A stiffened DKT shell element is formulated for the linear static analysis of stiffened plates and shells. Three-noded triangular shell elements and two-noded beam elements with 18 and 12 degrees of freedom are used respectively in the formulation. The stiffeners follow the nodal lines of the shell element. Eccentricity of the stiffener is taken into account. The dynamic and stability characteristic of the element is also investigated. With the developed computer program, the results obtained by the proposed element agrees fairly well with the existing literature.

No description available.

A high-order hybrid discontinuous Galerkin finite element method (DG-FEM) is developed for multi-layered curved panels having large deformation and finite strain. The kinematics of the multi-layered shells is presented at first. The Jacobian matrix and its determinant are also calculated. The weak form of the DG-FEM is next presented. In this case, the discontinuous basis functions can be employed for the displacement basis functions. The implementation details of the nonlinear FEM are next presented. Then, the Consistent Orthogonal Basis Function Space is developed. Given the boundary conditions and structure configurations, there will be a unique basis function space, such that the mass matrix is an accurate diagonal matrix. Moreover, the Consistent Orthogonal Basis Functions are very similar to mode shape functions. Based on the DG-FEM, three dedicated finite elements are developed for the multi-layered pipes, curved stiffeners and multi-layered stiffened hydrofoils. The kinematics of these three structures are presented. The smooth configuration is also obtained, which is very important for the buckling analysis with large deformation and finite strain. Finally, five problems are solved, including sandwich plates, 2-D multi-layered pipes, 3-D multi-layered pipes, stiffened plates and stiffened multi-layered hydrofoils. Material and geometric nonlinearities are both considered. The results are verified by other papers' results or ANSYS. / Master of Science

Métodos convencionais, tais como o método da chapa ortotrópica, têm sido aplicados por muitos anos no estudo de painéis reforçados pela sua simplicidade e facilidade de aplicação na determinação de tensões agentes nas fases iniciais da espiral projeto. Não estão disponíveis na literatura, porém, análises comparativas do método da chapa ortotrópica com procedimentos numéricos utilizando elementos finitos (MEF) que permitam a determinação da acurácia ou da ordem de grandeza dos desvios inerentes à aplicação desta metodologia. O presente trabalho apresenta análises comparativas entre estas duas metodologias na solução de painéis reforçados submetidos a carga lateral uniforme, tipicamente aplicados a estruturas navais (chapa em apenas um dos lados com reforçadores em T). Com este objetivo foram construídos modelos de painéis simplesmente apoiados e engastados (modelagem com elementos de viga e casca) com diferentes espaçamentos e diferentes inércias de reforçadores, configurando uma ampla matriz de análise paramétrica. Os resultados de deflexões e tensões nas vigas e chapas obtidos dos modelos MEF foram parametrizados em função das variáveis da chapa ortotrópica (razão de aspecto virtual), (coeficiente de torção) e K (parâmetro adimensional de tensões e de deflexão). Esta parametrização permite gerar curvas numéricas de tensão e deflexão dos modelos em estudo. As curvas numéricas assim geradas são comparadas com as curvas propostas pelo método da chapa ortotrópica para painéis reforçados simplesmente apoiados, de tal maneira que sua comparação permita, além de determinar a sensibilidade dos resultados numéricos em função das mudanças de inércia e espaçamento entre reforçadores, aferir o nível de desvio oriundo do uso da metodologia da chapa ortotrópica em relação ao método dos elementos finitos. Resultados mostram que as curvas derivadas da metodologia da chapa ortotrópica fornecem bons resultados para as deflexões e tensões transversais nas vigas no centro do painel reforçado. Para as tensões longitudinais nas vigas, uma curva corrigida de tensões longitudinais máximas é fornecida. No caso das curvas de tensões longitudinais e transversais na chapa, as curvas da chapa ortotrópica fornecem valores conservadores de tensão no centro do painel em relação aos valores obtidos dos modelos MEF. Adicionalmente, uma vez que o método da chapa ortotrópica só fornece curvas para chapa sem reforçadores no caso de condição de engaste, curvas numéricas das diferentes variáveis são fornecidas para esta condição. Analogias são feitas com a solução fornecida pelo método da chapa ortotrópica para painéis reforçados com razão de aspecto =, borda longitudinal engastada e borda transversal apoiada. Adicionalmente, resultados analíticos baseados na teoria de grelhas são comparados com os valores fornecidos pelas curvas numéricas para painel engastado obtendo-se resultados consistentes. Com esta análise foi possível determinar a aplicabilidade e limitações do método da chapa ortotrópica no estudo de painéis reforçados simplesmente apoiados. O estudo também fornece novas curvas numéricas para painéis reforçados engastados. / Conventional methods, such as the orthotropic plate, have been applied for many years in the study of stiffened plates to obtain the stresses acting on the structure in the early stages of the structural design, because of its simplicity and easy application. However, comparative analyses of the orthotropic plate method with numerical methods using finite element analyses (FEM) to determine its accuracy or inherent errors are not available in the literature. This study presents comparative analyses between the solutions of the two methodologies for reinforced panels subjected to lateral uniform load, typically applied to marine structures (plate only on one side with T beams). Models of reinforced panels were implemented for a simply supported and clamped boundary conditions with different spacing between stiffeners and different stiffeners`s inertia, setting up a broad array of parametric analysis. The deflections and stresses in beams and plate derived from the MEF analyses were parameterized as function of the orthotropic plate parameters: (virtual aspect ratio), (torsion coefficient) and K (dimensionless parameter of stress and deflection). This enables the generation of parametric numerical curves of stresses and deflections for the models under study. The numerical curves generated in this way were compared with the analytic curves proposed by the orthotropic plate theory for reinforced panels with simply supported boundary conditions. The comparisons allow, in addition to a sensitivity analysis of the numerical curves as a function of inertia and spacing between stiffeners, the assessment of inherent deviation for the orthotropic plate theory when compared with the finite element analyses. From the comparative analyses, it is possible to conclude that the curves proposed for the orthotropic theory for deflection and stresses of the transverse beam at the center of the reinforced panels have a good correlation with the numeric curves and provide accurate results. For the stresses on longitudinal beam, a revised curved for maximum stresses is provided. For the curves of plate stresses in the longitudinal and transverse directions at the center of the panels, the orthotropic plate theory provides conservative values when compared with the values of FEM models. The orthotropic plate method only provides curves for unstiffened plate under clamped boundary condition. Numerical curves for reinforced panels with clamped boundary condition are provided. Analogies are made between the solution provided by the orthotropic theory for a reinforced panel with an infinite virtual aspect ratio = , longitudinal edges clamped and transverse edges simply supported. Additionally, analytical results based on grillage theory were compared with the values provided by the numerical curves for clamped reinforced panels, obtaining a consistent results and a good correlation. This analysis provides a critic overview of the applicability and limitations of the orthotropic plate method for the analyses of reinforced panels with simply supported boundary condition. The study also provides new numerical solutions for reinforced panels with clamped boundary condition.

Métodos convencionais, tais como o método da chapa ortotrópica, têm sido aplicados por muitos anos no estudo de painéis reforçados pela sua simplicidade e facilidade de aplicação na determinação de tensões agentes nas fases iniciais da espiral projeto. Não estão disponíveis na literatura, porém, análises comparativas do método da chapa ortotrópica com procedimentos numéricos utilizando elementos finitos (MEF) que permitam a determinação da acurácia ou da ordem de grandeza dos desvios inerentes à aplicação desta metodologia. O presente trabalho apresenta análises comparativas entre estas duas metodologias na solução de painéis reforçados submetidos a carga lateral uniforme, tipicamente aplicados a estruturas navais (chapa em apenas um dos lados com reforçadores em T). Com este objetivo foram construídos modelos de painéis simplesmente apoiados e engastados (modelagem com elementos de viga e casca) com diferentes espaçamentos e diferentes inércias de reforçadores, configurando uma ampla matriz de análise paramétrica. Os resultados de deflexões e tensões nas vigas e chapas obtidos dos modelos MEF foram parametrizados em função das variáveis da chapa ortotrópica (razão de aspecto virtual), (coeficiente de torção) e K (parâmetro adimensional de tensões e de deflexão). Esta parametrização permite gerar curvas numéricas de tensão e deflexão dos modelos em estudo. As curvas numéricas assim geradas são comparadas com as curvas propostas pelo método da chapa ortotrópica para painéis reforçados simplesmente apoiados, de tal maneira que sua comparação permita, além de determinar a sensibilidade dos resultados numéricos em função das mudanças de inércia e espaçamento entre reforçadores, aferir o nível de desvio oriundo do uso da metodologia da chapa ortotrópica em relação ao método dos elementos finitos. Resultados mostram que as curvas derivadas da metodologia da chapa ortotrópica fornecem bons resultados para as deflexões e tensões transversais nas vigas no centro do painel reforçado. Para as tensões longitudinais nas vigas, uma curva corrigida de tensões longitudinais máximas é fornecida. No caso das curvas de tensões longitudinais e transversais na chapa, as curvas da chapa ortotrópica fornecem valores conservadores de tensão no centro do painel em relação aos valores obtidos dos modelos MEF. Adicionalmente, uma vez que o método da chapa ortotrópica só fornece curvas para chapa sem reforçadores no caso de condição de engaste, curvas numéricas das diferentes variáveis são fornecidas para esta condição. Analogias são feitas com a solução fornecida pelo método da chapa ortotrópica para painéis reforçados com razão de aspecto =, borda longitudinal engastada e borda transversal apoiada. Adicionalmente, resultados analíticos baseados na teoria de grelhas são comparados com os valores fornecidos pelas curvas numéricas para painel engastado obtendo-se resultados consistentes. Com esta análise foi possível determinar a aplicabilidade e limitações do método da chapa ortotrópica no estudo de painéis reforçados simplesmente apoiados. O estudo também fornece novas curvas numéricas para painéis reforçados engastados. / Conventional methods, such as the orthotropic plate, have been applied for many years in the study of stiffened plates to obtain the stresses acting on the structure in the early stages of the structural design, because of its simplicity and easy application. However, comparative analyses of the orthotropic plate method with numerical methods using finite element analyses (FEM) to determine its accuracy or inherent errors are not available in the literature. This study presents comparative analyses between the solutions of the two methodologies for reinforced panels subjected to lateral uniform load, typically applied to marine structures (plate only on one side with T beams). Models of reinforced panels were implemented for a simply supported and clamped boundary conditions with different spacing between stiffeners and different stiffeners`s inertia, setting up a broad array of parametric analysis. The deflections and stresses in beams and plate derived from the MEF analyses were parameterized as function of the orthotropic plate parameters: (virtual aspect ratio), (torsion coefficient) and K (dimensionless parameter of stress and deflection). This enables the generation of parametric numerical curves of stresses and deflections for the models under study. The numerical curves generated in this way were compared with the analytic curves proposed by the orthotropic plate theory for reinforced panels with simply supported boundary conditions. The comparisons allow, in addition to a sensitivity analysis of the numerical curves as a function of inertia and spacing between stiffeners, the assessment of inherent deviation for the orthotropic plate theory when compared with the finite element analyses. From the comparative analyses, it is possible to conclude that the curves proposed for the orthotropic theory for deflection and stresses of the transverse beam at the center of the reinforced panels have a good correlation with the numeric curves and provide accurate results. For the stresses on longitudinal beam, a revised curved for maximum stresses is provided. For the curves of plate stresses in the longitudinal and transverse directions at the center of the panels, the orthotropic plate theory provides conservative values when compared with the values of FEM models. The orthotropic plate method only provides curves for unstiffened plate under clamped boundary condition. Numerical curves for reinforced panels with clamped boundary condition are provided. Analogies are made between the solution provided by the orthotropic theory for a reinforced panel with an infinite virtual aspect ratio = , longitudinal edges clamped and transverse edges simply supported. Additionally, analytical results based on grillage theory were compared with the values provided by the numerical curves for clamped reinforced panels, obtaining a consistent results and a good correlation. This analysis provides a critic overview of the applicability and limitations of the orthotropic plate method for the analyses of reinforced panels with simply supported boundary condition. The study also provides new numerical solutions for reinforced panels with clamped boundary condition.

Noise and vibration suppression is an important aspect in the design process of structures and machines. Undesirable vibrations can cause fatigue in a structure and are, therefore, a risk to the safety of a structure. One of the most effective and widely used methods of mitigating these unwanted vibrations from a system is passive damping, by using a viscoelastic material. This dissertation will primarily focus on constrained layer passive damping treatments in structures and the investigation of associated complex modes. The key idea behind constrained damping treatment is to increase damping as affected by the presence of a highly damped core layer vibrating mainly in shear. Our main goal was to incorporate viscoelastic material in a thick stiffened panel with plate-strip stiffeners, to enhance the damping characteristics of the structure. First, we investigated complex damped modes in beams in the presence of a viscoelastic layer sandwiched between two elastic layers. The problem was solved using two approaches, (1) Rayleigh beam theory and analyzed using the principle of virtual work, and (2) by using 2D plane stress elasticity based finite-element method. The damping in the viscoelastic material was modeled using the complex modulus approach. We used FEM without any kinematic assumptions for the transverse shear in both the core and elastic layers. Moreover, numerical examples were studied, by including complex modulus in the base and constraining layers. The loss factor was calculated by modal strain energy method, and by solving a complex eigenvalue problem. The efficiency of the modal strain energy method was tested for different loss factors in the core layer. Complex mode shapes of the beam were also examined in the study, and a comparison was made between viscoelastically damped and non-proportionally damped structures. Secondly, we studied the free vibration response of an integrally stiffened and/or stepped plate. The stiffeners used here were plate-strip stiffeners, unlike the rib stiffeners often investigated by researchers. Both plate and stiffeners were analyzed using the first-order shear deformation theory. The deflections and rotations were assumed as a product of Timoshenko beam functions, chosen appropriately according to the given boundary conditions. Unlike Navier and Levy solution techniques, the approach used here can also be applied to fully clamped, free and cantilever supported stiffened plates. The governing differential equations were solved using the Rayleigh-Ritz method. The development of the stiffness and the mass matrices in the Ritz analysis was found to consume a huge amount of CPU time due to the recursive integration of Timoshenko beam functions. An approach is suggested to greatly decrease this amount of CPU time, by replacing the recursive integration in a loop structure in the computer program, with the analytical integration of the integrand in the loop. The numerical results were compared with the exact solutions available in the literature and the commercially available finite-element software ABAQUS. Some parametric studies were carried out to show the influence of certain important parameters on the overall natural frequencies of the stiffened plate. Finally, we investigated the damped response of an adhesively bonded plate employing plate-strip stiffeners, using FSDT for both the plate and stiffeners. The problem was analyzed using the principle of virtual work. At first, we did not consider damping in the adhesive in order to validate our code, by comparing our results with those available in the literature as well as with the results obtained using ABAQUS 3D model. The results were found to be highly satisfactory. We also considered the effect of changing the stiffness of the adhesive layer on the vibration of the bonded system. As a second step, we included damping in the stiffened structure using complex modulus approach, a widely used technique to represent the rheology of the viscoelastic material. We observed an overall increase in the natural frequencies of the system, due to the damping provided by the viscoelastic material. Moreover, it was noticed that when the thickness of the adhesive layer is increased, the natural frequencies and loss factor of the stiffened structure decrease. A viscoelastic material with high loss factor and small thickness will be a perfect design variable to obtain overall high damping in the structure. / Ph. D.

In this study, the &ldquo / Free Flexural (or Bending) Vibrations of Stiffened Plates or Panels&rdquo / are investigated in detail. Two different Groups of &ldquo / Stiffened Plates&rdquo / will be considered. In the first group, the &ldquo / Type 4&rdquo / and the &ldquo / Type 6&rdquo / of &ldquo / Group I&rdquo / of the &ldquo / Integrally-Stiffened and/or Stepped-Thickness Plate or Panel Systems&rdquo / are theoretically analyzed and numerically solved by making use of the &ldquo / Mindlin Plate Theory&rdquo / . Here, the natural frequencies and the corresponding mode shapes, up to the sixth mode, are obtained for each &ldquo / Dynamic System&rdquo / . Some important parametric studies are also presented for each case. In the second group, the &ldquo / Class 2&rdquo / and the &ldquo / Class 3&rdquo / of the &ldquo / Bonded and Stiffened Plate or Panel Systems&rdquo / are also analyzed and solved in terms of the natural frequencies with their corresponding mode shapes. In this case, the &ldquo / Plate Assembly&rdquo / is constructed by bonding &ldquo / Stiffening Plate Strips&rdquo / to a &ldquo / Base Plate or Panel&rdquo / by dissimilar relatively thin adhesive layers. This is done with the purpose of reinforcing the &ldquo / Base Plate or Panel&rdquo / by these &ldquo / Stiffening Strips&rdquo / in the appropriate locations, so that the &ldquo / Base Plate or Panel&rdquo / will exhibit satisfactory dynamic response. The forementioned &ldquo / Bonded and Stiffened Systems&rdquo / may also be used to repair a damaged (or rather cracked) &ldquo / Base Plate or Panel&rdquo / . Here in the analysis, the &ldquo / Base Plate or Panel&rdquo / , the &ldquo / Stiffening Plate Strips&rdquo / as well as the in- between &ldquo / adhesive layers&rdquo / are assumed to be linearly elastic continua. They are assumed to be dissimilar &ldquo / Orthotropic Mindlin Plates&rdquo / . Therefore, the effects of shear deformations and rotary moments of inertia are considered in the theoretical formulation. In each case of the &ldquo / Group I&rdquo / and &ldquo / Group II&rdquo / problems, the &ldquo / Governing System of Dynamic Equations&rdquo / for every problem is reduced to the &ldquo / First Order Ordinary Differential Equations&rdquo / . In other words the &ldquo / Free Vibrations Problem&rdquo / , in both cases, is an &ldquo / Initial and Boundary Value Problem&rdquo / is reduced to a &ldquo / Two- Point or Multi-Point Boundary Value Problem&rdquo / by using the present &ldquo / Solution Technique&rdquo / . For this purpose, these &ldquo / Governing Equations&rdquo / are expressed in &ldquo / compact forms&rdquo / or &ldquo / state vector&rdquo / forms. These equations are numerically integrated by the so-called &ldquo / Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)&rdquo / . In the numerical results, the mode shapes together with their corresponding non-dimensional natural frequencies are presented up to the sixth mode and for various sets of &ldquo / Boundary Conditions&rdquo / for each structural &ldquo / System&rdquo / . The effects of several important parameters on the natural frequencies of the aforementioned &ldquo / Systems&rdquo / are also investigated and are graphically presented for each &ldquo / Stiffened and Stiffened and Bonded Plate or Panel System&rdquo / . Additionally, in the case of the &ldquo / Bonded and Stiffened System&rdquo / , the significant effects of the &ldquo / adhesive material properties&rdquo / (i.e. the &ldquo / Hard&rdquo / adhesive and the &ldquo / Soft&rdquo / adhesive cases) on the dynamic response of the &ldquo / plate assembly&rdquo / are also presented.