The key to the co-rotational (CR) finite element is the separation between the rigid body motion and the deformational motion. It is this separation which makes it superior to other methods in the analysis of large displacement problems. Since the dynamic analysis of a guyed transmission line system contains large displacements from the vibration of the cable, it is considered appropriate to utilize the technique in the analysis. This thesis re-formulates and simplifies the CR method for such a purpose. Numerical tests show that the time step required for convergence in the present technique is ten times less than that is required for convergence in ANSYS. In the construction of the equation for the prediction of the longitudinal load factor (LLF) for the A402-M guyed transmission line due to cable break events, the tower is modelled using a simplified model of a detailed lattice tower. The simplified model considers latticed tower segment as an equivalent beam segment. The use of the simplified model enables to perform the broken wire dynamic analysis of the ten-span transmission line system within a day or two on a personal computer. Two initiating events are considered: all conductors on one arm break and all cables in one span break. Based on the analysis results, it is found that the LLFs for the all cables break event for the A402-M tower are 5% less than that calculated using the EPRI equation. It is therefore recommended that either the LLFs derived from the EPRI equation or from the proposed equation be used in the design of a guyed transmission tower for the broken wire event. The developed procedure can also be used to predict the LLF for the other type transmission line systems.

The key to the co-rotational (CR) finite element is the separation between the rigid body motion and the deformational motion. It is this separation which makes it superior to other methods in the analysis of large displacement problems. Since the dynamic analysis of a guyed transmission line system contains large displacements from the vibration of the cable, it is considered appropriate to utilize the technique in the analysis. This thesis re-formulates and simplifies the CR method for such a purpose. Numerical tests show that the time step required for convergence in the present technique is ten times less than that is required for convergence in ANSYS. In the construction of the equation for the prediction of the longitudinal load factor (LLF) for the A402-M guyed transmission line due to cable break events, the tower is modelled using a simplified model of a detailed lattice tower. The simplified model considers latticed tower segment as an equivalent beam segment. The use of the simplified model enables to perform the broken wire dynamic analysis of the ten-span transmission line system within a day or two on a personal computer. Two initiating events are considered: all conductors on one arm break and all cables in one span break. Based on the analysis results, it is found that the LLFs for the all cables break event for the A402-M tower are 5% less than that calculated using the EPRI equation. It is therefore recommended that either the LLFs derived from the EPRI equation or from the proposed equation be used in the design of a guyed transmission tower for the broken wire event. The developed procedure can also be used to predict the LLF for the other type transmission line systems.

The purpose of the work presented in this thesis is to implement co-rotational beam elements and branch-switching procedures in order to analyse elastic and elastoplasticinstability problems. For the 2D beam elements, the co-rotational framework is taken from Crisfield [23]. The main objective is to compare three different local elasto-plastic elements. The 3D co-rotational formulation is based on the work of Pacoste and Eriksson [73],with new items concerning the parameterisation of the finite rotations, the definitionof the local frame, the inclusion of warping effects through the introduction of aseventh nodal degree of freedom and the consideration of rigid links. Differenttypes of local formulations are considered, including or not warping effects. It isshown that at least some degree of non-linearity must be introduced in the localstrain definition in order to obtain correct results for certain classes of problems. Within the present approach any cross-section can be modelled, and particularly, the centroid and shear center are not necessarily coincident.Plasticity is introduced via a von Mises material with isotropic hardening. Numericalintegration over the cross-section is performed. At each integration point, theconstitutive equations are solved by including interaction between the normal andshear stresses. Concerning instabilities, a new numerical method for the direct computation of elasticcritical points is proposed. This is based on a minimal augmentation procedure asdeveloped by Eriksson [32–34]. In elasto-plasticity, a literature survey, mainly concernedwith theoretical aspects is first presented. The objective is to get a completecomprehension of the phenomena and to give a basis for the two branch-switchingprocedures presented in this thesis.A large number of examples are used in order to assess the performances of the elements and the path-following procedures. / QC 20100512

In this study, a new vector form intrinsic finite element (VFIFE) for the plate is developed and applied to study the responses of a traditional plate member applied to engineering structures. The VFIFE method is a solution procedure for the mechanic problems by adopting the traditional co-rotational explicit finite element method developed by Belyschko and Hsieh (1973). Three different shape-functions including the simplest polynomial form shape-function (Poly), non-conforming area coordinate shape-function (BCIZ) and the conforming area coordinate shape-function (BCIZC) are utilized to simulate the displacement field of the plate. For a system with nonzero rigid-body displacement, the equilibrium will be difficult to achieve in the global coordinate system when the traditional finite element method is applied. By separating the rigid-body motions from the deformed motions, this problem can be easily taken care. In numerical examples, the accuracy and efficiency of this new developed vector form intrinsic finite element for plate simulation are also examined. It is found that compared to the analytical solution, the accuracy is excellent, while compared to traditional finite element method, the efficiency is also encouraging. This new VIFIFE plate element was also applied to the analysis for the sheet plate members in the harbor structures such as the sheep-pile wharf structural system. It was found that not only can the global behaviors of the pile be clearly observed but also local variations in deformations of the steel sheet are clearly shown.

Thanks to the advancement of additive manufacturing, periodic metallic lattice structures are gaining more and more attention. A major attraction of them is that their design can be tailored to specific applications by changing the basic repetitive pattern of the lattice, called the unit cell. This may involve the selection of optimal strut diameters and orientations, as well as the connectivity and strut lengths. Numerical simulation plays a vital role in understanding the mechanical behavior of metallic lattices and it enables the optimization of design parameters. However, conventional numerical modeling strategies in which each strut is represented by one or more beam finite elements yield prohibitively time­ consuming simulations for metallic lattices in engineering­ scale applications. The reasons are that millions of struts are involved, as well as that geometrical and material nonlinearities at the strut level need to be incorporated. The aim of this thesis is the development of multi­scale quasicontinuum (QC) frameworks to substantially reduce the simulation time of nonlinear mechanical models of metallic lattices. For this purpose, this thesis generalizes the QC method by a multi­-field interpolation enabling amongst others the representation of varying diameters in the struts’ axial directions (as a consequence of the manufacturing process). The efficiency is further increased by a new adaptive scheme that automatically adjusts the model reduction whilst controlling the (elastic or elastoplastic) model’s accuracy. The capabilities of the proposed methodology are demonstrated using numerical examples, such as indentation tests and scratch tests, in which the lattice is modeled using geometrically nonlinear elastic and elastoplastic beam finite elements. They show that the multi­scale framework combines a high accuracy with substantial model reduction that are out of reach of direct numerical simulations. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

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Este trabalho contextualiza o problema da análise estrutural bidimensional de risers verticais ou lançados em catenária livre, fazendo uma breve descrição das etapas para a modelagem dessas estruturas. O problema que este trabalho se propõe a resolver é o da análise dinâmica não linear destas estruturas, no domínio do tempo, apresentando uma formulação que seja capaz de representar de forma adequada as etapas de modelagem destes sistemas. A modelagem foi dividida em duas etapas. A primeira delas é referente à fase de lançamento do riser, com o objetivo de determinar a configuração deformada de equilíbrio, assim como os esforços solicitantes internos decorrentes dessa configuração deformada. Ressalta-se que para os casos de risers em catenária livre, considera-se também o contato unilateral da estrutura com o solo marinho. A segunda etapa é a modelagem da fase de operação da estrutura, por meio de um modelo dinâmico bidimensional. Em ambas as etapas, a formulação apresentada considera os efeitos de acoplamento fluidoestrutura. No caso dos risers em catenária, considera-se também o efeito da interação solo-estrutura. Todo o desenvolvimento das equações foi realizado utilizando-se o método dos elementos finitos MEF. A formulação desenvolvida contempla dois elementos finitos, um de treliça e outro de barra, utilizando-se um sistema de coordenadas corrotacionais. A utilização deste sistema de coordenadas possibilitou a adoção de teorias estruturais de pequenas deformações, para a análise de problemas que envolvem grandes deslocamentos e rotações finitas. Além da formulação do problema, também foi apresentado o projeto da ferramenta computacional RiserSys, que é específica para o estudo de risers nas configurações reta (vertical) e em catenária livre. Muito embora não seja o objetivo deste trabalho a implementação computacional do código nesta ferramenta e o estudo de casos referentes a fenômenos de dinâmica não linear nessas estruturas, nas considerações finais, propõe-se, como trabalhos futuros, a utilização desta formulação para o estudo da compressão dinâmica e a instabilidade paramétrica. / This work addresses the problem of the bidimensional analysis of risers, either straight or free hanging, giving a brief description of the modeling steps of these structures. The problem that it is meant to be solved is the nonlinear dynamic analysis in the time domain of these structures, presenting a formulation capable of correctly modeling the steps of the analysis of the system. The modeling was divided into two steps. The first one is referred to the riser installation, in which the objective was to find the deformed configuration of equilibrium and its internal forces. For the free hanging risers, the unilateral contact with the seabed is taken into account. The second step of the modeling is the phase of operation, using a bidimensional dynamic model. Both steps of the modeling consider the fluid-structure coupling phenomenon. For the free hanging risers, the soil-structure interaction is taken into account. All the analyses were performed using the finite element method FEM. Two finite elements were formulated 2D truss and 2D Bernoulli Euler beam both using a co-rotational coordinate system. The co-rotational coordinate system allowed the use of small-strain theory to develop these finite elements to study problems that involve large displacements. Besides the problem formulation, the project of a computational code, named RiserSys, was described. RiserSys is a dedicated computational tool to analyze straight and free hanging risers. Although the objective of this work is not the computational implementation and the analysis of cases studies, in the concluding chapter it is proposed, as future work, the use of the formulation presented herewith to analyze non-linear dynamic phenomena that may take place in these systems, such as dynamic compression and parametric instability.

Abstract This study focuses on the development of a plate-shell element using the vector form intrinsic finite element (VFIFE) method to analyze the structural behavior of thin shell structure subjected to various exerting forces. The shell element employed here is the flat three-node triangular shell element proposed by Bathe and Ho, which is obtained by superimposing CST (constant strain triangle) element with DKT (discrete Kirchhoff theory) triangular plate element. The nodal coordinates, displacements, rotations, and the motion equations of the structure are defined in a fixed global set of coordinates. The strains of the shell element, the element internal nodal forces and the element stiffness matrix are defined in terms of co-rotational coordinates, which are corresponding to the configuration of the shell element. Based on the co-rotational coordinate principle, the nodal displacement between two adjacent time steps can be separated into displacements induced from rigid body motion or deformation, and the incremental internal nodal forces can also be obtained. Finally, following the Newton's 2nd law, the equations of motion can be built to analyze the dynamic responses of thin shell structures. The theory derived in this study, were further verified to be able to simulate the behavior of thin shell structures subjected to both static and dynamic loadings. This new analytical model was proved to be an effective tool that can be an alternertive to traditional finite element procedure to solve for complicated engineering problems in thin shell structures.

Este trabalho contextualiza o problema da análise estrutural bidimensional de risers verticais ou lançados em catenária livre, fazendo uma breve descrição das etapas para a modelagem dessas estruturas. O problema que este trabalho se propõe a resolver é o da análise dinâmica não linear destas estruturas, no domínio do tempo, apresentando uma formulação que seja capaz de representar de forma adequada as etapas de modelagem destes sistemas. A modelagem foi dividida em duas etapas. A primeira delas é referente à fase de lançamento do riser, com o objetivo de determinar a configuração deformada de equilíbrio, assim como os esforços solicitantes internos decorrentes dessa configuração deformada. Ressalta-se que para os casos de risers em catenária livre, considera-se também o contato unilateral da estrutura com o solo marinho. A segunda etapa é a modelagem da fase de operação da estrutura, por meio de um modelo dinâmico bidimensional. Em ambas as etapas, a formulação apresentada considera os efeitos de acoplamento fluidoestrutura. No caso dos risers em catenária, considera-se também o efeito da interação solo-estrutura. Todo o desenvolvimento das equações foi realizado utilizando-se o método dos elementos finitos MEF. A formulação desenvolvida contempla dois elementos finitos, um de treliça e outro de barra, utilizando-se um sistema de coordenadas corrotacionais. A utilização deste sistema de coordenadas possibilitou a adoção de teorias estruturais de pequenas deformações, para a análise de problemas que envolvem grandes deslocamentos e rotações finitas. Além da formulação do problema, também foi apresentado o projeto da ferramenta computacional RiserSys, que é específica para o estudo de risers nas configurações reta (vertical) e em catenária livre. Muito embora não seja o objetivo deste trabalho a implementação computacional do código nesta ferramenta e o estudo de casos referentes a fenômenos de dinâmica não linear nessas estruturas, nas considerações finais, propõe-se, como trabalhos futuros, a utilização desta formulação para o estudo da compressão dinâmica e a instabilidade paramétrica. / This work addresses the problem of the bidimensional analysis of risers, either straight or free hanging, giving a brief description of the modeling steps of these structures. The problem that it is meant to be solved is the nonlinear dynamic analysis in the time domain of these structures, presenting a formulation capable of correctly modeling the steps of the analysis of the system. The modeling was divided into two steps. The first one is referred to the riser installation, in which the objective was to find the deformed configuration of equilibrium and its internal forces. For the free hanging risers, the unilateral contact with the seabed is taken into account. The second step of the modeling is the phase of operation, using a bidimensional dynamic model. Both steps of the modeling consider the fluid-structure coupling phenomenon. For the free hanging risers, the soil-structure interaction is taken into account. All the analyses were performed using the finite element method FEM. Two finite elements were formulated 2D truss and 2D Bernoulli Euler beam both using a co-rotational coordinate system. The co-rotational coordinate system allowed the use of small-strain theory to develop these finite elements to study problems that involve large displacements. Besides the problem formulation, the project of a computational code, named RiserSys, was described. RiserSys is a dedicated computational tool to analyze straight and free hanging risers. Although the objective of this work is not the computational implementation and the analysis of cases studies, in the concluding chapter it is proposed, as future work, the use of the formulation presented herewith to analyze non-linear dynamic phenomena that may take place in these systems, such as dynamic compression and parametric instability.

Dans la première partie de la thèse, les schémas d’intégration conservatifs sont appliqués aux poutres co-rotationnelles 2D. Les cinématiques d'Euler-Bernoulli et de Timoshenko sont abordées. Ces formulations produisent des expressions de l'énergie interne et l'énergie cinétique complexe et fortement non-linéaires. L’idée centrale de l’algorithme consiste à définir, par intégration, le champ des déformations en fin de pas à partir du champ de vitesses de déformations et non à partir du champ des déplacements au travers de la relation déplacement-déformation. La même technique est appliquée aux termes d’inerties. Ensuite, une poutre co-rotationnelle plane avec rotules généralisées élasto-(visco)-plastiques aux extrémités est développée et comparée au modèle fibre avec le même comportement pour des problèmes d'impact. Des exemples numériques montrent que les effets de la vitesse de déformation influencent sensiblement la réponse de la structure. Dans la seconde partie de cette thèse, une théorie de poutre spatiale d’Euler-Bernoulli géométriquement exacte est développée. Le principal défi dans la construction d’une telle théorie réside dans le fait qu’il n’existe aucun moyen naturel de définir un trièdre orthonormé dans la configuration déformée. Une nouvelle méthodologie permettant de définir ce trièdre et par conséquent de développer une théorie de poutre spatiale en incorporant l'hypothèse d'Euler- Bernoulli est fournie. Cette approche utilise le processus d'orthogonalisation de Gram-Schmidt couplé avec un paramètre rotation qui complète la description cinématique et décrit la rotation associée à la torsion. Ce processus permet de surmonter le caractère non-unique de la procédure de Gram-Schmidt. La formulation est étendue au cas dynamique et un schéma intégration temporelle conservant l'énergie est également développé. De nombreux exemples démontrent l’efficacité de cette formulation. / In the first part of the thesis, energymomentum conserving algorithms are designed for planar co-rotational beams. Both Euler-Bernoulli and Timoshenko kinematics are addressed. These formulations provide us with highly complex nonlinear expressions for the internal energy as well as for the kinetic energy which involve second derivatives of the displacement field. The main idea of the algorithm is to circumvent the complexities of the geometric non-linearities by resorting to strain velocities to provide, by means of integration, the expressions for the strain measures themselves. Similarly, the same strategy is applied to the highly nonlinear inertia terms. Next, 2D elasto-(visco)-plastic fiber co-rotational beams element and a planar co-rotational beam with generalized elasto-(visco)-plastic hinges at beam ends have been developed and compared against each other for impact problems. In the second part of this thesis, a geometrically exact 3D Euler-Bernoulli beam theory is developed.The main challenge in defining a three-dimensional Euler-Bernoulli beam theory lies in the fact that there is no natural way of defining a base system at the deformed configuration. A novel methodology to do so leading to the development of a spatial rod formulation which incorporates the Euler-Bernoulli assumption is provided. The approach makes use of Gram-Schmidt orthogonalisation process coupled to a one-parametric rotation to complete the description of the torsional cross sectional rotation and overcomes the non-uniqueness of the Gram-Schmidt procedure. Furthermore, the formulation is extended to the dynamical case and a stable, energy conserving time-stepping algorithm is developed as well. Many examples confirm the power of the formulation and the integration method presented.