This thesis presents a multi-purpose sensor concept viable for the simultaneous measurement of pressure, temperature and thickness of plate structures. It also establishes the knowledge base necessary for future sensor design. Thermal-Acousto Photonic Non-Destructive Evaluation (TAP-NDE) is employed to remotely initiate and acquire interrogating ultrasonic waves. Parameters including pressure, temperature and plate thickness are determined through exploring the dispersion features of the interrogating waves. A theoretical study is performed, through which a modified wave propagation theory applicable to homogeneous, isotropic, linear elastic materials is formulated along with an associated numerical model. A numerical scheme for solving the model is also developed using FEMLAB, a finite element based PDE solver. Gabor Wavelet Transform (GWT) is employed to map numerical time waveforms into the joint time-frequency domain. Wave time-frequency information enables dispersion curves to be extracted and material pressure, temperature and thickness to be determined. A sensor configuration design integrating the wave generation and sensing components of the proven TAP-NDE technology is also developed. Conclusions of the research are drawn from wave dispersion obtained corresponding to the following ranges of parameters: 300-500kHz for frequency, 25-300oC for temperature, 1-3mm for plate thickness, and 6 10 1?? - 7 1 10 ?? N/m for pressure. Each of the three parameters considered in the study has a different level of impact on plate wave dispersion. Plate thickness is found to have the most impact on wave dispersion, followed by temperature of the plate. The effect attributable to pressure is the least prominent among the three parameters considered. Plate thickness and temperature can be readily measured while simultaneously resolved using dispersion curves. However, pressure variation can only be differentiated when the plate is smaller than 1mm in thickness. It is observed that the thicker the plate, the faster the frequency group velocity. Also, the group velocities of all frequency components considered are seen to increase with increasing temperature, but decrease with increasing pressure.

The primary goal of the thesis is to provide some answers to the questions related to the key steps in the process of adaptive modeling of plates. Since the adaptivity depends on reliable error estimates, a large part of the thesis is related to the derivation of computational procedures for discretization error estimates as well as model error estimates. A practical comparison of some of the established discretization error estimates is made. Special attention is paid to what is called equilibrated residuum method, which has a potential to be used both for discretization error and model error estimates. It should be emphasized that the model error estimates are quite hard to obtain, in contrast to the discretization error estimates. The concept of model adaptivity for plates is in this work implemented on the basis of equilibrated residuum method and hierarchic family of plate finite element models.The finite elements used in the thesis range from thin plate finite elements to thick plate finite elements. The latter are based on a newly derived higher order plate theory, which includes through the thickness stretching. The model error is estimated by local element-wise computations. As all the finite elements, representing the chosen plate mathematical models, are re-derived in order to share the same interpolation bases, the difference between the local computations can be attributed mainly to the model error. This choice of finite elements enables effective computation of the model error estimate and improves the robustness of the adaptive modeling. Thus the discretization error can be computed by an independent procedure.Many numerical examples are provided as an illustration of performance of the derived plate elements, the derived discretization error procedures and the derived modeling error procedure. Since the basic goal of modeling in engineering is to produce an effective model, which will produce the most accurate results with the minimum input data, the need for the adaptive modeling will always be present. In this view, the present work is a contribution to the final goal of the finite element modeling of plate structures: a fully automatic adaptive procedure for the construction of an optimal computational model (an optimal finite element mesh and an optimal choice of a plate model for each element of the mesh) for a given plate structure.

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L’objectif principal de la thèse est de répondre à des questions liées aux étapes clé d’un processus de l’adaptation de modèles de plaques. Comme l’adaptativité dépend des estimateurs d’erreurs fiables, une part importante du rapport est dédiée au développement des méthodes numériques pour les estimateurs d’erreurs aussi bien dues à la discrétisation qu’au choix du modèle. Une comparaison des estimateurs d’erreurs de discrétisation d’un point de vue pratique est présentée. Une attention particulière est prêtée a la méthode de résiduels équilibrés (en anglais, "equilibrated residual method"), laquelle est potentiellement applicable aux estimations des deux types d’erreurs, de discrétisation et de modèle.Il faut souligner que, contrairement aux estimateurs d’erreurs de discrétisation, les estimateurs d’erreur de modèle sont plus difficiles à élaborer. Le concept de l’adaptativité de modèles pour les plaques est implémenté sur la base de la méthode de résiduels équilibrés et de la famille hiérarchique des éléments finis de plaques. Les éléments finis dérivés dans le cadre de la thèse, comprennent aussi bien les éléments de plaques minces et que les éléments de plaques épaisses. Ces derniers sont formulés en s’appuyant sur une théorie nouvelle de plaque, intégrant aussi les effets d’étirement le long de l’épaisseur. Les erreurs de modèle sont estimées via des calculs élément par élément. Les erreurs de discrétisation et de modèle sont estimées d’une manière indépendante, ce qui rend l’approche très robuste et facile à utiliser. Les méthodes développées sont appliquées sur plusieurs exemples numériques. Les travaux réalisés dans le cadre de la thèse représentent plusieurs contributions qui visent l’objectif final de la modélisation adaptative, ou une procédure complètement automatique permettrait de faire un choix optimal du modèle de plaques pour chaque élément de la structure. / The primary goal of the thesis is to provide some answers to the questions related to the key steps in the process of adaptive modeling of plates. Since the adaptivity depends on reliable error estimates, a large part of the thesis is related to the derivation of computational procedures for discretization error estimates as well as model error estimates. A practical comparison of some of the established discretization error estimates is made. Special attention is paid to what is called equilibrated residuum method, which has a potential to be used both for discretization error and model error estimates. It should be emphasized that the model error estimates are quite hard to obtain, in contrast to the discretization error estimates. The concept of model adaptivity for plates is in this work implemented on the basis of equilibrated residuum method and hierarchic family of plate finite element models.The finite elements used in the thesis range from thin plate finite elements to thick plate finite elements. The latter are based on a newly derived higher order plate theory, which includes through the thickness stretching. The model error is estimated by local element-wise computations. As all the finite elements, representing the chosen plate mathematical models, are re-derived in order to share the same interpolation bases, the difference between the local computations can be attributed mainly to the model error. This choice of finite elements enables effective computation of the model error estimate and improves the robustness of the adaptive modeling. Thus the discretization error can be computed by an independent procedure.Many numerical examples are provided as an illustration of performance of the derived plate elements, the derived discretization error procedures and the derived modeling error procedure. Since the basic goal of modeling in engineering is to produce an effective model, which will produce the most accurate results with the minimum input data, the need for the adaptive modeling will always be present. In this view, the present work is a contribution to the final goal of the finite element modeling of plate structures: a fully automatic adaptive procedure for the construction of an optimal computational model (an optimal finite element mesh and an optimal choice of a plate model for each element of the mesh) for a given plate structure.

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.

Composite structures are extremely useful for aerospace, automotive, marine and civil applications due to their very high specific structural properties. These structures are subjected to severe dynamic loading in their service life. Repeated exposure to these severe loading conditions can induce structural damage which ultimately may precipitate a catastrophic failure. Therefore, an interest in the continuous inspection and maintenance of engineering structures has grown tremendously in recent years. Sensitive aerospace applications can have small design margins and any inadequacy in knowledge of the system may cause design failure. Structures made from composite materials posses complicated failure mechanism as compared to those made from conventional metallic materials. In composite structural design, it is hence very important to properly model geometric intricacies and various imperfections such as delaminations and cracks. Two important issues are addressed in this thesis: (1) structural modeling of nonlinear delamination and uncertainty propagation in nonlinear characteristics of composite plate structures and (2) development of a model based damage detection system to handle uncertainty issues. An earlier proposed shear deformable C0 composite plate finite element is modified to alleviate modeling uncertainty issues associated with a damage detection problem. Parabolic variation of transverse shear stresses across the plate thickness is incorporated into the modified formulation using mixed shear interpolation technique. Validity of the proposed modification is established through available literature. Correction of the transverse shear stress term in the formulation results in about 2 percent higher solution accuracy than the earlier model. It is found that the transverse shear effect increases with higher modes of the plate deformation. Transverse shear effects are more prominent in sandwich plates. This refined composite plate finite element is used for large deformation dynamic analysis of delaminated composite plates. The inter-laminar contact at the delaminated region in composite plates is modeled with the augmented Lagrangian approach. Numerical simulations are carried out to investigate the effect of delamination on the nonlinear transient behavior of composite plates. Results obtained from these studies show that widely used unconditionally stable β-Newmark method presents numerical instability problems in the transient simulation of delaminated composite plate structures with large deformation. To overcome this instability issue, an energy and momentum conserving composite implicit time integration scheme presented by Bathe and Baig is used for the nonlinear dynamic analysis. It is also found that a proper selection of the penalty parameter is very crucial in the simulation of contact condition. It is shown that an improper selection of penalty parameter in the augmented Lagrangian formulation may lead to erroneous prediction of dynamic response of composite delaminated plates. Uncertainties associated with the mathematical characterization of a structure can lead to unreliable damage detection. Composite structures also show considerable scatter in their structural response due to large uncertainties associated with their material properties. Probabilistic analysis is carried out to estimate material uncertainty effects in the nonlinear frequencies of composite plates. Monte Carlo Simulation with Latin Hypercube Sampling technique is used to obtain the variance of linear and nonlinear natural frequencies of the plate due to randomness in its material properties. Numerical results are obtained for composite plates with different aspect ratio, stacking sequence and oscillation amplitude ratio. It is found that the nonlinear frequencies show increasing non-Gaussian probability density function with increasing amplitude of vibration and show dual peaks at high amplitude ratios. This chaotic nature of the dispersion of nonlinear eigenvalues is also revealed in eigenvalue sensitivity analysis. For fault isolation, variations in natural frequencies, modal curvatures and curvature damage factors due to damage are investigated. Effects of various physical uncertainties like, material and geometric uncertainties on the success of damage detection is studied. A robust structural damage detection system is developed based on the statistical information available from the probabilistic analysis carried out on beam type structures. A new fault isolation technique called sliding window defuzzifier is proposed to maximize the success rate of a Fuzzy Logic System (FLS) in damage detection. Using the changes in structural measurements between the damaged and undamaged state, a fuzzy system is generated and the rule-base and membership functions are generated using probabilistic informations. The FLS is demonstrated using frequency and mode shape based measurements for various beam type structures such as uniform cantilever beam, tapered beam in single as well as in multiple damage conditions. The robustness of the FLS is demonstrated with respect to the highly uncertain input information called measurement deltas (MDs). It is said, if uncertainty level is larger than or close to the changes in damage indicator due to damage, the true information would be submerged in the noise. Then the actual damaged members may not be identified accurately and/or the healthy members may be wrongly detected as damaged giving false warning. However, this being the case, the proposed FLS with new fault isolation technique tested with these noisy data having large variation and overlaps shows excellent robustness. It is observed that the FLS accurately predicts and isolates the damage levels up-to considerable uncertainty and noise levels in single as well as multiple damage conditions. The robustness of the FLS is also demonstrated for delamination detection in composite plates having very high material property uncertainty. Effects of epistemic uncertainty on damage detection in composite plates is addressed. The effectiveness of the proposed refined Reddy type shear deformable composite plate element is demonstrated for reducing the modeling or epistemic uncertainty in delamination detection.