam models is questionable, and using an equivalent plate model would be more promising. An efficient method, Equivalent Plate Analysis or simply EPA, using an equivalent plate model, is developed in the present work for studying the static and free-vibration problems of built-up wing structures composed of skins, spars, and ribs. The model includes the transverse shear effects by treating the built-up wing as a plate following the Reissner-Mindlin theory (FSDT). The Ritz method is used with the Legendre polynomials being employed as the trial functions. Formulations are such that there is no limitation on the wing thickness distribution. This method is evaluated, by comparing the results with those obtained using MSC/NASTRAN, for a set of examples including both static and dynamic problems. The Equivalent Plate Analysis (EPA) as explained above is also used as a basis for generating other efficient methods for the early design stage of wing structures, such that they can be incorporated with optimization tools into the process of searching for an optimal design. In the search for an optimal design, it is essential to assess the structural responses quickly at any design space point. For such purpose, the FEA or even the above EPA, which establishes the stiffness and mass matrices by integrating contributions spar by spar, rib by rib, are not efficient enough. One approach is to use the Artificial Neural Network (ANN), or simply called Neural Network (NN) as a means of simulating the structural responses of wings. Upon an investigation of applications of NN in structural engineering, methods of using NN for the present purpose are explored in two directions, i.e. the direct application and the indirect application. The direct method uses FEA or EPA generated results directly as the output. In the indirect method, the wing inner-structure is combined with the skins to form an "equivalent" material. The constitutive matrix, which relates the stress vector to the strain vector, and the density of the equivalent material are obtained by enforcing mass and stiffness matrix equities with regard to the EPA in a least-square sense. Neural networks for these material properties are trained in terms of the design variables of the wing structure. It is shown that this EPA with indirect application of Neural Networks, or simply called an Equivalent Skin Analysis (ESA) of the wing structure, is more efficient than the EPA and still fairly good results can be obtained. Another approach is to use the sensitivity techniques. Sensitivity techniques are frequently used in structural design practices for searching the optimal solutions near a baseline design. In the present work, the modal response of general trapezoidal wing structures is approximated using shape sensitivities up to the second order, and the use of second order sensitivities proved to be yielding much better results than the case where only first order sensitivities are used. Also different approaches of computing the derivatives are investigated. In a design space with a lot of design points, when sensitivities at each design point are obtained, it is shown that the global variation in the design space can be readily given based on these sensitivities. / Ph. D.

L’utilisation des multicouches prend de plus en plus d’ampleur dans le domaine des sciences de l’ingénieur, tout d’abord dans l’industrie, et plus récemment de plus en plus en Génie Civil. Qu’il s’agisse de complexes mêlant des polymères, du bois ou du béton, des efforts importants sont nécessaires pour la modélisation fine de ce type de matériaux. En effet, des phénomènes induits par l’anisotropie et l’hétérogénéité sont associés à ces multi-matériaux : effets de bords, dilatations thermiques différentielles, délaminages/décollements ou non linéarités de type viscosité, endommagement, plasticité dans les couches ou aux interfaces. Parmi les modèles proposés dans la littérature, on trouve par exemple des modèles monocouche équivalente ou de type "Layerwise" (une cinématique par couche). Appartenant à cette deuxième catégorie, des modèles ont été développés depuis quelques années dans le laboratoire Navier et permettent une description suffisamment fine pour aborder les problématiques spécifiques citées plus haut tout en conservant un caractère opératoire certain. En introduisant des efforts d’interfaces comme des efforts généralisés du modèle, ces approches ont montré leur efficacité vis-à-vis de la représentation des détails au niveau inter- et intra-couches. Il est alors aisé de proposer des comportements et des critères d’interfaces et d’être efficace pour la modélisation du délaminage ou décollement, phénomène très présent dans les composites multicouches assemblés et collés. Par conséquent, un programme éléments finis MPFEAP a été développé dans le laboratoire Navier. Le modèle a également été introduit sous la forme d’un User Element dans ABAQUS, dans sa forme la plus simple (interfaces parfaites).Un nouveau model layerwise est proposé dans ce mémoire pour les plaques multicouches, appelé "Statically Compatible Layerwise Stresses with first-order membrane stress approximations per layer in thickness direction" SCLS1. Le modèle est conforme aux équations d’équilibre 3D ainsi qu’aux conditions aux limites de bord libre. En outre, une version raffinée du nouveau modèle est obtenu en introduisant plusieurs couches mathématiques par couche physique. Le nouveau modèle a été mis en œuvre dans une nouvelle version du code éléments finis MPFEAP.En parallèle, un programme d’éléments finis basé sur la théorie Bending-Gradient développée dans le laboratoire Navier est proposé ici. Le modèle est une nouvelle théorie de plaque épaisse chargée hors-plan où les inconnues statiques sont celles de la théorie Love-Kirchhoff, à laquelle six composantes sont ajoutées représentant le gradient du moment de flexion. La théorie Bending- Gradient est obtenue à partir de la théorie Generalized-Reissner: cette dernière implique quinze degrés de liberté cinématiques, huit d’entre eux étant lié uniquement à la déformation de Poisson hors-plan, et donc l’idée principale de la théorie de plaque Bending-Gradient est de simplifier la théorie Generalized-Reissner en réglant ces huit d.o.f. à zéro et de négliger la contribution de la contrainte normale σ33 dans l’équation constitutive du modèle de plaque. Un programme éléments finis appelé BGFEAP a été développé pour la mise en œuvre de l’élément de Bending-Gradient. Un User Element dans Abaqus a été aussi développé pour la théorie Bending-Gradient / The use of multilayer is becoming increasingly important in the field of engineering, first in the industry, and more recently more and more in Civil Engineering. Whether complex blend of polymers, wood or concrete, significant efforts are required for accurate modeling of such materials. Indeed, phenomena induced anisotropy and heterogeneity are associated with these multi-material: edge effects, differential thermal expansion, delamination/detachment or nonlinearities viscosity type damage, plasticity in layers or interfaces. Among the models proposed in the literature, we found for example equivalent monolayer model or of "LayerWise" type (a kinematic per layer). Belonging to the second category, models have been developed in recent years in Navier allow a sufficiently detailed description to address specific issues mentioned above while maintaining a surgical nature. By introducing interface forces as generalized forces of the model, these approaches have demonstrated their effectiveness vis-à-vis the representation of details at inter- and intra-layers. It is then easy to offer behaviors and interfaces criteria and to be effective for modeling delamination or detachment, phenomenom very present in multilayered composites assembled and glued together. Therefore, a finite element program MPFEAP was developed in Navier laboratory. The model was also introduced as a User Element in ABAQUS, in its simplest form (perfect interfaces).A new layerwise model for multilayered plates is proposed in this dissertation, named Statically Compatible Layerwise Stresses with first-order membrane stress approximations per layer in thickness direction SCLS1. The model complies exactly with the 3D equilibrium equations and the free-edge boundary conditions. Also, a refined version of the new model is obtained by introducing several mathematical layers per physical layer. The new model has been implemented in a new version of the in-house finite element code MPFEAP.In parallel, a finite element program based on the Bending-Gradient theory which was developed in Navier laboratory, is proposed here. The model is a new plate theory for out-of-plane loaded thick plates where the static unknowns are those of the Love-Kirchhoff theory, to which six components are added representing the gradient of the bending moment. The Bending-Gradient theory is obtained from the Generalized-Reissner theory: the Generalized-Reissner theory involves fifteen kinematic degrees of freedom, eight of them being related only to out-of-plane Poisson’s distortion and thus, the main idea of the Bending-Gradient plate theory is to simplify the Generalized-Reissner theory by setting these eight d.o.f. to zero and to neglect the contribution of the normal stress σ33 in the plate model constitutive equation. A finite element program called BGFEAP has been developed for the implementation of the Bending-Gradient element. A User Element in Abaqus was also developed for the Bending-Gradient theory

In aerospace applications, use of laminates made of composite materials as face sheets in sandwich panels are on the rise. These composite laminates have low transverse shear and transverse normal moduli compared to the in-plane moduli. It is also seen that the corresponding transverse strength values are very low compared to the in-plane strength leading to delaminations. Further, in sandwich structures, the core is subjected to significant transverse shear stresses. Therefore the interlaminar stresses (i.e., transverse shear and normal) can govern the design of sandwich structures. As a consequence, the first step in achieving efficient designs is to develop the ability to reliably estimate interlaminar stresses. Stress analysis of the composite sandwich structures can be carried out using 3-D finite elements for each layer. Owing to the enormous computational time and resource requirements for such a model, this process of analysis is rendered inefficient. On the other hand, existing plate/shell finite elements, when appropriately chosen, can help quickly predict the 2-D displacements with reasonable accuracy. However, their ability to calculate the thickness-wise distributions of interlaminar shear and normal stresses and 3-D displacements remains as a research goal. Frequently, incremental refinements are offered over existing solutions. In this scenario, an asymptotically correct dimensional reduction from 3-D to 2-D, if possible, would serve to benchmark any ongoing research. The employment of a mathematical technique called the Variational Asymptotic Method (VAM) ensures the asymptotical correctness for this purpose. In plates and sandwich structures, it is typically possible to identify (purely from the defined material distributions and geometry) certain parameters as small compared to others. These characteristics are invoked by VAM to derive an asymptotically correct theory. Hence, the 3-D problem of plates is automatically decomposed into two separate problems (namely 1-D+2-D), which then exchange relevant information between each other in both ways. The through-the-thickness analysis of the plate, which is a 1-D analysis, provides asymptotic closed form solutions for the 2-D stiffness as well as the recovery relations (3-D warping field and displacements in terms of standard plate variables). This is followed by a 2-D plate analysis using the results of the 1-D analysis. Finally, the recovery relations regenerate all the required 3-D results. Thus, this method of developing reduced models involves neither ad hoc kinematic assumptions nor any need for shear correction factors as post-processing or curve-fitting measures. The results are most general and can be made as accurate as desired, while the procedure is computationally efficient. In the present work, an asymptotically correct plate theory is formulated for composite sandwich structures. In developing this theory, in addition to the small parameters (such as small strains, small thickness-to-wavelength ratios etc.,) pertaining to the general plate theory, additional small parameters characterizing (and specific to) sandwich structures (viz., smallness of the thickness of facial layers com-pared to that of the core and smallness of elastic material stiffness of the core in relation to that of the facesheets) are used in the formulation. The present approach also satisfies the interlaminar displacement continuity and transverse equilibrium requirements as demanded by the exact 3-D formulation. Based on the derived theory, numerical codes are developed in-house. The results are obtained for a typical sandwich panel subjected to mechanical loading. The 3-D displacements, inter-laminar normal and shear stress distributions are obtained. The results are compared with 3-D elasticity solutions as well as with the results obtained using 3-D finite elements in MSC NASTRAN®. The results show good agreement in spite of the major reduction in computational effort. The formulation is then extended for thermo-elastic deformations of a sandwich panel. This thesis is organized chronologically in terms of the objectives accomplished during the current research. The thesis is organized into six chapters. A brief organization of the thesis is presented below. Chapter-1 briefly reviews the motivation for the stress analysis of sandwich structures with composite facesheets. It provides a literature survey on the stress analysis of composite laminates and sandwich plate structures. The drawbacks of the existing anlaytical approaches as opposed to that of the VAM are brought out. Finally, it concludes by listing the main contributions of this research. Chapter-2 is dedicated to an overview of the 3-D elasticity formulation of composite sandwich structures. It starts with the 3-D description of a material point on a structural plate in the undeformed and deformed configurations. Further, the development of the associated 3-D strain field is also described. It ends with the formulation of the potential energy of the sandwich plate structure. Chapter-3 develops the asymptotically correct theory for composite sandwich plate structure. The mathematical description of VAM and the procedure involved in developing the dimensionally reduciable structural models from 3-D elasticity functional is first described. The 1-D through-the-thickness analysis procedure followed in developing the 2-D plate model of the composite sandwich structure is then presented. Finally, the recovery relations (which are one of the important results from 1-D through-the-thickness analysis) to extract 3-D responses of the structure are obtained. The developed formulation is applied to various problems listed in chapter 4. The first section of this chapter presents the validation study of the present formulation with available 3-D elasticity solutions. Here, composite sandwich plates for various length to depth ratios are correlated with available 3-D elasticity solutions as given in [23]. Lastly, the distributions of 3-D strains, stresses and displacements along the thickness for various loadings of a typical sandwich plate structure are correlated with corresponding solutions using well established 3-D finite elements of MSC NASTRAN® commerical FE software. The developed and validated formulation of composite sandwich structure for mechanical loading is extended for thermo-elastic deformations. The first sections of this chapter describes the seamless inclusion of thermo-elastic strains into the 3-D elasticity formulation. This is followed by the 1-D through-the-thickness analysis in developing the 2-D plate model. Finally, it concludes with the validation of the present formulation for a very general thermal loading (having variation in all the three co-ordinate axes) by correlating the results from the present theory with that of the corresponding solutions of 3-D finite elements of MSC NASTRAN® FE commercial software. Chapter-6 summarises the conclusions of this thesis and recommendations for future work.

The manufacture, laminate design, and modeling of a part with complex geometry are explored. The ultimate goal of the research is to produce a model that accurately predicts part stiffness. This is validated with experimental results of composite parts, which refine material properties for use in a final prototype part model. The secondary goal of this project is to explore manufacturing methods for improved manufacturability of the complex part. The manufacturing portion of the thesis and feedback into material model has incorporated a senior project team to perform research on manufacturing and create composite part to be used for experimental testing. The senior project was designed, led, and managed by the author with support from the committee chair. Finite element modeling was refined using data from coupon 3-point bend testing to improve estimates on material properties. These properties were fed into a prototype part model which predicted deflection of composite parts with different layups and materials. The results of the model were compared to experimental results from prototype part testing and 3rd party analysis. The results showed that an accurate mid-plane shell element model could be used to accurately predict deflection for 2 of 3 experimental parts. There are recommendations in the thesis to further validate the models and experimental testing.

No description available.

This thesis is about using structural-dynamics based methods to address the existing challenges in the field of Structural Health Monitoring (SHM). Particularly, new structural-dynamics based methods are presented, to model areas of damage, to do damage diagnosis and to estimate and predict the sensitivity of structural vibration properties like natural frequencies to the presence of damage. Towards these objectives, a general analytical procedure, which yields nth-order expressions governing mode shapes and natural frequencies and for damaged elastic structures such as rods, beams, plates and shells of any shape is presented. Features of the procedure include the following: 1. Rather than modeling the damage as a fictitious elastic element or localized or global change in constitutive properties, it is modeled in a mathematically rigorous manner as a geometric discontinuity. 2. The inertia effect (kinetic energy), which, unlike the stiffness effect (strain energy), of the damage has been neglected by researchers, is included in it. 3. The framework is generic and is applicable to wide variety of engineering structures of different shapes with arbitrary boundary conditions which constitute self adjoint systems and also to a wide variety of damage profiles and even multiple areas of damage. To illustrate the ability of the procedure to effectively model the damage, it is applied to beams using Euler-Bernoulli and Timoshenko theories and to plates using Kirchhoff's theory, supported on different types of boundary conditions. Analytical results are compared with experiments using piezoelectric actuators and non-contact Laser-Doppler Vibrometer sensors. Next, the step of damage diagnosis is approached. Damage diagnosis is done using two methodologies. One, the modes and natural frequencies that are determined are used to formulate analytical expressions for a strain energy based damage index. Two, a new damage detection parameter are identified. Assuming the damaged structure to be a linear system, the response is expressed as the summation of the responses of the corresponding undamaged structure and the response (negative response) of the damage alone. If the second part of the response is isolated, it forms what can be regarded as the damage signature. The damage signature gives a clear indication of the damage. In this thesis, the existence of the damage signature is investigated when the damaged structure is excited at one of its natural frequencies and therefore it is called ``partial mode contribution". The second damage detection method is based on this new physical parameter as determined using the partial mode contribution. The physical reasoning is verified analytically, thereupon it is verified using finite element models and experiments. The limits of damage size that can be determined using the method are also investigated. There is no requirement of having a baseline data with this damage detection method. Since the partial mode contribution is a local parameter, it is thus very sensitive to the presence of damage. The parameter is also shown to be not affected by noise in the detection ambience.