Os materiais compostos de fibras longas vêm se destacando entre o conjunto de novos materiais em desenvolvimento, com larga aplicação na indústria e também na construção civil. Elabora. se aqui um texto introdutório no campo das placas laminadas constituídas de lâminas em compostos de fibras longas. A partir das propriedades dos materiais constituintes, fibra e matriz, são apresentadas as teorias para a determinação das propriedades equivalentes das lâminas. A teoria da anisotropia elástica é formulada e a teoria dos laminados em flexão é desenvolvida. Conclusões com respeito ao acoplamento de esforços em tais estruturas são mostradas. Os modos básicos de ruptura da fibra, matriz e da interface entre ambas são apresentados, bem como os modos básicos de delaminação. Alguns critérios de ruptura são mostrados, assim como um critério de escoamento. Ao fim alguns exemplos ilustram a análise pelo método dos elementos finitos de tais estruturas feita por programa disponível em literatura, com a implementação de subrotina para análise da temperatura. / Long fiber composite materials have been standing out among the group of new materials in development with wide industrial application and also in civil construccion. Here is elaborated an introductory text in laminated plates field constituted of long fiber composite laminae. Starting from constituent materials properties, fiber and matrix, the theories for determination of laminae equivalent properties are presented. Elastic anisotropy theory is formulated and the bending laminated theory is developed. Conclusions about the coupling efforts in such structures are showed. Fiber, matrix and the interface between both failure basic modes are presented, as well as delamination basic modes. Some failure criteria are showed, as well as a yielding criteria. At the end some examples illustrate the finite element method analysis of such structures made by available literature programme with temperature analysis subroutine implementation.

Os materiais compostos de fibras longas vêm se destacando entre o conjunto de novos materiais em desenvolvimento, com larga aplicação na indústria e também na construção civil. Elabora. se aqui um texto introdutório no campo das placas laminadas constituídas de lâminas em compostos de fibras longas. A partir das propriedades dos materiais constituintes, fibra e matriz, são apresentadas as teorias para a determinação das propriedades equivalentes das lâminas. A teoria da anisotropia elástica é formulada e a teoria dos laminados em flexão é desenvolvida. Conclusões com respeito ao acoplamento de esforços em tais estruturas são mostradas. Os modos básicos de ruptura da fibra, matriz e da interface entre ambas são apresentados, bem como os modos básicos de delaminação. Alguns critérios de ruptura são mostrados, assim como um critério de escoamento. Ao fim alguns exemplos ilustram a análise pelo método dos elementos finitos de tais estruturas feita por programa disponível em literatura, com a implementação de subrotina para análise da temperatura. / Long fiber composite materials have been standing out among the group of new materials in development with wide industrial application and also in civil construccion. Here is elaborated an introductory text in laminated plates field constituted of long fiber composite laminae. Starting from constituent materials properties, fiber and matrix, the theories for determination of laminae equivalent properties are presented. Elastic anisotropy theory is formulated and the bending laminated theory is developed. Conclusions about the coupling efforts in such structures are showed. Fiber, matrix and the interface between both failure basic modes are presented, as well as delamination basic modes. Some failure criteria are showed, as well as a yielding criteria. At the end some examples illustrate the finite element method analysis of such structures made by available literature programme with temperature analysis subroutine implementation.

In this thesis, we study the static and free vibration response of symmetric and antisymmetric cross-ply laminated plates using different plate theories. Governing equations for two displacement-based third-order equivalent-single-layer theories have been developed. The first one is called the General Third-Order Theory (GTOT), and the second one is called the General Third-Order Theory of Reddy (GTTR). The displacement field of the second theory can be obtained from the first by imposing the condition of zero shear stresses at the bounding planes of the plate. The governing equations, analytical solutions, and finite element model of GTTR have been obtained in terms of tracers. Proceeding in this manner, the governing equations, analytical solutions, and finite element models of some lower-order plate theories fall out by just assigning appropriate values to the tracers (typically 1 or 0). While analytical and finite element solutions have been obtained for GTTR and its derivative cases, only finite element solutions have been obtained for GTOT. The analytical solutions are of two types. The Navier-type solution is for rectangular plates simply supported on all four edges. In the Levy-type solution, two sides of the plate have to be simply-supported, while the remaining two sides can have any combination of free, clamped, or simply-supported boundary conditions. The results obtained from the different theories have been compared with exact solutions from existing literature . The response characteristics of the plates, like deflections, stresses, and frequencies, as well as the parameters affecting them have been studied. Some of the parameters investigated are span-to-thickness ratios, boundary conditions, loadings, and lamination schemes. The performance of the different theories in predicting plate responses have been evaluated. / Master of Science

An Analytical Strip Method (ASM) for the analysis of stiffened and non-stiffened antisymmetric laminated composite plates is derived by considering the bending-extension coupling effect for bending, free vibration and buckling. A system of three equations of equilibrium, governing the general response of arbitrarily laminated composite plates, is reduced to a single eighth order partial differential equation in terms of a displacement function. The displacement function is solved in a single series form to determine the displacement, fundamental frequency, and buckling load of antisymmetric cross-ply and angle-ply laminated composite plates. The solution is applicable to rectangular plates with two opposite edges simply supported, while the other edges are simply supported, clamped, free, beam supported, or any combinations of these boundary conditions. This method overcomes the limitations of other analytical methods (Navier’s and Lévy’s), and provides an alternative to numerical, semi-numerical, and approximate methods of analysis. Numerical examples of bending, free vibration, and buckling of antisymmetric laminated composite plates are presented in tabular and graphical form. Whenever possible, the results of the present study are compared with those published in the literature and/or ANSYS solutions. The comparison firmly establishes that this method could be used for the analysis of antisymmetric laminated composite plates. Future research needs are identified for the aspects that have not been reached by the present study and others.

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

In this thesis, optimal placement of adhesively bonded piezoelectric patches on laminated plates and the determination of geometry of the bonding area to maximize actuation effect are studied. A new finite element model, in which each layer is considered to be a separate plate, is developed. The adhesive layer is modeled as a distributed spring system. In this way, relative transverse normal and shear motion of the layers are allowed. Effect of delamination on the adhesive layer stresses is also studied and investigated through several case studies. Optimization problems, having single and multiple objectives, are investigated for both actuator placement and selective bonding examples. In these case studies, 2D and 3D Pareto fronts are also obtained. &amp / #8216 / Hide and Seek Simulated Annealing&amp / #8217 / method is adapted for discrete problems and used as the optimization technique for single-objective problems. Finally, Multiple Cooling Multi Objective Simulated Annealing optimization algorithm is adapted and used in multi-objective optimization case studies.

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Orientador: Aloisio Ernesto Assan / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-07T16:33:50Z (GMT). No. of bitstreams: 1 Volpini_EstevaoXavier_M.pdf: 3994255 bytes, checksum: 682eea9ccb0ec139a6d062e4466cd140 (MD5) Previous issue date: 2006 / Resumo: Este estudo tem por objetivo implementar, em programa já existente para a análise de placas laminadas de compósitos, a análise dinâmica de placas laminadas sob ação de carregamento forçado com integração direta pelo algoritmo de Newmark. O programa inicial de elementos finitos, que realiza a análise estática, foi desenvolvido por Tápia (1998), usando o elemento finito de Kosmatka (1994), formulado com a teoria de deformação por cisalhamento de primeira ordem de Reissner-Mindlin. Cassiano (2002) implementou nesse programa o cálculo das freqüências naturais. Neste trabalho foi introduzida a análise dinâmica forçada, através da integração direta no tempo, empregando o método de Newmark. Exemplos comparativos com variações das espessuras das placas, do número de lâminas, das orientações das fibras e das vinculações das bordas, mostram o excelente comportamento do elemento finito aqui empregado / Abstract: : The aim of this study is the dynamic analysis of laminated composite plates under forced transverse vibration with time direct-integration method. The original program, with the static analysis, was developed by Tapia (1998) using the element proposed by Kosmatka (1994), formulated with first-order shear deformation theory of Reissner-Mindlin. Later Cassiano (2002) introduced into this finite element code the evaluation of the natural frequencies. In this thesis the dynamic analysis by means of a direct time integration method, which was formulated by Newmark, was performed. Comparative examples with several plates thicknesses, number of laminates, orientation of the fibers and boundary constraints, show the excellent performance of the finite element used herein / Mestrado / Estruturas / Mestre em Engenharia Civil

A hybrid method is presented for the analysis of layers, plates, and multi-layered systems consisting of isotropic and linear elastic materials. The problem is formulated for the general case of a multi-layered system using a total potential energy formulation and employing the layerwise laminate theory of Reddy. A one-dimensional finite element model is used for the analysis of the multi-layered system through its thickness, and integral Fourier transforms are used to obtain the exact solution for the in-plane problem. Explicit expressions are obtained for the fundamental solution of the typical infinite layer, which are applied in the two-dimensional boundary integral equation model to produce the integral representation of the solution. The boundary integral equation model is two-dimensional, displacement-based and assumes piecewise continuous distribution of the displacement components through the system's thickness. The developed model describes the three-dimensional displacement field, the stress field, the strains and the interlaminar stresses over the entire domain of the problem as continuous functions of the position. This detailed three-dimensional analysis is achieved by incorporating only contour integrals. The boundary integral equations are discretized using the boundary element method and a numerical model is developed for the single numerical layer (element). This model is extended to the case of a multilayered system by introducing appropriate continuity conditions at the interfaces between the layers (firmly bonded layers, or separation, slip and friction between the layers). Assembly of the element matrices yields the global system of equations, which can be solved via iterative techniques. In addition, numerical techniques are developed for the evaluation of the boundary and domain integrals involved in the construction of the element matrices. The singular boundary integrals are computed using a special coordinate transformation, along with a subdivision of the boundary element and a transformation of the Gauss points. The domain integrals (regular, singular or near-singular) are transformed to regular definite integrals along the boundary through a semi-analytical approach. The proposed method provides a simple, efficient, and versatile model for a three-dimensional analysis of thick plates or multilayered systems. It can also be used to study plates resting on elastic foundations or plates with internal supports. The proposed method can be applied in an obvious manner to anisotropic materials and vibration problems. / Ph. D.

Bolted cores made of coated silicon steel sheets constitute a vital part of heavy electrical equipment for transformers, motors and turbogenerators. Bolted laminates are eminently suitable for facilitating smooth magnetic flux paths, but, unfortunately, they are unable to suppress interlaminate shearing caused by flexural vibration generating noise levels often exceeding 100 dB during operation. The resulting din and cacophony in the surrounding has become a major environmental concern. This thesis makes an attempt to develop theoretical, experimental and numerical models for evolving an effective stiffness approach enhancing the design and analysis underlying nonlinear flexure of bolted laminates. While large machine cores contain thousands of thin sheets bolted together along with end plates, this thesis reports the results obtained on two different assemblies. Two 375 mm long 60 mm wide and 10 mm thick plates assembled with 3, 4 or 5 bolts constitute the first configuration. The second one which is much more realistic comprises 80 coated 270 micron silicon steel sheets with end plates of 2 or 4 mm thickness held together by 3 or 5 bolts. Static 3 point bend tests on these bolted assemblies are followed by instrumented impact tests. Static bending tests highlight the role of frictional nonlinearity inducing a drop in the stiffness due to sliding between the plates. An experimentally determined effective modulus in the initial linear range is utilized for static and dynamic finite element simulations. Nonlinear response of bolted plates is simulated using contact elements in between the sliding plates, plates and the bolts heads. Since the first fundamental mode of vibration dominates the tribomechanical vibration induced noise, the primary focus is on the fundamental frequency in bending. There is generally a good overall agreement in all the results obtained through theory, experiment and FE simulation. Experiments, however, unveil quite complex nonlinear effects induced by friction and plasticity outside the scope of this thesis. However, the low amplitude response of bolted laminates which is reasonably well captured in this thesis represents the starting point for initiating a more elaborate effort for addressing large amplitude nonlinear flexure in bolted laminates. These findings shed light on estimating and controlling noise and vibration levels in heavy electric machines.