The objective of the present study is the computational and analytical modelling of a stress and strain state of the composite laminated structures. The exact three dimensional solution is derived for laminated anisotropic thick cylinders with both constant and variable material properties through the thickness of a layer. The governing differential equations are derived in a such form that to satisfy the stress functions and are given for layered cylindrical shell with open ends. The solution then extended to the laminated cylindrical shells with closed ends, that is to pressure vessels. Based on the accurate three-dimensional stress analysis an approach for the optimal design of the thick pressure vessels is formulated. Cylindrical pressure vessels are optimised taking the fibre angle as a design variable to maximise the burst pressure. The effect of the axial force on the optimal design is investigated. Numerical results are given for both single and laminated (up to five layers) cylindrical shells. The maximum burst pressure is computed using the three-dimensional interactive Tsai-: Wu failure criterion, which takes into account the influence of all stress components to the failure. Design optimisation of multilayered composite pressure vessels are based on the use of robust multidimensional methods which give fast convergence. Transverse shear and normal deformation higher-order theory for the solution of dynamic problems of laminated plates and shells is studied. The theory developed is based on the kinematic hypotheses which are derived using iterative technique. Dynamic effects, such as forces of inertia and the direct influence of external loading on the stress and strain components are included at the initial stage of derivation where kinematic hypotheses are formulated. The proposed theory and solution methods provide a basis for theoretical and applied studies in the field of dynamics and statics of the laminated shells, plates and their systems, particularly for investigation of dynamic processes related to the highest vibration forms and wave propagation, for optimal design etc. Geometrically nonlinear higher-order theory of laminated plates and shells with shear and normal deformation is derived. The theory takes into account both transverse shear and normal deformations. The number of numerical results are obtained based on the nonlinear theory developed. The results illustrate importance of the influence of geometrical nonlinearity, especially, at high levels of loading and in case when the laminae exhibit significant differences in their elastic properties. / Thesis (Ph.D.)-University of Natal, Durban, 1995.

The goal of this research was to investigate the tensile fatigue behavior of a carbon fiber / epoxy composite material. Specifically, the stress levels at which cracks initiated in static and fatigue loading in the 90 degree plies of a "quasi-cross ply layup" [0/905]S was investigated. For layups which contain them, cracks in composite laminates initiate and propagate from 90 degree plies (including the ubiquitous "quasi-isotropic layup" 0/±45/90). Thus, this work provides valuable insight into the fatigue behavior of the plies which originate fatigue damage. Unidirectional off-axis 90 degree and 10 degree specimens were also tested, but the bulk of testing was done on the cross-ply laminates. The project sponsors, Boeing, were in the process of extending a failure model to the case of fatigue. The body of work presented here provided empirical data for that effort. Several different inspection techniques were used to investigate for cracking in the 90 degree plies, including: x-ray images, edge replicates, dye penetrants, and optical microscopy. Plots of the stress level at which crack initiation occurred will be presented, as well as images illustrating damage development in these layups. Comparisons are made to the experimental results of other investigations of this type of layup. Explorations of the effect of R-ratio (including R = 0.1 and 0.5), loading frequency (including 3, 10, and 30 Hz), and surface roughness (hand polished specimen edges to 1500 grit smoothness) on fatigue crack initiation were also performed. For the most damaging case (10 Hz, R = 0.1, no polishing), the crack initiation strain (0.00276) was one half of the strain at which cracks initiated in static monotonic loading (0.0054), and was 16% of the cross-ply specimen's (0 degree fiber dominated) ultimate strain value of (0.018).

Orientadores: Éder Lima de Albuquerque, Paulo Sollero / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-22T09:21:57Z (GMT). No. of bitstreams: 1 Doval_PauloCesarMarques_D.pdf: 6139026 bytes, checksum: 105e98efc86e87888cfa20e7b32d931d (MD5) Previous issue date: 2013 / Resumo: Este trabalho apresenta um método de elementos de contorno para a análise de estabilidade de placas de materiais compósitos laminados. A formulação do método proposto não necessita de discretização do domínio, nem de soluções particulares para a solução do problema. Isto torna a formulação proposta diferente das formulações de elementos de contorno existentes, aplicadas à análise de estabilidade estrutural. O método é aplicado a um problema importante em engenharia computacional, que é a estabilidade de placas de materiais isotrópicos e de compósitos laminados. O desempenho é avaliado através de comparação com os resultados de elementos finitos e resultados analíticos, mostrando boa concordância com os mesmos. No entanto, a vantagem em relação ao método dos elementos finitos, especificamente, em análise de estabilidade de placas de materiais compósito laminados, é que se torna um problema de autovalor com um número reduzido de graus de liberdade, uma vez que somente o contorno e poucos pontos internos são necessários na discretização do problema / Abstract: This work presents a boundary element method to the analysis of buckling plates. Neither domain discretization, nor particular solutions are necessary in the proposed formulation. This becomes the proposed formulation different from the existent boundary element formulations applied to structural stability analysis. The method is applied to an important problem in computational engineering that is the stability of perforated and non perforated plates of composite laminate materials. The performance is assessed through comparison with finite element results. The proposed formulation agrees quite well with finite element. However, the stability analysis is a much smaller eigenvalue problem if boundary elements are used instead of finite elements, provided that only the boundary and fewer internal points are necessary in the discretization / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica

An efficient reliability technique has been developed based on Response Surface Methodology (RSM) in conjunction with the First Order Second Moment (FOSM) reliability method. The technique is applied when the limit state function cannot be obtained explicitly in terms of the design variables, i.e., when the analysis is performed using numerical techniques such as finite elements. The technique has proven to be efficient because it can handle problems with large numbers of design variables and correlated as well as nonnormal random variables. When compared with analytical results, the method has shown excellent agreement. The technique contains a sensitivity analysis scheme which can be used to reduce the computation time resulting in nearly the same accuracy. This technique allows the extension of most finite element codes to account for probabilistic analysis, where statistical variations can be added to the design variables. An explicit solution for rocket motors consisting of propellant and steel case under environmental temperature variations is compared to the RSM technique. The method is then used for the analysis of rocket motors subjected to mechanical loads for which the stress analysis is performed using the finite element method. The technique is also applied to study the reliability of a laminated composite plate with geometric nonlinearity subjected to static and time dependent loadings. Different failure modes were considered as well as different meshes. Results have shown that when the relative size of the element is introduced into the probabilistic model, the same reliability value is obtained regardless of the number of elements in the mesh. This is good because it allows the technique to be used for problems where the failure region is unknown. / Ph. D.

The failure behavior of composite laminates is modeled numerically using the Generalized Layerwise Plate Theory (GLPT) of Reddy and a progressive failure algorithm. The Layerwise Theory of Reddy assumes a piecewise continuous displacement field through the thickness of the laminate and therefore has the ability to capture the interlaminar stress fields near the free edges and cut outs more accurately. The progressive failure algorithm is based on the assumption that the material behaves like a stable progressively fracturing solid. A three-dimensional stiffness reduction scheme is developed and implemented to study progressive failures in composite laminates. The effect of various parameters such as out-of-plane material properties, boundary conditions, and stiffness reduction methods on the failure stresses and strains of a quasi-isotropic composite laminate with free edges subjected to tensile loading is studied. The ultimate stresses and strains predicted by the Generalized Layerwise Plate Theory (GLPT) and the more widely used First Order Shear Deformation Theory (FSDT) are compared with experimental results. The predictions of the GLPT are found to be in good agreement with the experimental results both qualitatively and quantitatively, while the predictions of FSDT are found to be different from experimental results both qualitatively and quantitatively. The predictive ability of various phenomenological failure criteria is evaluated with reference to the experimental results available in the literature. The effect of geometry of the test specimen and the displacement boundary conditions at the grips on the ultimate stresses and strains of a composite laminate under compressive loading is studied. The ultimate stresses and strains are found to be quite sensitive to the geometry of the test specimen and the displacement boundary conditions at the grips. The degree of sensitivity is observed to depend strongly on the lamination sequence. The predictions of the progressive failure algorithm are in agreement with the experimental trends. Finally, the effect of geometric nonlinearity on the first-ply and ultimate failure loads of a composite laminate subjected to bending load is studied. The geometric nonlinearity is taken in to account in the von Kármán sense. It is demonstrated that the nonlinear failure loads are quite different from the linear failure loads, depending on the lamination sequence, boundary conditions, and span-to-depth ratio of the test specimen. Further, it is shown that the First order Shear Deformation Theory (FSDT) and the Generalized Layerwise Plate Theory (GLPT) predict qualitatively different results. / Ph. D.

The design of composite laminated panels is a combinatorial problem when the orientation of the fibers in each layer is restricted to a discrete pool of angles. Additionally, composite laminates often have many optimal and near-optimal designs, and the designer may benefit by knowing many of those designs. Genetic algorithms are well suited for laminate design because they can handle the combinatorial nature of the problem and they permit the designer to obtain many near-optimal designs. However, their computational cost is high for most structural optimization problems. This work describes several attempts to reduce the cost of optimizing composite laminates using genetic algorithms. First, the use of a genetic algorithm to maximize the buckling load of a fixed thickness composite laminate is studied. Various genetic parameters, including population size, probability of mutation, and probability of crossover are optimized by numerical experiments. A new genetic operator - stack swap - is proposed and shown to be effective in reducing the cost of the optimization. Second, the genetic algorithm is revised and improved for minimum thickness design of composite laminated plates. The influence on the genetic search of the penalty functions enforcing failure constraints is studied. Combining fixed and proportional penalty functions is found to be the most efficient strategy. Improved selection, mutation, and stack swap operators are proposed. The use of an operator called scaling mutation that projects designs towards the feasible domain is investigated. The improvements in the genetic algorithm are shown to reduce the average price of the search by more than 50%. Next, the improved genetic algorithm for minimum thickness laminate design is applied to a more complex wing box-beam optimization problem. Tuning the genetic algorithm on this problem shows that, because the maximum length of a search is limited, the optimal population size does not grow with the size of the design space. If the probability of applying stack swap is reduced with the number of independent laminates in the wing box, stack swap enhances the performance of the genetic search on the wing box -beam problem. Finally, the possibility of running many searches is investigated. It is empirically shown that several short searches can be more efficient than a long one, especially when high levels of reliability are required. An example is given where a genetic algorithm is specifically modified for better efficiency in the context of repeated short runs. A procedure is studied that enables predicting reliability at later stages of the search. / Ph. D.

Carbon Fiber / Epoxy Laminates are increasingly being used in the primary structure of aircraft. To make effective use these materials, it is necessary to consider the ability of a laminate to resist damage, as well as material strength and stiffness. A possible means for improving damage tolerance is the use of non-traditional composite laminates, in which the longitudinal 0 plies are replaced with 5 or 10 plies. The main objectives of this collaborative Georgia Tech / Boeing research was the characterization of these non-traditional laminates, and the determination of appropriate lamina-level analytical techniques that are capable of predicting the changes caused by the use of slightly off-axis longitudinal plies. A quasi-isotropic [45/90/-45/theta/45/90/-45/-theta]s and hard [45/theta/-45/theta/90/45]s lay-up, where theta =0,5 or 10, were tested in open hole tension, filled hole tension, open hole compression, single shear bearing, and unnotched tension. These coupon level tests illustrated the effects of lay-up, notch constraint, and load type on traditional and non-traditional laminates. Die penetrant enhanced in-situ radiography was performed to determine the extent of damage suppression. The use of non-traditional laminates was found to reduce longitudinal ply cracking and delamination, with significant effect on the stress distribution around the notch. The use of non-traditional laminates also resulted in a 15%-20% improvement in bearing strength of the traditional laminates. Several predictive techniques were implemented to evaluate their ability to predict the effect of slight changes in ply orientations. A progressive damage model was written to compare Tsai-Wu, Hashin, and Maximum Stress unnotched strength criterion. Additionally, several semi-empirical failure theories for notched strength prediction were compared with linear and bi-linear cohesive zone models to determine applicability to non-traditional laminates.

The focus of the current research is to investigate the potential of using bistable unsymmetric cross-ply laminated composites as a means for achieving structures with morphed characteristics. To this end, an investigation of the design space for laminated composites exhibiting bistable behavior is undertaken and the key parameters controlling their behavior are identified. For this purpose a nonlinear Finite Element methodology using ABAQUS code is developed to predict both the cured shapes and the stability characteristics of unsymmetric cross-ply laminates. In addition, an experimental program is developed to validate the analytically predicted results through comparison with test data. A new method is proposed for attaching piezoelectric actuators to a bistable panel in order to preserve its favorable stability characteristics as well as optimizing the actuators performance. The developed nonlinear FE methodology is extended to predict the actuation requirements of bistable panels. Actuator requirements, predicted using the nonlinear FE analysis, are found to be in agreement with the test results. The current research also explores the potential for implementing bistable panels for Uninhabited Aerial Vehicle (UAV) wing configuration. To this end, a set of bistable panels is manufactured by combining symmetric and unsymmetric balanced and unbalanced stacking sequence and their stability characteristics are predicted. A preliminary analysis of the aerodynamic characteristics of the manufactured panels is carried out and the aerodynamic benefits of manufactured bistable panel are noted.

Hybrid polymer laminates of polycarbonate and PMMA have generated considerable interest among researchers as an alternative to traditional glass armours because of their potential for reduced cost and weight. Generally, the development of ballistic armour is carried out experimentally which is an expensive task in terms of time and cost. Numerical simulation provides a much greater facility to understand the phenomenon of ballistic impact and the effects of various parameters on the response to such impact. In addition it provides an easy means of comparing the impact performance of different materials as well as combination of materials forming hybrid laminates. The aim of this research was to develop a numerical modelling capability to simulate the ballistic response of hybrid polymer laminates, specifically polycarbonate and PMMA, using a commercially available finite element code LS-DYNA. The challenge was to work within the limitations of the material models and the failure algorithms available within LS-DYNA, and still try to reproduce the behaviour observed experimentally by previous researchers, initially on monolithic plates of polycarbonate and PMMA and then on hybrid laminates. The first part of the study focuses on a detailed literature survey on mechanical and dynamic characterisation of polycarbonate and PMMA as well as experimental and numerical studies previously conducted on ballistic behaviour of these materials as well as their combinations. The material properties of the polymers compiled from this literature survey were used as input for the selected LS-DYNA material model. Impact simulations were carried on monolithic and laminated media of polycarbonate and PMMA and where possible these were compared to experimental results. It was observed that the results agreed with the experimental data qualitatively. Quantitatively the results showed some discrepancies which were attributed to the limitations faced in simulating the exact test conditions numerically. Numerical simulations were carried out to study the effects of variations in laminate thickness and plate support diameters as well as to examine the influence of the bond between the layers. Finally the impact response of four different combinations of polycarbonate and PMMA are compared to each other for different laminate thicknesses.

Cette thèse comprend deux parties : Détermination des contraintes résiduelles dans les composites stratifiés ±θ induites par le cycle thermique de fabrication et Etude de leurs influences sur le com-portement mécanique de ces stratifiés. Limitée par la théorie actuelle, la détermination expérimentale des contraintes résiduelles dans les stratifiés ±θ a été très difficile. Dans notre étude, la méthode du trou incrémental a été employée afin de relaxer les contraintes résiduelles et les déformations provoquées ont été mesurées par les jauges de déformation. Une nouvelle approche proposée dans cette thèse permet d’associer les déformations autour du trou et les contraintes résiduelles au sein du stratifié ±θ. Les coefficients de calibration ont été déterminés par la simulation numérique. Grâce à l’approche développée, nous avons constaté une relation linéaire entre les contraintes résiduelles et l’angle θ du stratifié [02/θ2]s. En adaptant un modèle thermoélastique du matériau, les résultats expérimentaux ont pu être modélisés numériquement. Ensuite, nous avons étudié l’influence de l’épaisseur du stratifié, du cycle de cuisson et du vieillissement hydrothermique sur la distribution des contraintes résiduelles. A l’aide de la technique d’émission acoustique, les influences des contraintes résiduelles sur l’endommagement et le comportement mécanique des stratifiés ont été étudiées grâce aux essais de traction. Enfin, l’importance des contraintes résiduelles sur la rupture transversale du stratifié a été mise en évidence en comparant avec les résultats théoriques / This thesis work consists of two main parts: Deter-mination of residual stresses in composites laminates ±θ, introduced by the thermal cycle during the manufacturing process of laminates and Study of their influences on the mechanical behavior of these laminates. Limited by the current theory, the exper-imental determination of residual stresses in the laminates ±θ was very difficult. In this work, the incremental hole drilling method was performed for the residual stresses relaxation and then the gener-ated strains around the hole were measured with strain gages. The new approach proposed in this thesis allows associating the strains around the hole and the residual stresses in the laminates ±θ. The calibration coefficients were determined by the numerical simulation. With this approach, we found a linear relationship between the residual stresses and the fiber orientation angle θ for the composite laminates [02/θ2]s. By adapting a thermoelastic ma-terial model, the results obtained by our new ap-proach were modelized by the numerical study. Then we studied the influence of laminate thickness, curing cycle and hydrothermal ageing on the distri-bution of residual stresses. With the help of acoustic emission technique, the influences of the residual stresses on the damage and the mechanical behavior of composite laminates were studied through tensile tests. Finally, the importance of the residual stresses on the transverse failure of composite laminates was demonstrated comparing with the theoretical results