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An algorithm is presented for the solution of mechanical contact problems using the displacement based Finite Element Method. The corrections are applied as forces at the global level, together with any corrections for other nonlinearities, without having to nominate either body as target or contactor. The technique requires statically reducing the global stiffness matrices to each degree of freedom involved in contact. Nodal concentrated force are redistributed as continuous tractions. These tractions are re-integrated over the element domains of the opposing body. This creates a set of virtual elements which are assembled to provide a convenient mesh of the properties of the opposing body no matter what its actual discretizaton into elements. Virtual nodal quantities are used to calculate corrective forces that are optimal to first order. The work also presents a derivation of refereritial strain tensors. This sheds new light on the updated Lagrangian formulation, gives a complete and correct incremental form for the Lagrangian strain tensor and illustrates the role of the reference configuration and what occurs when it is changed. / Thesis / Doctor of Philosophy (PhD)

An algorithm is presented for the solution of mechanical contact problems using the displacement based Finite Element Method. The corrections are applied as forces at the global level, together with any corrections for other nonlinearities, without having to nominate either body as target or contactor. The technique requires statically reducing the global stiffness matrices to each degree of freedom involved in contact. Nodal concentrated force are redistributed as continuous tractions. These tractions are re-integrated over the element domains of the opposing body. This creates a set of virtual elements which are assembled to provide a convenient mesh of the properties of the opposing body no matter what its actual discretizaton into elements. Virtual nodal quantities are used to calculate corrective forces that are optimal to first order. The work also presents a derivation of refereritial strain tensors. This sheds new light on the updated Lagrangian formulation, gives a complete and correct incremental form for the Lagrangian strain tensor and illustrates the role of the reference configuration and what occurs when it is changed. / Thesis / Doctor of Philosophy (PhD)

<p>Boundary-contact problems (BCPs) are studied within the frames of</p><p>classical mathematical theory of elasticity and plasticity</p><p>elaborated by Landau, Kupradze, Timoshenko, Goodier, Fichera and</p><p>many others on the basis of analysis of two- and three-dimensional</p><p>boundary value problems for linear partial differential equations.</p><p>A great attention is traditionally paid both to theoretical</p><p>investigations using variational methods and boundary singular</p><p>integral equations (Muskhelishvili) and construction of solutions</p><p>in the form that admit efficient numerical evaluation (Kupradze).</p><p>A special family of BCPs considered by Shtaerman, Vorovich,</p><p>Alblas, Nowell, and others arises within the frames of the models</p><p>of squeezing thin multilayer elastic sheets. We show that</p><p>mathematical models based on the analysis of BCPs can be also</p><p>applied to modeling of the clich\'{e}-surface printing contacts</p><p>and paper surface compressibility in flexographic printing.</p><p>The main result of this work is formulation and complete</p><p>investigation of BCPs in layered structures, which includes both</p><p>the theoretical (statement of the problems, solvability and</p><p>uniqueness) and applied parts (approximate and numerical</p><p>solutions, codes, simulation).</p><p>We elaborate a mathematical model of squeezing a thin elastic</p><p>sheet placed on a stiff base without friction by weak loads</p><p>through several openings on one of its boundary surfaces. We</p><p>formulate and consider the corresponding BCPs in two- and</p><p>three-dimensional bands, prove the existence and uniqueness of</p><p>solutions, and investigate their smoothness including the behavior</p><p>at infinity and in the vicinity of critical points. The BCP in a</p><p>two-dimensional band is reduced to a Fredholm integral equation</p><p>(IE) with a logarithmic singularity of the kernel. The theory of</p><p>logarithmic IEs developed in the study includes the analysis of</p><p>solvability and development of solution techniques when the set of</p><p>integration consists of several intervals. The IE associated with</p><p>the BCP is solved by three methods based on the use of</p><p>Fourier-Chebyshev series, matrix-algebraic determination of the</p><p>entries in the resulting infinite system matrix, and</p><p>semi-inversion. An asymptotic theory for the BCP is developed and</p><p>the solutions are obtained as asymptotic series in powers of the</p><p>characteristic small parameter.</p><p>We propose and justify a technique for the solution of BCPs and</p><p>boundary value problems with boundary conditions of mixed type</p><p>called the approximate decomposition method (ADM). The main idea</p><p>of ADM is simplifying general BCPs and reducing them to a chain</p><p>of auxiliary problems for 'shifted' Laplacian in long rectangles</p><p>or parallelepipeds and then to a sequence of iterative problems</p><p>such that each of them can be solved (explicitly) by the Fourier</p><p>method. The solution to the initial BCP is then obtained as a</p><p>limit using a contraction operator, which constitutes in</p><p>particular an independent proof of the BCP unique solvability.</p><p>We elaborate a numerical method and algorithms based on the</p><p>approximate decomposition and the computer codes and perform</p><p>comprehensive numerical analysis of the BCPs including the</p><p>simulation for problems of practical interest. A variety of</p><p>computational results are presented and discussed which form the</p><p>basis for further applications for the modeling and simulation of</p><p>printing-plate contact systems and other structures of</p><p>flexographic printing. A comparison with finite-element solution</p><p>is performed.</p>

Dependendo da magnitude, falhas na coluna de revestimento podem gerar grandes perdas econômicas e ambientais. Dada a complicada revisão e manutenção do revestimento durante a operação do poço, este deve ser projetado com robustez suficiente para suportar as solicitações em sua vida útil. As conexões de revestimento têm sido consideradas na literatura como os componentes mais propensos à falha. Testes são geralmente utilizados para qualificar a capacidade última das conexões no projeto de revestimento; porém, tendem a ser caros e demandam tempo considerável. Com o objetivo de diminuir os custos dos testes, modelos em elementos finitos são amplamente usados como alternativa e em complemento aos testes para avaliar o comportamento das conexões. Este trabalho apresenta um estudo de conexões de revestimento com base em modelos em elementos finitos, considerando a aplicação de torque de aperto, tração e pressão interna, tomando como caso de estudo uma conexão API 8 Round LTC 9 5/8 47 lb/ft L80. Na modelagem numérica adota-se axissimetría, a inclusão da elastoplasticidade com endurecimento isotrópico controlado pela superfície de falha de Von Mises, não linearidade geométrica e modelagem de contato para grandes deslizamentos com inclusão de fricção tangencial às superfícies de contato. Com uso de critérios mencionados na literatura e hipóteses de falha - principalmente dadas em função das pressões nos filetes, afastamento entre filetes e excessiva plasticidade - o modelo em elementos finitos desenvolvido foi utilizado para avaliar a capacidade da conexão ante os modos de falha por desacoplamento e vazamento. Os resultados da análise são satisfatórios quando comparados às resistências calculadas pela normativa API, e dados e observações experimentais presentes nas referências. Do estudo obtém-se um método para modelagem, que permite reproduzir os fenômenos observados em conexões de revestimento e estimar os modos de falha, podendo ser estendida a análise para conexões com diferentes geometrias. Este estudo é a base para pesquisas futuras sobre modelagem em elementos finitos de testes de conexões, definição de estados limites e de estudos de confiabilidade estrutural em conexões de revestimento de poço. / Casing failures can potentially generate large economic losses and environmental damages, depending on their magnitude. Opportunities for casing evaluation and repair during operation are limited; hence, casing has to be designed with sufficient robustness to bear the loads applied during service life. Casing connections have been considered in the literature as the weak points of the casing column, following observed failures. Testing is generally used to qualify connections; however, they are expensive and demand a lot of time. Aiming to diminish the costs of testing, finite element models are widely used as an alternative and complement to tests to evaluate the behavior of casing connections. This work proposes to study casing connections using finite element models, considering the application of loads of make-up, traction, and internal pressure, taking for study case an API 8 Round LTC 9 5/8 casing connection. The finite element modeling assumed axisymmetry, elastoplastic material with isotropic hardening controlled by the Von Mises yielding surface, geometrical non linearity and inclusion of contact formulation for large slides and tangential frictional behavior between the casing connection mating surfaces. Using criteria mentioned in the literature - mainly in function of flank contact pressures, opening between flanks and effects of excessive plasticity - the developed finite element model was used to evaluate the capacity of the connection for jump-out and leakage failure modes. The results of the analyses were satisfactory when compared to the capacity calculated by the API standards, and experimental observations presented in the literature. From the study, a methodology is obtained for finite element modeling of casing connections, allowing study of the behavior and analysis of failure modes in casing connections, which can be extended for connections with different geometries. This study is the base for future investigations on finite element modeling of connection testing, on limit state definition for various failure modes, and for the study of structural reliability of casing connections.

Boundary-contact problems (BCPs) are studied within the frames of classical mathematical theory of elasticity and plasticity elaborated by Landau, Kupradze, Timoshenko, Goodier, Fichera and many others on the basis of analysis of two- and three-dimensional boundary value problems for linear partial differential equations. A great attention is traditionally paid both to theoretical investigations using variational methods and boundary singular integral equations (Muskhelishvili) and construction of solutions in the form that admit efficient numerical evaluation (Kupradze). A special family of BCPs considered by Shtaerman, Vorovich, Alblas, Nowell, and others arises within the frames of the models of squeezing thin multilayer elastic sheets. We show that mathematical models based on the analysis of BCPs can be also applied to modeling of the clich\'-surface printing contacts and paper surface compressibility in flexographic printing. The main result of this work is formulation and complete investigation of BCPs in layered structures, which includes both the theoretical (statement of the problems, solvability and uniqueness) and applied parts (approximate and numerical solutions, codes, simulation). We elaborate a mathematical model of squeezing a thin elastic sheet placed on a stiff base without friction by weak loads through several openings on one of its boundary surfaces. We formulate and consider the corresponding BCPs in two- and three-dimensional bands, prove the existence and uniqueness of solutions, and investigate their smoothness including the behavior at infinity and in the vicinity of critical points. The BCP in a two-dimensional band is reduced to a Fredholm integral equation (IE) with a logarithmic singularity of the kernel. The theory of logarithmic IEs developed in the study includes the analysis of solvability and development of solution techniques when the set of integration consists of several intervals. The IE associated with the BCP is solved by three methods based on the use of Fourier-Chebyshev series, matrix-algebraic determination of the entries in the resulting infinite system matrix, and semi-inversion. An asymptotic theory for the BCP is developed and the solutions are obtained as asymptotic series in powers of the characteristic small parameter. We propose and justify a technique for the solution of BCPs and boundary value problems with boundary conditions of mixed type called the approximate decomposition method (ADM). The main idea of ADM is simplifying general BCPs and reducing them to a chain of auxiliary problems for 'shifted' Laplacian in long rectangles or parallelepipeds and then to a sequence of iterative problems such that each of them can be solved (explicitly) by the Fourier method. The solution to the initial BCP is then obtained as a limit using a contraction operator, which constitutes in particular an independent proof of the BCP unique solvability. We elaborate a numerical method and algorithms based on the approximate decomposition and the computer codes and perform comprehensive numerical analysis of the BCPs including the simulation for problems of practical interest. A variety of computational results are presented and discussed which form the basis for further applications for the modeling and simulation of printing-plate contact systems and other structures of flexographic printing. A comparison with finite-element solution is performed.

Thin films that are functionally gradient improve the mechanical properties of film-substrate layered materials. Mechanical properties of such materials are found by using indentation tests. In this study, finite element models are developed to simulate the indentation test. The models are based on an axisymmetric half space of a specimen subjected to spherical indentation. The film layer through the thickness is modeled to have either homogeneous material properties or nonhomogeneous material properties that vary linearly. Maximum indenter displacement, and maximum normal and shear stresses at the interface are compared between the homogeneous model and the nonhomogeneous model for pragmatic contact length to film thickness ratios of 0.2 to 0.4, and film to substrate moduli ratios of 1 to 200 to 1. Additionally, a coefficient is derived from regression of the stress data produced by these models and compared to that used to define the pressure field in the axisymmetric Hertzian contact model. The results of this study suggest that a displacement boundary condition to an indenter produces the same results as a pressure distribution boundary condition. The critical normal stresses that occur between modeling a film as a nonhomogeneous and as a homogeneous material vary from 19% for a modulus ratio of 2.5:1 to as high as 66% for a modulus ratio of 200:1 indicating that the modeling techniques produced very different maximum normal stresses. The difference in the maximum shear stress between the nonhomogeneous and the homogeneous models varied from 19% for a 2.5:1 modulus ratio to 57% for the 200:1 modulus ratio but reached values as low as 6% for the 50:1 modulus ratio. The maximum contact depth between the nonhomogeneous and the homogeneous models varied from 14% for the 2.5:1 case to as much as 75% in the 200:1 case. The results from the reapplication of the pressure field derived from the regression coefficients and the R2 values from these regression models indicate the correctness of the regression model used as well as its ability to replicate the normal stresses in the contact area and maximum indenter displacements in a FEA model for both the homogeneous and the nonhomogeneous models for modulus ratios ranging from 2.5:1 to 200:1. The agreement between the regression based coefficients and the force based coefficients suggests the validity for the use of the theoretical axisymmetric Hertzian contact model for defining the pressure field in the contact area and displacements for both the homogeneous case and the nonhomogeneous case for the considered film to substrate moduli ratios and contact length to film thickness ratios.

Dependendo da magnitude, falhas na coluna de revestimento podem gerar grandes perdas econômicas e ambientais. Dada a complicada revisão e manutenção do revestimento durante a operação do poço, este deve ser projetado com robustez suficiente para suportar as solicitações em sua vida útil. As conexões de revestimento têm sido consideradas na literatura como os componentes mais propensos à falha. Testes são geralmente utilizados para qualificar a capacidade última das conexões no projeto de revestimento; porém, tendem a ser caros e demandam tempo considerável. Com o objetivo de diminuir os custos dos testes, modelos em elementos finitos são amplamente usados como alternativa e em complemento aos testes para avaliar o comportamento das conexões. Este trabalho apresenta um estudo de conexões de revestimento com base em modelos em elementos finitos, considerando a aplicação de torque de aperto, tração e pressão interna, tomando como caso de estudo uma conexão API 8 Round LTC 9 5/8 47 lb/ft L80. Na modelagem numérica adota-se axissimetría, a inclusão da elastoplasticidade com endurecimento isotrópico controlado pela superfície de falha de Von Mises, não linearidade geométrica e modelagem de contato para grandes deslizamentos com inclusão de fricção tangencial às superfícies de contato. Com uso de critérios mencionados na literatura e hipóteses de falha - principalmente dadas em função das pressões nos filetes, afastamento entre filetes e excessiva plasticidade - o modelo em elementos finitos desenvolvido foi utilizado para avaliar a capacidade da conexão ante os modos de falha por desacoplamento e vazamento. Os resultados da análise são satisfatórios quando comparados às resistências calculadas pela normativa API, e dados e observações experimentais presentes nas referências. Do estudo obtém-se um método para modelagem, que permite reproduzir os fenômenos observados em conexões de revestimento e estimar os modos de falha, podendo ser estendida a análise para conexões com diferentes geometrias. Este estudo é a base para pesquisas futuras sobre modelagem em elementos finitos de testes de conexões, definição de estados limites e de estudos de confiabilidade estrutural em conexões de revestimento de poço. / Casing failures can potentially generate large economic losses and environmental damages, depending on their magnitude. Opportunities for casing evaluation and repair during operation are limited; hence, casing has to be designed with sufficient robustness to bear the loads applied during service life. Casing connections have been considered in the literature as the weak points of the casing column, following observed failures. Testing is generally used to qualify connections; however, they are expensive and demand a lot of time. Aiming to diminish the costs of testing, finite element models are widely used as an alternative and complement to tests to evaluate the behavior of casing connections. This work proposes to study casing connections using finite element models, considering the application of loads of make-up, traction, and internal pressure, taking for study case an API 8 Round LTC 9 5/8 casing connection. The finite element modeling assumed axisymmetry, elastoplastic material with isotropic hardening controlled by the Von Mises yielding surface, geometrical non linearity and inclusion of contact formulation for large slides and tangential frictional behavior between the casing connection mating surfaces. Using criteria mentioned in the literature - mainly in function of flank contact pressures, opening between flanks and effects of excessive plasticity - the developed finite element model was used to evaluate the capacity of the connection for jump-out and leakage failure modes. The results of the analyses were satisfactory when compared to the capacity calculated by the API standards, and experimental observations presented in the literature. From the study, a methodology is obtained for finite element modeling of casing connections, allowing study of the behavior and analysis of failure modes in casing connections, which can be extended for connections with different geometries. This study is the base for future investigations on finite element modeling of connection testing, on limit state definition for various failure modes, and for the study of structural reliability of casing connections.

This thesis is about modal analysis of the rotor blades row tied with Z-tie. Thesis was solved by finite element system ANSYS. Cyclic symmetry was used in this thesis with the aim of obtain eigen frequency of bladed disc. The next aim of this thesis was to find eigen frequency of the free rotor blades and to compare it with frequency obtained from experiment. 3D model was created by 3D scanner and CAD system CATIA.

No description available.