The thesis aims to investigate the golf swing dynamic behaviors by a suitable computer simulation. The FEM analysis software DYNA was used to analyze the golf swing motion. The swing model was made by driving moment at two revolving joints to provide torque of golf swing. The point is to set the model under the three-dimension gravity field to analyze the influences of club head speed, loft angle, lie angle and stresses in the shaft caused by different shaft flexes and club head weights. Form the finding of the study, the dynamic response and the shaft flex play important parts in swing motion. Comparing the results of the experiments of other research, the relationship among swing motion factors and their dynamic responses were conducted. It is believed that this thesis will provide some reliable computer stimulation data for the reference in sport science.

Reinforced concrete (RC) shear wall buildings constitute a significant portion of the building inventory in many earthquake-prone regions. A similar type of structural system is fully-grouted reinforced masonry (RM) shear wall structures. The accurate determination of the nonlinear response of reinforced concrete and reinforced masonry (RC/RM) walls subjected to lateral loading is of uttermost importance for ensuring the safety of the built environment. Analytical models provide a cost efficient and comprehensive tool to study the nonlinear response of RC/RM structures, as compared to experimental tests. Predictive models should capture nonlinear material behavior as well as the geometrically nonlinear response of RC/RM shear wall structures during major seismic events. This thesis outlines the formulation and validation of a nonlinear shell element for the simulation of RC/RM structures. The proposed shell element enhances an existing formulation of a four-node Discrete Kirchhoff shell element through the inclusion of a corotational approach to account for geometric nonlinearities and of nonlinear material models to capture the effect of cracking and crushing in concrete or masonry and the nonlinear hysteretic behavior of reinforcing steel. The analytical results obtained from multiple linear and nonlinear analyses are compared against theoretical solutions and experimental test data. These comparative validation studies show the enhanced shell element can satisfactorily capture the salient features of the response of nonlinear reinforced concrete/masonry shear wall structures including axial-shear-flexure interaction, damage patterns, and in-plane and out-of-plane loading. / Master of Science

This work is a stepping stone towards developing higher order shell element for simulating composite manufacturing procedure. In this study, a continuum approach suitable for combined material and geometrically nonlinear analysis for an eight node solid shell element SS8 is explained. The formulation of SS8 comprises two ingredients to alleviate undesirable locking effects: 1) Assumed Natural Strain concept, which has proven to alleviate the curvature thickness and transverse shear locking problems. 2) Enhanced Assumed Strain, which adds enhanced degrees of freedom to improve the in-plane response of the element and the curvature thickness locking problem. This formulation has been extended to represent geometric and material non-linearity using Total Lagrangian approach. Finally, finite strain formulation has been verified by numerical examples. Results when compared to continuum shell element in ABAQUS show a reasonable agreement with a relative error of less than 2%.

This thesis is a summary of my research works at the MSM department of the University of Liège since 1989. These research works are devoted to the numerical simulation of the three-dimensional sheet metal forming processes by the finite element method. Several research areas, including the finite element modelling, the time-integration technique of material constitutive laws and the 3D contact treatments are covered. The theoretical methodologies, the numerical implementation and industrial applications will be presented. The thesis begins with a brief overview made in chapter 1. In chapter 2, a 8-node mixed brick element based on the HU-WASHIZU variational principle is developed (JET3D element). Special attention is paid to avoid hourglass modes as well as locking phenomena, including "shear locking" and "volumetric locking" in nonlinear analysis. Numerical examples are used at the end of this chapter to assess the performance and applicability of this element. In chapter 3, a 3D four-node shallow element, which was originally developed by Ph. JETTEUR and then has been improved by him and his co-workers, is recalled (COQJ4 element). Special care is taken to the finite rotation problems and a new formulation for the finite rotation is developed. An example is used at the end of the chapter to show the performance of the proposed formulation for the finite rotation problems. A special contact element is developed for the shell element in chapter 4. In this chapter, some basics aspects of numerical tretments of contact problem are discussed and some attentions are paid to the contact searching algorithms, which has proved to be very important in 3D cases. In chapter 5, the appropriate constitutive equations are examined together with the techniques of time-integration and the evaluation of the tangent stiffness matrix. Much attention is paid to the implicit integration methods, which have proved to be very efficient for large increments of deformation. Finally, in chapter 6, two benchmark tests are used as validation of the code. Special attention is paid to the possibility of using dynamic explicit procedure in the numerical simulation of sheet metal forming, although it is often characterised as a quasi-static process. All the developments made in the thesis have been implemented into the finite element code LAGAMINE developed since 1982 at the MSM department of the University of Liège.

The Thirteenth East Asia-Pacific Conference on Structural Engineering and Construction, September 11-13, 2013, Sapporo, Japan (EASEC-13)

Finite element analysis of laminated shells using a three-noded flat triangular shell element is presented. The flat shell element is obtained by combining the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element similar to the Allman element, but derived from the Linear Strain Triangular (LST) element. Though this combination has been employed in the literature for linear static analysis of laminated plates, the results presented are not adequate to ascertain that the element would perform well in the case of static and dynamic analysis of general shells. The element is first thoroughly tested for linear static analysis of laminated plates and shells and is extended for free vibration, thermal, and geometrically nonlinear analysis. The major drawback of the DKT plate bending element is that the transverse displacement is not explicitly defined within the interior of the element. Hence obtaining the consistent mass matrix or the derivatives of the transverse displacement that are required for forming the geometric stiffness matrix is not straight forward. This problem is alleviated by borrowing shape functions from other similar elements or using simple displacement fields. In the present research, free vibration analysis is performed both by using a lumped mass matrix and a so called consistent mass matrix, obtained by borrowing shape functions from an existing element, in order to compare the performance of the two methods. The geometrically nonlinear analysis is performed using an updated Lagrangian formulation employing Green strain and Second Piola-Kirchhoff (PK2) stress measures. A linear displacement field is used for the transverse displacement in order to compute the derivatives of the transverse displacement that are required to compute the geometric stiffness or the initial stress matrix. Several numerical examples are solved to demonstrate the accuracy of the formulation for both small and large rotation analysis of laminated plates and shells. The results are compared with those available in the existing literature and those obtained using the commercial finite element package ABAQUS and are found to be in good agreement. The element is employed for two main applications involving large flexible structures. The first application is the control of thermal deformations of a spherical mirror segment, which is a segment of a multi-segmented primary mirror used in a space telescope. The feasibility of controlling the surface distortions of the mirror segment due to arbitrary thermal fields, using discrete and distributed actuators, is studied. This kind of study was required for the design of a multi-segmented primary mirror of a next generation space telescope. The second application is the analysis of an inflatable structure, being considered by the US Army for housing vehicles and personnel. The tent structure is made up of membranes supported by arches stiffened by internal pressure. The updated Lagrangian formulation of the flat shell element has been developed primarily for the nonlinear analysis of the tent structure, since such a structure is expected to undergo large deformations and rotations under the action of environmental loads like the wind and snow loads. The wind load is modeled as a nonuniform pressure load and the snow load as lumped concentrated loads. Since the direction of the pressure load is assumed to be normal to the current configuration of the structure, it changes as the structure undergoes deformation. This is called the follower action. As a result, the pressure load is a function of the displacements and hence contributes to the tangent stiffness matrix in the case of geometrically nonlinear analysis. The thermal load also contributes to the system tangent stiffness matrix. In the case of the thermal load this contribution is similar to the initial stress matrix and hence no additional effort is required to compute this contribution. In the case of the pressure load, this contribution (called the pressure stiffness) is in general unsymmetric but can be systematically derived from the principle of virtual work. The follower effects of the pressure load have been included in the updated Lagrangian formulation of the flat shell element and have been validated using standard examples in the literature involving deformation-dependent pressure loads. The element can be used to obtain the nonlinear response of the tent structure under wind and snow loads. / Ph. D.

Um modelo de elementos finitos de casca capaz de representar estruturas soldadas, sem adicionar erros significativos em termos da rigidez estrutural, poderia ser amplamente empregado em problemas dinâmicos em que o método da tensão estrutural (hot spot) é aplicado para análises de vida em fadiga. O âmbito deste trabalho é formular uma técnica de modelagem capaz de fazê-lo. Para alcançar esse objetivo, uma otimização paramétrica para a representação de estruturas soldadas através de elementos de casca foi realizada. As variáveis de projeto propostas na formulação empregada foram definidas como o comprimento do tamanho de perna e a espessura do elemento de casca representando o filete de solda. O foco da otimização foi encontrar uma faixa de espessura/tamanho de perna que não modificasse significativamente as primeiras frequências naturais e conseguisse entregar resultados similares aos obtidos por um modelo sólido. Programação linear sequencial foi empregada na otimização. A estrutura analisada foi do tipo T, com seção constante e espessura e profundidade diversas, sob diferentes modos de carregamento. Uma vez que os parâmetros ótimos foram encontrados, duas diferentes metodologias de modelagem foram propostas e comparadas com outras três bem estabelecidas e apresentadas em normas e na literatura. Os resultados foram comparados quanto às primeiras frequências naturais, massa total, tensão estrutural e vida em fadiga. / A finite element shell model capable of representing a welded structure without any significantly error on its stiffness could be widely applied to dynamic problems in which the structural stress method (hot-spot approach) is employed for fatigue analysis. The scope of the present work is to formulate a modeling technique capable of doing so. In order to accomplish it, a parametric optimization for simulating welded structures using shell elements is made, the design variables in the proposed formulation are defined as the weld leg length and thickness of the shell element representing the weld fillet. The main goal of the optimization was to find a range of thickness/leg length which would not change significantly the first natural frequencies, and still deliver results similar to the ones obtained by a solid model. Sequential linear programming optimizations are performed in a T-shaped structure under different loading scenarios, with constant section and different plate thicknesses and depths. Once the optimal parameters are found, two different modeling techniques are presented and compared with three well established methodologies presented in standards and the literature. The differences in the results are compared for first natural frequencies, total mass, hot spot stress and fatigue life.

Um modelo de elementos finitos de casca capaz de representar estruturas soldadas, sem adicionar erros significativos em termos da rigidez estrutural, poderia ser amplamente empregado em problemas dinâmicos em que o método da tensão estrutural (hot spot) é aplicado para análises de vida em fadiga. O âmbito deste trabalho é formular uma técnica de modelagem capaz de fazê-lo. Para alcançar esse objetivo, uma otimização paramétrica para a representação de estruturas soldadas através de elementos de casca foi realizada. As variáveis de projeto propostas na formulação empregada foram definidas como o comprimento do tamanho de perna e a espessura do elemento de casca representando o filete de solda. O foco da otimização foi encontrar uma faixa de espessura/tamanho de perna que não modificasse significativamente as primeiras frequências naturais e conseguisse entregar resultados similares aos obtidos por um modelo sólido. Programação linear sequencial foi empregada na otimização. A estrutura analisada foi do tipo T, com seção constante e espessura e profundidade diversas, sob diferentes modos de carregamento. Uma vez que os parâmetros ótimos foram encontrados, duas diferentes metodologias de modelagem foram propostas e comparadas com outras três bem estabelecidas e apresentadas em normas e na literatura. Os resultados foram comparados quanto às primeiras frequências naturais, massa total, tensão estrutural e vida em fadiga. / A finite element shell model capable of representing a welded structure without any significantly error on its stiffness could be widely applied to dynamic problems in which the structural stress method (hot-spot approach) is employed for fatigue analysis. The scope of the present work is to formulate a modeling technique capable of doing so. In order to accomplish it, a parametric optimization for simulating welded structures using shell elements is made, the design variables in the proposed formulation are defined as the weld leg length and thickness of the shell element representing the weld fillet. The main goal of the optimization was to find a range of thickness/leg length which would not change significantly the first natural frequencies, and still deliver results similar to the ones obtained by a solid model. Sequential linear programming optimizations are performed in a T-shaped structure under different loading scenarios, with constant section and different plate thicknesses and depths. Once the optimal parameters are found, two different modeling techniques are presented and compared with three well established methodologies presented in standards and the literature. The differences in the results are compared for first natural frequencies, total mass, hot spot stress and fatigue life.

Um modelo de elementos finitos de casca capaz de representar estruturas soldadas, sem adicionar erros significativos em termos da rigidez estrutural, poderia ser amplamente empregado em problemas dinâmicos em que o método da tensão estrutural (hot spot) é aplicado para análises de vida em fadiga. O âmbito deste trabalho é formular uma técnica de modelagem capaz de fazê-lo. Para alcançar esse objetivo, uma otimização paramétrica para a representação de estruturas soldadas através de elementos de casca foi realizada. As variáveis de projeto propostas na formulação empregada foram definidas como o comprimento do tamanho de perna e a espessura do elemento de casca representando o filete de solda. O foco da otimização foi encontrar uma faixa de espessura/tamanho de perna que não modificasse significativamente as primeiras frequências naturais e conseguisse entregar resultados similares aos obtidos por um modelo sólido. Programação linear sequencial foi empregada na otimização. A estrutura analisada foi do tipo T, com seção constante e espessura e profundidade diversas, sob diferentes modos de carregamento. Uma vez que os parâmetros ótimos foram encontrados, duas diferentes metodologias de modelagem foram propostas e comparadas com outras três bem estabelecidas e apresentadas em normas e na literatura. Os resultados foram comparados quanto às primeiras frequências naturais, massa total, tensão estrutural e vida em fadiga. / A finite element shell model capable of representing a welded structure without any significantly error on its stiffness could be widely applied to dynamic problems in which the structural stress method (hot-spot approach) is employed for fatigue analysis. The scope of the present work is to formulate a modeling technique capable of doing so. In order to accomplish it, a parametric optimization for simulating welded structures using shell elements is made, the design variables in the proposed formulation are defined as the weld leg length and thickness of the shell element representing the weld fillet. The main goal of the optimization was to find a range of thickness/leg length which would not change significantly the first natural frequencies, and still deliver results similar to the ones obtained by a solid model. Sequential linear programming optimizations are performed in a T-shaped structure under different loading scenarios, with constant section and different plate thicknesses and depths. Once the optimal parameters are found, two different modeling techniques are presented and compared with three well established methodologies presented in standards and the literature. The differences in the results are compared for first natural frequencies, total mass, hot spot stress and fatigue life.

Examensarbetet behandlar ett brotvärsnitt som inte entydigt kan betraktas som ett balktvärsnitt eller plattvärsnitt. Med de måttdefinitioner som används vid broprojektering ska en plattkonstruktion ha en bredd som är fem gånger höjden, annars ska konstruktionen ses som en balk där även balkens längd definieras att vara större än tre gånger höjden. Brotvärsnittet som studeras i detta examensarbete kan alltså definieras både som ett plattvärsnitt och som ett balktvärsnitt. Målet med arbetet är att undersöka om det är möjligt att finna en metod att konstruera denna typ av tvärsnitt som befinner sig i gränslandet mellan två definitioner. Skillnaderna mellan en plattas och en balks verkningssätt ligger i att plattan antas bära last i två riktningar medan en balk enbart bär last i en riktning. Examensarbetet är genomfört i sammarbete med WSP Bro- och vattenbyggnad i Örebro, som konstruerade en bro med just detta tvärsnitt. Bro 344 över parkstråk i trafikplats Rinkeby å ramp mot Ärvinge, är 181 m lång bro i 9 spann och finns belägen vid trafikplats Rinkeby som är en del utav Trafikverkets projekt, E18 Hjulsta – Kista. Lasterna som används i analyserna är betongens egentyngd, utbredd last av beläggning och vertikala trafiklaster. I ett första skede i arbetet analyseras modellerna med rörliga trafiklaster. Det framkom dock under arbetets gång att förenklingar vad gäller trafiklasterna måste göras då arbetet skulle bli för omfattande annars. En statisk boggilast placeras ut i ett spann mitt i mellan dess tredjedelspunkt och halva spannlängden. Beräkningar utförs i en mjukvara där modellen både byggs upp av skalelement som en långsträckt platta där snittkrafter kommer ut som enhet per meter och med balkelement som en halvinspänd balk där snittkrafter kommer ut i enhet per balk. Mjukvaran som används är ett tredimensionellt finit element program, SOFISTIK, som likt många andra FE-program erbjuder användarvänliga modelleringsmiljöer, hanterar rörliga laster och har en mängd inbyggda moduler och funktioner. Beräkningarna som sedan utvärderas och jämförs är dels SOFISTIKs olika resultat för skalmodellen och balkmodellen. Där dimensionerande armeringsmängder beräknas för max fältmoment och max stödmoment. Dessa resultat från SOFISTIKs skalmodell respektive balkmodell jämförs också med resultat från de mjukvaror som användes vid dimensioneringen från början, vilket var för skalmodellanalysen Brigade Standard och för balkanalysen Strip Step 3. Armeringsmängderna jämförs slutligen genom att studera tre fall: •   Skalmodell SOFISTIK - Brigade Standard •   Balkmodell SOFISTIK - Strip Step 3 •   SOFISTIK skalmodell – balkmodell Jämförelserna visar att både skalmodellerna från de olika programmen (SOFISTIK – Brigade Standard) och balkmodellerna från de olika programmen (SOFISTIK – Strip Step 3) ger likvärdiga armeringsmängder vilket ger en trygg verifiering av modellerna. Vidare visar jämförelse mellan skal- och balkmodell i SOFISTIK att balkmodellen ger avsevärt högre armeringsmängder, både i fält och över stöd. ar / The aim of this Master thesis is to study a cross section of a bridge that cannot be unambiguously considered to be defined as a beam cross-section or a slab cross-section. With the given definitions used in bridge engineering, a slab construction has to have a width wider than five times the height, otherwise it should be regarded as a beam construction. The length of a beam construction is also defined to be three times longer than the height. The cross section in this thesis can thus be treated as both a slab cross-section and as a beam cross-section. The aim of this work is to investigate whether it is possible to find a method to construct this type of cross-section that falls within both these two definitions. The difference in mode of action between a plate and a beam is that the plate is assumed to carry loads in two directions while a beam only carries load in one direction. The work done in this report has been performed in cooperation with the consulting company WSP Bridge & Hydraulic Design in Örebro who has constructed a bridge with the studied section, Bro 344 över parkstråk i trafikplats Rinkeby å ramp mot Ärvinge. This bridge is 181 m long in 9 spans and are located at the traffic interchange Rinkeby which is part of the Swedish Transport Administration project, E18 Hjulsta - Kista. The loads, which are discussed and analyzed are the deadweight of the concrete, distributed load of road surface and vertical traffic loads. In the first stage of the work the models are being analyzed with moving traffic loads, it appears, however, during the process that simplifications in terms of the moving traffic loads must be made, when the work would be too wide otherwise. A static bogie-load is deployed in one of the spans, in between the third point and half the span length. Calculations are performed using a computer software, in which the bridge is modeled both by shell elements and by beam elements. The shell-model is created as an elongated plate section in which the force comes out as unit per meter. The beam-model is considered as a semi-restrained beam in which the section forces come out in unit for the whole beam. Software used is a three-dimensional finite element program, SOFISTIK. As many other FEprograms SOFISTIK provide a user-friendly modeling workspace, it handles variable and moving loads and has a variety of embedded modules and functions. The calculations which are being evaluated and compared, is at the first hand the different results in between the shell-model and the beam-model from the models made in SOFISTIK. The amounts of designing reinforcement are calculated for the maximum bending moment and for the minimum bending moment. Those results, also compares with results from other software, the software used in the design from the beginning, which for the shell-analyze the software Brigade Standard and for the beam-analyze the software Strip Step 3. The amounts of design reinforcement are finally compared by studying three cases: •   The Shell-model from SOFISTIK - Brigade Standard •   Beam-model from SOFISTIK - Strip Step 3 •   SOFISTIK the shell-model – the beam-model The comparisons show that both the shell-models from the two different programs (SOFISTIK and Brigade Standard) and the beam-models from the different two programs (SOFISTIK - Strip Step 3) give equivalent amounts of reinforcement which provides a secure verification of the models. Furthermore the comparison between the shell-model and the beam-model, in SOFISTIK , shows that the beam-model provides significantly higher amounts of reinforcement in both the field and at the support.