In this work an attempt has been made to develop theories for finite element static and dynamic stress analysis tailored for use with composite layered plates and shells in this way it was hoped to provide accurate values of the stresses particularly transverse shear stresses through the thickness, and to perform accurate natural frequency analysis by including non-linear effects such as centrifugal stiffening. Initial derivations were based upon first order facet shell element analysis and first order curved shell element analysis. Subsequently, derivations were produced for higher order element analysis. A programming package has been developed based upon the above derivations, and containing a banded solver as well as a frontal solver, capable of analysing structures build up from uniform or variable thickness layers and with a multiple number of layers having constant or variable dimension. Results obtained with the aid of the present package have been compared with results derived from experimental work as well as with results derived from available analytical solutions. Investigations have been carried out for existing compressor blades, made of isotropic material and layered composite material, respectively. The results obtained from the package have been compared with available experimental results produced by RR or carried out at Cranfield. It has been shown that the above mentioned derivations produce comparable results and the package has proved to be reliable and accurate.

Shape control of a structure with distributed piezoelectric actuators can be achieved through optimally selecting the loci, shapes and sizes of the piezoelectric actuators and choosing the electric fields applied to the actuators. Shape control can be categorised as either static or dynamic shape control. Whether it is a transient or gradual change, static or dynamic shape control, both aim to determine the loci, sizes, and shapes of piezoelectric actuators, and the applied voltages such that a desired structural shape is achieved effectively. This thesis is primarily concerned with establishing a finite element formulation for the general smart laminated composite plate structure, which is capable to analyse static and dynamic deformation using non-rectangular elements. The mechanical deformation of the smart composite plate is modelled using a third order plate theory, while the electric field is simulated based on a layer-wise theory. The finite element formulation for static and dynamics analysis is verified by comparing with available numerical results. Selected experiments have also been conducted to measure structural deformation and the experimental results are used to correlate with those of the finite element formulation for static analysis. In addition, the Linear Least Square (LLS) method is employed to study the effect of different piezoelectric actuator patch pattern on the results of error function, which is the least square error between the calculated and desired structural shapes in static structural shape control. The second issue of this thesis deals with piezoelectric actuator design optimisation (PADO) for quasi-static shape control by finding the applied voltage and the configuration of piezoelectric actuator patch to minimise error function, whereas the piezoelectric actuator configuration is defined based on the optimisation technique of altering nodal coordinates (size/shape optimisation) or eliminating inefficient elements in a structural mesh (topology optimisation). Several shape control algorithms are developed to improve the structural shape control by reducing the error function. Further development of the GA-based voltage and piezoelectric actuator design optimisation method includes the constraint handling, where the error function can be optimised subjected to energy consumption or other way around. The numerical examples are presented in order to verify that the proposed algorithms are applicable to quasi-static shape control based on voltage and piezoelectric actuator design optimisation (PADO) in terms of minimising the error function. The third issue is to use the present finite element formulation for a modal shape control and for controlling resonant vibration of smart composite plate structures. The controlled resonant vibration formulation is developed. Modal analysis and LLS methods are also employed to optimise the applied voltage to piezoelectric actuators for achieving the modal shapes. The Newmark direct time integration method is used to study harmonic excitation of smart structures. Numerical results are presented to induce harmonic vibration of structure with controlled magnitude via adjusting the damping and to verify the controlled resonant vibration formulation.

Shape control of a structure with distributed piezoelectric actuators can be achieved through optimally selecting the loci, shapes and sizes of the piezoelectric actuators and choosing the electric fields applied to the actuators. Shape control can be categorised as either static or dynamic shape control. Whether it is a transient or gradual change, static or dynamic shape control, both aim to determine the loci, sizes, and shapes of piezoelectric actuators, and the applied voltages such that a desired structural shape is achieved effectively. This thesis is primarily concerned with establishing a finite element formulation for the general smart laminated composite plate structure, which is capable to analyse static and dynamic deformation using non-rectangular elements. The mechanical deformation of the smart composite plate is modelled using a third order plate theory, while the electric field is simulated based on a layer-wise theory. The finite element formulation for static and dynamics analysis is verified by comparing with available numerical results. Selected experiments have also been conducted to measure structural deformation and the experimental results are used to correlate with those of the finite element formulation for static analysis. In addition, the Linear Least Square (LLS) method is employed to study the effect of different piezoelectric actuator patch pattern on the results of error function, which is the least square error between the calculated and desired structural shapes in static structural shape control. The second issue of this thesis deals with piezoelectric actuator design optimisation (PADO) for quasi-static shape control by finding the applied voltage and the configuration of piezoelectric actuator patch to minimise error function, whereas the piezoelectric actuator configuration is defined based on the optimisation technique of altering nodal coordinates (size/shape optimisation) or eliminating inefficient elements in a structural mesh (topology optimisation). Several shape control algorithms are developed to improve the structural shape control by reducing the error function. Further development of the GA-based voltage and piezoelectric actuator design optimisation method includes the constraint handling, where the error function can be optimised subjected to energy consumption or other way around. The numerical examples are presented in order to verify that the proposed algorithms are applicable to quasi-static shape control based on voltage and piezoelectric actuator design optimisation (PADO) in terms of minimising the error function. The third issue is to use the present finite element formulation for a modal shape control and for controlling resonant vibration of smart composite plate structures. The controlled resonant vibration formulation is developed. Modal analysis and LLS methods are also employed to optimise the applied voltage to piezoelectric actuators for achieving the modal shapes. The Newmark direct time integration method is used to study harmonic excitation of smart structures. Numerical results are presented to induce harmonic vibration of structure with controlled magnitude via adjusting the damping and to verify the controlled resonant vibration formulation.

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.

L'objectif de cette thèse est de développer des modèles d'homogénéisation analytiques de panneaux sandwichs en nid d'abeilles. A la différence des méthodes classiques, l'effet des peaux est pris en compte, conduisant à des propriétés mécaniques très différentes. Dans les cas des tractions, flexions, cisaillement dans le plan, cisaillements transversaux et torsion, différentes séries de fonctions analytiques sont proposées pour prendre en compte la redistribution des contraintes entre les parois du nid d'abeilles. Nous avons étudié l'influence de la hauteur du nid d'abeilles sur les propriétés élastiques. Les courbes des modules obtenues avec le modèle proposé sont bien bornées par les valeurs obtenues avec la théorie des poutres. Les contraintes d'interface sont également étudiées afin de comparer avec les modèles existant pour le problème de traction. De nombreux calculs numériques ont été réalisés avec nos H-modèles pour les problèmes de tractions, de flexions, de traction-flexion couplés, de cisaillement dans le plan, de cisaillement transversal et de torsion. De très bon accords ont été obtenus entre les résultats issus des H-modèles et ceux issus des calculs en éléments finis de coques en maillant complètement les panneaux sandwichs. Nos H-modèles ont été appliquées aux calculs de grandes plaques sandwichs industrielles en nid d'abeilles. La comparaison desrésultats entre les H-modèles et les calculs en éléments finis de coques du logiciel Abaqus sont en très bon accord. / The aim of this thesis is to develop an analytical homogenization model for the honeycomb core sandwich panels. Unlike conventional methods, the skin effects are taken into account, leading to a very different mechanical properties. In the cases of extensions, bendings, in-plane shear, transverse shears andtorsion, different analytical function series are proposed to consider the stress redistribution between the honeycomb walls. We have studied the influence of the height of the core on its homogenized properties. The moduli curves obtained by the present H-models are well bounded by the moduli values obtained by the beam theory. The interface stresses are also studied to compare with existing models for stretching problem. Many numerical computations with our H-models have been done for the problems of stretching, bending, in-plan and transverse shearing, as well as torsion. Very good agreement has been achieved between the results of the H-models and the results obtained by finite element simulations by completely meshing thesandwich panel with shell elements. Our H-models have been applied to the computations of industrial large sandwich panels with honeycomb core. The comparison of the results between the H-models and the simulations with Abaqus shell elements are in very good agreement.

In this study, Ritz method has been employed to analyze the following problems: free vibrations of plates with curvilinear stiffeners, the lowest 100 frequencies of thick isotropic plates, free vibrations of thick quadrilateral laminates and free vibrations and static deformations of rectangular laminates, and sandwich structures. Admissible functions in the Ritz method are chosen as a product of the classical Jacobi orthogonal polynomials and weight functions that exactly satisfy the prescribed essential boundary conditions while maintaining orthogonality of the admissible functions. For free vibrations of plates with curvilinear stiffeners, made possible by additive manufacturing, both plate and stiffeners are modeled using a first-order shear deformation theory. For the thick isotropic plates and laminates, a third-order shear and normal deformation theory is used. The accuracy and computational efficiency of formulations are shown through a range of numerical examples involving different boundary conditions and plate thicknesses. The above formulations assume the whole plate as an equivalent single layer. When the material properties of individual layers are close to each other or thickness of the plate is small compared to other dimensions, the equivalent single layer plate (ESL) theories provide accurate solutions for vibrations and static deformations of multilayered structures. If, however, sufficiently large differences in material properties of individual layers such as those in sandwich structure that consists of stiff outer face sheets (e.g., carbon fiber-reinforced epoxy composite) and soft core (e.g., foam) exist, multilayered structures may exhibit complex kinematic behaviors. Hence, in such case, C_z⁰ conditions, namely, piecewise continuity of displacements and the interlaminar continuity of transverse stresses must be taken into account. Here, Ritz formulations are extended for ESL and layerwise (LW) Nth-order shear and normal deformation theories to model sandwich structures with various face-to-core stiffness ratios. In the LW theory, the C⁰ continuity of displacements is satisfied. However, the continuity of transverse stresses is not satisfied in both ESL and LW theories leading to inaccurate transverse stresses. This shortcoming is remedied by using a one-step well-known stress recovery scheme (SRS). Furthermore, analytical solutions of three-dimensional linear elasticity theory for vibrations and static deformations of simply supported sandwich plates are developed and used to investigate the limitations and applicability of ESL and LW plate theories for various face-to-core stiffness ratios. In addition to natural frequency results obtained from ESL and LW theories, the solutions of the corresponding 3-dimensional linearly elastic problems obtained with the commercial finite element method (FEM) software, ABAQUS, are provided. It is found that LW and ESL (even though its higher-order) theories can produce accurate natural frequency results compared to FEM with a considerably lesser number of degrees of freedom. / Doctor of Philosophy / In everyday life, plate-like structures find applications such as boards displaying advertisements, signs on shops and panels on automobiles. These structures are typically nailed, welded, or glued to supports at one or more edges. When subjected to disturbances such as wind gusts, plate-like structures vibrate. The frequency (number of cycles per second) of a structure in the absence of an applied external load is called its natural frequency that depends upon plate's geometric dimensions, its material and how it is supported at the edges. If the frequency of an applied disturbance matches one of the natural frequencies of the plate, then it will vibrate violently. To avoid such situations in structural designs, it is important to know the natural frequencies of a plate under different support conditions. One would also expect the plate to be able to support the designed structural load without breaking; hence knowledge of plate's deformations and stresses developed in it is equally important. These require mathematical models that adequately characterize their static and dynamic behavior. Most mathematical models are based on plate theories. Although plates are three-dimensional (3D) objects, their thickness is small as compared to the in-plane dimensions. Thus, they are analyzed as 2D objects using assumptions on the displacement fields and using quantities averaged over the plate thickness. These provide many plate theories, each with its own computational efficiency and fidelity (the degree to which it reproduces behavior of the 3-D object). Hence, a plate theory can be developed to provide accurately a quantity of interest. Some issues are more challenging for low-fidelity plate theories than others. For example, the greater the plate thickness, the higher the fidelity of plate theories required for obtaining accurate natural frequencies and deformations. Another challenging issue arises when a sandwich structure consists of strong face-sheets (e.g., made of carbon fiber-reinforced epoxy composite) and a soft core (e.g., made of foam) embedded between them. Sandwich structures exhibit more complex behavior than monolithic plates. Thus, many widely used plate theories may not provide accurate results for them. Here, we have used different plate theories to solve problems including those for sandwich structures. The governing equations of the plate theories are solved numerically (i.e., they are approximately satisfied) using the Ritz method named after Walter Ritz and weighted Jacobi polynomials. It is shown that these provide accurate solutions and the corresponding numerical algorithms are computationally more economical than the commonly used finite element method. To evaluate the accuracy of a plate theory, we have analytically solved (i.e., the governing equations are satisfied at every point in the problem domain) equations of the 3D theory of linear elasticity. The results presented in this research should help structural designers.

Recent developments show the applications of smart structure in different engineering fields. Smart structures can be used for shape and vibration control, structural health monitoring etc. Smart materials can be integrated to composite structure to enhance its abilities. Fiber reinforced composites are the advanced materials of choice in aerospace applications due to its high strength and stiffness, light weight and ability to tailor according to the design requirements. Due to complex manufacturing process and varying operating conditions, composites are susceptible to variation in material properties and damages. The present study focuses on the effect of uncertainties in material properties and damages on a smart composite structure. A cantilevered composite plate with surface mounted piezoelectric sensor/ actuator is considered in this study. The sensors and the actuators are connected through a conventional feedback controller and the controller is configured for vibration control application. Matrix cracks are considered as damage in the composite plate. To study the effect of material uncertainty, probabilistic analysis is performed considering composite material properties and piezoelectric coefficients as independent Gaussian random variables. Numerical results show that there is substantial change in dynamic response of the smart composite plate due to material uncertainties and damage. Deviation due to material uncertainty and damage can be compensated by actively tuning the feedback control system. Feedback control parameters can be properly adjusted to match the baseline response. Here baseline case represents the response of the undamaged smart composite plate with deterministic material properties. The change in feedback control parameters are identified as damage indicator. Feedback control based damage detection method is proposed for structural health monitoring in smart composite structure and robustness of the method is studied considering material uncertainties. Fractal dimension based damage detection method is proposed to detect localized matrix cracks in a composite plate with spatially varying material properties. Variation in material properties follows a two dimensional homogeneous Gaussian random field. Fractal dimension is used to extract the damage information from the static response of composite plate with localized matrix cracks. It is found that fractal dimension based approach is capable of detecting the location of the single and multiple damages from the static deflection curve. Robustness of the fractal dimension based damage detection method is studied considering spatial uncertainties in material properties.

In this Thesis, the problem of the Free Vibrations Analysis of Doubly Stiffened Composite, Orthotropic and/or Isotropic, Base Plates or Panels (with Orthotropic Stiffening Plate Strips) is investigated. The composite plate or panel system is made of an Orthotropic and/or Isotropic Base Plate stiffened or reinforced by adhesively bonded Upper and Lower Orthotropic Stiffening Plate Strips. The plates are assumed to be the Mindlin Plates connected by relatively very thin adhesive layers. The general problem under study is considered in terms of three problems, namely Main PROBLEM I Main PROBLEM II and Main PROBLEM III. The theoretical formulation of the Main PROBLEMS is based on a First Order Shear Deformation Plate Theory (FSDPT) that is, in this case, the Mindlin Plate Theory. The entire composite system is assumed to have simple supports along the two opposite edges so that the Classical Levy&#039 / s Solutions can be applied in that direction. Thus, the transverse shear deformations and the rotary moments of inertia of plates are included in the formulation. The very thin, yet elastic deformable adhesive layers are considered as continua with transverse normal and shear stresses. The damping effects in the plates and the adhesive layers are neglected. The sets of the systems of equations of the Mindlin Plate Theory are reduced to a set of the Governing System of First Order Ordinary Differential Equations in the state vector form. The sets of the Governing System for each Main PROBLEM constitute a Two-Point Boundary Value Problem in the y-direction which is taken along the length of the plates. Then, the system is solved by the Modified Transfer Matrix Method (with Interpolation Polynomials and/or Chebyshev Polynomials)which is a relatively semi-analytical and numerical technique. The numerical results and important parametric studies of the natural modes and the corresponding frequencies of the composite system are presented.

La thèse s'inscrit dans le cadre du projet ECOCIS (Eco-composite pour l'Isolation). Ce projet vise la conception, le développement et la validation des performances d'un composite à base de polypropylène renforcé avec des fibres de bois (également appelé bois-plastique) pour utilisation en plaque de bardage par l'extérieur. Ce nouveau matériau s'inscrit dans la problématique de valorisation de la ressource bois sous forme de matériaux élaborés.On s'intéresse plus particulièrement à l'utilisation de la farine de bois issue des déchets des scieries pour le renforcement d'une matrice thermoplastique en polypropylène (PP) recyclé. Le premier avantage de ce composite est qu'il est écologique vu que le polypropylène est recyclable et les fibres de bois sont biodégradable et dérivent d'une ressource renouvelable. De plus, l'association des fibres de bois et de PP donne naissance à un matériau qui présente des propriétés bien meilleures que les composants initiaux.Une compagne expérimentale a été organisée, qui se concentre sur les essais de caractérisation du matériau en traction, en flexion, au choc Charpy. Des mesures complémentaires de dilatation thermique et de vieillissement artificiel sont également considérées. Ces essais vont permettre de déterminer la loi de comportement du matériau et de comprendre l'évolution de ses propriétés avec les différents paramètres. Une fois les propriétés du matériau ont été validées, l'étape suivante consiste à mettre ce matériau en valeur en le transformant à des plaques de bardages pour une utilisation à l'extérieur. Une caractérisation des plaques en flexion, au choc et à la résistance au vent a été réalisée afin de valider la possibilité d'utilisation de ce matériau en bardage par l'extérieur / The thesis is part of ECOCIS project (Eco-composite for insulation). This project involves the design, development and validation of the performance of a polypropylene-based composite reinforced with wood fibers (also known as wood-plastic) for use in cladding plate from the outside. This new material is part of the valuation issue of wood resources in the form of prepared materials.It focuses on the use of wood flour from waste from sawmills for reinforcing a thermoplastic matrix of polypropylene (PP) recycled. The first advantage of this composite is that it is environmentally friendly because recyclable polypropylene and wood fibers are biodegradable and derived from a renewable resource. Moreover, the combination of wood fiber and PP gives rise to a material with much better properties than the original components.An experimental companion was organized, focusing on the characterization tests of traction material, bending, Charpy impact. Additional measurements of thermal expansion and artificial aging are also considered. These tests will help determine the behavior law of the material and to understand the evolution of its properties with different parameters. Once the properties of the material have been validated, the next step is to put this material by converting it into value for cladding plates for outdoor use. A characterization of the plates in bending, impact and wind resistance was performed to validate the potential use of this cladding material from the outside

No description available.