Dissertations / Theses on the topic '3D beam element'

Le nouvel élément de poutre est une évolution d'un élément de Timoshenko poutre avec un nœud supplémentaire situé à mi-longueur. Ce nœud supplémentaire permet l'introduction de trois composantes supplémentaires de contrainte afin que la loi constitutionnelle 3D complète puisse être utilisée directement. L'élément proposé a été introduit dans un code d'éléments finis dans Matlab et une série d'exemples de linéaires/petites contraintes ont été réalisées et les résultats sont systématiquement comparés avec les valeurs correspondantes des simulations ABAQUS/Standard 3D. Ensuite, la deuxième étape consiste à introduire le comportement orthotrope et à effectuer la validation de déplacements larges / petites contraintes basés sur la formulation Lagrangienne mise à jour. Une série d'analyses numériques est réalisée qui montre que l'élément 3D amélioré fournit une excellente performance numérique. En effet, l'objectif final est d'utiliser les nouveaux éléments de poutre 3D pour modéliser des fils dans une préforme composite textile. A cet effet, la troisième étape consiste à introduire un comportement de contact et à effectuer la validation pour un nouveau contact entre 3D poutres à section rectangulaire. La formulation de contact est dérivée sur la base de formulation de pénalité et de formulation Lagrangian mise à jour utilisant des fonctions de forme physique avec l'effet de cisaillement inclus. Un algorithme de recherche de contact efficace, qui est nécessaire pour déterminer un ensemble actif pour le traitement de contribution de contact, est élaboré. Et une linéarisation constante de la contribution de contact est dérivée et exprimée sous forme de matrice appropriée, qui est facile à utiliser dans l'approximation FEM. Enfin, on présente quelques exemples numériques qui ne sont que des analyses qualitatives du contact et de la vérification de l'exactitude et de l'efficacité de l'élément de 3D poutre proposé<br>The new beam element is an evolution of a two nodes Timoshenko beam element with an extra node located at mid-length. That extra node allows the introduction of three extra strain components so that full 3D stress/strain constitutive relations can be used directly. The second step is to introduce the orthotropic behavior and carry out validation for large displacements/small strains based on Updated Lagrangian Formulation. A series of numerical analyses are carried out which shows that the enhanced 3D element provides an excellent numerical performance. Indeed, the final goal is to use the new 3D beam elements to model yarns in a textile composite preform. For this purpose, the third step is introducing contact behavior and carrying out validation for new 3D beam to beam contact with rectangular cross section. The contact formulation is derived on the basis of Penalty Formulation and Updated Lagrangian formulation using physical shape functions with shear effect included. An effective contact search algorithm is elaborated. And a consistent linearization of contact contribution is derived and expressed in suitable matrix form, which is easy to use in FEM approximation. Finally, some numerical examples are presented which are only qualitative analysis of contact and checking the correctness and the effectiveness of the proposed 3D beam element

This dissertation developed a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements. As a proof of concept, a joint 2D-beam approach is studied for planar-inplane deformation of strip-beams. This approach is developed for obtaining understanding needed to do the joint 3D-beam model. A Matlab code is developed to solve achieve this 2D-beam approach. For joint 2D-beam approach, the static response of a basic 2D-beam model is studied. The whole beam structure is divided into two parts. The root part where the boundary condition is applied is constructed as a 2D model. The free end part is constructed as a beam model. To assemble the two different dimensional model, a transformation matrix is used to achieve deflection continuity or load continuity at the interface. After the transformation matrix from deflection continuity or from load continuity is obtained, the 2D part and the beam part can be assembled together and solved as one linear system. For a joint 3D-beam approach, the static and dynamic response of a basic 3D-beam model is studied. A Fortran program is developed to achieve this 3D-beam approach. For the uniform beam constrained at the root end, similar to the joint 2D-beam analysis, the whole beam structure is divided into two parts. The root part where the boundary condition is applied is constructed as a 3D model. The free end part is constructed as a beam model. To assemble the two different dimensional models, the approach of load continuity at the interface is used to combine the 3D model with beam model. The load continuity at the interface is achieved by stress recovery using the variational-asymptotic method. The beam properties and warping functions required for stress recovery are obtained from VABS constitutive analysis. After the transformation matrix from load continuity is obtained, the 3D part and the beam part can be assembled together and solved as one linear system. For a non-uniform beam example, the whole structure is divided into several parts, where the root end and the non-uniform parts are constructed as 3D models and the uniform parts are constructed as beams. At all the interfaces, the load continuity is used to connect 3D model with beam model. Stress recovery using the variational-asymptotic method is used to achieve the load continuity at all interfaces. For each interface, there is a transformation matrix from load continuity. After we have all the transformation matrices, the 3D parts and the beam parts are assembled together and solved as one linear system.

The main purpose of this thesis is to develop a 3D beam element in order to model wind turbine wings made of composite materials. The proposed element is partly based on the formulation of the classical beam element of constant cross-section without shear deformation (Euler-Bernoulli) and including Saint-Venant torsional effects for isotropic materials, similarly to the one presented in Batoz &amp; Dhatt (1990, pp.147-190). The main novelty consists in the addition of the coupling between axial and bending with torsional effects that may arise when using composite materials. PreComp, a free access code developed by the National Renewable Energy Laboratory (NREL) to provide structural properties for composite blades, is used to obtain the section properties for the beam element. Its performance is assessed, showing its inaccuracy especially when calculating torsional related constants when webs are present in the cross-section. Shell models of constant cross-section cantilever blades are developed to assess the performance of the beam elements, including or not coupling terms. Natural frequencies and displacements under static loads are compared for different study cases of increasing complexity. For fiber-reinforced materials, elements with coupling terms show good agreement with the shell model, especially for the dynamic problem. Elements without coupling terms are unable to capture the dynamic behavior, as these terms seem to have a higher effect on the results when compared to the static case (especially the FT term).

Mid-rise to tall timber buildings are internationally gaining popularity. Reaching heights greater than 5 to 6 storeys has been made possible by the availability of engineered wood products, such as Laminated Veneer Lumber (LVL), Glued laminated timber (Glulam) and Cross Laminated Timber (CLT). These buildings are referred to as “mass timber buildings”. As the height of timber buildings increases, so do their potential risks of progressive collapse. Progressive collapse is characterised by a local failure of a load-bearing structural element which may propagate through the whole building, and ultimately causes its partial or entire collapse. While progressive collapse mechanisms of reinforced concrete and steel buildings have been widely researched, limited studies have been carried out on mass timber buildings. Their ability to resist progressive collapse and their load transfer mechanisms after the loss of a load-bearing element are currently unclear. First, to gain an initial understanding of the progressive collapse behaviour of post-and-beam mass timber buildings, a series of scaled-down 1×2-bay (2D) timber frame substructures were tested under a middle column removal scenario. The behaviour of the frames and the ability of three types of commercially used beam-to-column connections and a proposed novel connection, to develop catenary action under large deformations was measured. The system capacity in terms of the Uniformly Distributed Pressure (UDP) was also quantified. The test results showed that only the proposed novel connector was able to sustain the design pressure in international design specifications if no dynamic increase factor was considered, and therefore presented a potential solution to improve the robustness of post-and-beam mass timber buildings. Furthermore, progressive collapse of post-and-beam mass timber buildings cannot be resisted by the frame alone using the investigated currently used connections and alternative load paths must be found. Second to further explore the mechanisms of post-and-beam mass timber buildings against progressive collapse, four scaled-down 2×2-bay (3D) substructures, with CLT panels, were constructed and tested in the laboratory. Three substructures were tested under an edge column removal scenario, with substructures manufactured from two different types of beam-to-column connections. Namely, two tests were performed with a connection type commonly used in Australia, and one test with the proposed novel connection investigated earlier. The last substructure was subjected to two different corner column removal scenarios, with the substructure tested twice under different CLT panels configurations. The substructure was assembled from the commonly used in Australia beam-to-column connection. In all tests, two Uniformly Distributed Pressures (UDP) were applied to the floors in two stages: (i) a constant UDP of 4.8 kPa was first applied to the bays not adjacent to the removed column and (ii) an idealised UDP was then increasingly applied to the remaining bay(s) through a hydraulic jack connected to a six-point loading tree. The load redistribution mechanisms (alternative load paths), the structural response and failure modes were recorded. In general, experimental test results showed that the applied load was principally transferred to the three columns the closest to the removed column and that the CLT panels spanning over two bays were efficient in resisting the load. The layout of the CLT panels plays a critical role in resisting progressive collapse. A simplified analytical model, consistent with the current industry design practice and pre-defined alternative load paths, was used to predict the ultimate resistance capacity of the tested specimens and compared to the experimental capacities. Overall, the simplified methodology was found to be conservative. Third, finite element (FE) models were developed using the component model and validated against the 2D and 3D experimental results. The properties of the springs to be used in the component model were obtained from additional experimental component tests. CLT panels were simulated using layered shell elements while beam elements were used for the beams and columns. In the 2D numerical model, the ultimate load was accurately predicted and the development of compressive arch and catenary actions were well reproduced. The validated 2D model was then used to build the 3D model. For all tests, the 3D numerical models accurately predicted the overall load-displacement responses, load redistribution mechanisms, failure modes and strain developments in the beams and CLT panels. The validated numerical models were used to conduct a series of parametric studies to further examine the structural responses of the post-and-beam mass timber buildings. The results indicated that the structural capacity would be reduced when only using onebay long CLT panels, compared to using either staggered or all two-bay long CLT panels. Also, beam-to-column connections of the frames connected to the removed column could locally support the CLT panels above, providing an additional alternative load path for the structure in the context of progressive collapse, which is normally neglected in industry design practice.<br>Thesis (PhD Doctorate)<br>Doctor of Philosophy (PhD)<br>School of Eng & Built Env<br>Science, Environment, Engineering and Technology<br>Full Text

Utbredningen av en brand inuti en byggnad kan leda till global eller lokal strukturell kollaps, särskilt i stålramkonstruktioner. Faktum är att stålkonstruktioner är särskilt utsatta för termiska angrepp på grund av ett högt värde av stålkonduktivitet och tvärsnitten med små tjockleken. Som en viktig aspekt av konstruktionen bör brandsäkerhetskrav uppnås antingen enligt föreskrivande regler eller enligt antagande av prestationsbaserad brandteknik. Trots möjligheten att använda enkla metoder som involverar membersanalys kombinerat med nominella brandkurvor, är en mer exakt analys av det termomekaniska beteendet hos en stålkonstruktion ett tilltalande alternativ eftersom det kan leda till mer ekonomiska och effektiva lösningar genom att ta hänsyn till möjliga gynnsamma mekanismer. Denna analys kräver vanligtvis utredning av delar av strukturen eller till och med av hela strukturen. För detta ändamål och för att få en djupare kunskap om strukturelementens beteende vid förhöjd temperatur bör numerisk simulering användas. I denna avhandling utvecklades och användes termomekaniska finita element som är lämpliga för analys av stålkonstruktioner utsätta för brand. Relevanta fallstudier utfördes. Utvecklingen av både ett termomekaniskt skal- och 3D balkelement baserade på en korotationsformulering presenteras. De flesta relevanta strukturfall kan undersökas på ett adekvat sätt genom att antingen använda något av dessa element eller kombinera dem. Korotationsformuleringen är väl lämpad för analyser av strukturer där stora förskjutningar, men små töjningar förekommer, som i fallet med stålkonstruktioner i brand. Elementens huvuddrag beskrivs, liksom deras karakterisering i termomekaniskt sammanhang. I detta avseende övervägdes materialnedbrytningen på grund av temperaturökningen och den termiska expansionen av stål vid härledningen av elementen. Dessutom presenteras en grenväxlingsprocedur för att utföra preliminära instabilitetsanalyser och få viktig inblick i efterknäckningsbeteendet hos stålkonstruktioner som utsätts för brand. Tillämpningen av de utvecklade numeriska verktygen ges i den del av avhandlingen som ägnas åt det publicerade forskningsarbetet. Flera aspekter av knäckningen av stålkonstruktionselement vid förhöjd temperatur diskuteras. I Artikel I tillhandahålls överväganden om påverkan av geometriska imperfektioner på beteendet hos komprimerade stålplattor och kolonner vid förhöjda temperaturer, liksom implikationer och resultat av användningen av grenväxlingsprocedur. I Artikel II valideras det föreslagna 3D-balkelementet genom meningsfulla fallstudier där torsionsdeformationer är signifikanta. De utvecklade balk- och skalelementen används i en undersökning av knäckningsmotstånd hos komprimerade vinkel-, Tee- och korsformade stålprofiler vid förhöjd temperatur som presenteras i Artikel III. En förbättrad knäckningskurva för design presenteras i detta arbete. Som ett exempel på tillämpningen av principerna för brandsäkerhetsteknik presenteras en omfattande analys i Artikel IV. Två relevanta brandscenarier identifieras för den undersökta byggnaden, som modelleras och analyseras i programmet SAFIR.<br>The ignition and the propagation of a fire inside a building may lead to global or local structural collapse, especially in steel framed structures. Indeed, steel structures are particularly vulnerable to thermal attack because of a high value of steel conductivity and of the small thickness that characterise the cross-sections. As a crucial aspect of design, fire safety requirements should be achieved either following prescriptive rules or adopting performance-based fire engineering. Despite the possibility to employ simple methods that involve member analysis under nominal fire curves, a more accurate analysis of the thermomechanical behaviour of a steel structural system is an appealing alternative, as it may lead to more economical and efficient solutions by taking into account possible favourable mechanisms. This analysis typically requires the investigation of parts of the structure or even of the whole structure. For this purpose, and in order to gain a deeper knowledge about the behaviour of structural members at elevated temperature, numerical simulation should be employed. In this thesis, thermomechanical finite elements, suited for the analyses of steel structures in fire, were developed and exploited in numerical simulation of relevant case studies. The development of a shell and of a 3D beam thermomechanical finite element based on a corotational formulation is presented. Most of the relevant structural cases can be adequately investigated by either using one of these elements or combining them. The corotational formulation is well suited for the analyses of structures in which large displacements, but small strains occur, as in the case of steel structures in fire. The main features of the elements are described, as well as their characterization in the thermomechanical context. In this regard, the material degradation due to the temperature increase and the thermal expansion of steel were considered in the derivation of the elements. In addition, a branch-switching procedure to perform preliminary instability analyses and get important insight into the post-buckling behaviour of steel structures subjected to fire is presented. The application of the developed numerical tools is provided in the part of the thesis devoted to the published research work. Several aspects of the buckling of steel structural elements at elevated temperature are discussed. In paper I, considerations about the influence of geometrical imperfections on the behaviour of compressed steel plates and columns at elevated temperatures are provided, as well as implications and results of the employment of the branch-switching procedure. In Paper II, the proposed 3D beam element is validated for meaningful case studies, in which torsional deformations are significant. The developed beam and shell elements are employed in an investigation of buckling resistance of compressed angular, Tee and cruciform steel profiles at elevated temperature presented in Paper III. An improved buckling curve for design is presented in this work. Furthermore, as an example of the application of Fire Safety Engineering principles, a comprehensive analysis is proposed in Paper IV. Two relevant fire scenarios are identified for the investigated building, which is modelled and analysed in the software SAFIR.

<p>This report investigates the feasibility and accuracy of determining fastener flexibility with 3D FE and representing fasteners in FE load distribution models with simple elements such as springs or beams. A detailed study of 3D models compared to experimental data is followed by a parametric study of different shell modelling techniques. These are evaluated and compared with industry semi-empirical equations.</p><p>The evaluated 3D models were found to match the experimental values with good precision. Simulations based on these types of 3D models may replace experimental tests. Two different modelling techniques were also evaluated for use in load distribution models. Both were verified to work very well with representing fastener installations in lap-joints using the ABAQUS/Standard solver. Further improvement of one of the models was made through a modification scale factor. Finally, the same modelling technique was verified using the NASTRAN solver.</p><p>To summarize, it is concluded that:</p><p>• Detailed 3D-models with material properties defined from stress-strain curves correspond well to experiments and simulations may replace actual flexibility tests.</p><p>• At mid-surface modelling of the connecting parts, beam elements with a circular cross section as a connector between shell elements is an easy and accurate modelling technique, with the only data input of bolt material and dimension.</p><p>• Using connector elements is accurate only if the connecting parts are modelled in the same plane, i.e. with no offset. Secondary bending due to offset should only be accounted for once and only once throughout the analysis, and it is already included in the flexibility input.</p>

Les éléments de poutres classiques (Euler-Bernoulli, Timoshenko, Vlassov…), sont tous basés sur certaines hypothèses simplificatrices, qui ont pour conséquence de fixer la forme de la cinématique de l'élément. Ceci revient à réduire un modèle ayant par définition une infinité de d.d.l., à un modèle avec un nombre fini de d.d.l.. Quel que soit donc le chargement auquel sera soumise la poutre, elle se déformera toujours selon la cinématique adoptée au départ. L'objectif de cette thèse est de s'affranchir des hypothèses inhérentes aux modèles de poutres classiques, pour développer un nouveau modèle de poutre enrichie, capable de représenter d'une manière précise les déformations globales aussi bien que locales. Ce type d'élément, permettra la représentation de la flexion transversale dans une poutre, de capturer des effets locaux, produits par exemple par un câble d'ancrage ou de précontrainte sur un tablier de pont, ou encore de traiter le traînage de cisaillement sur des poutres à grandes largeurs. Après un bref rappel de quelques théories de poutres classiques, on présentera dans les deux premiers articles, une nouvelle méthode pour la détermination de modes transversaux et de gauchissements, basée sur une analyse aux valeurs propres d'un modèle mécanique de la section pour l'obtention de la base des modes transversaux, et un procédé d'équilibre itératif pour la détermination de la base des modes de gauchissements. La cinématique ainsi définie, le PTV sera utilisé pour obtenir les équations d'équilibre de la poutre, pour ensuite en déduire la matrice de raideur à partir de leur solution analytique. Dans le troisième article, une nouvelle méthode est proposée pour l'obtention d'une cinématique plus appropriée, où les bases des modes transversaux et de gauchissements sont obtenues en fonction des chargements extérieurs. Cette méthode est basée sur l'application de la méthode des développements asymptotiques à la résolution des équations fortes décrivant l'équilibre d'une poutre<br>The available classical beam elements (such as Euler-Bernoulli, Timoshenko, Vlassov…), are all based on some hypothesis, that have the effect of defining the kinematic of the beam. This is equivalent to reducing a model with an infinity of d.o.f., to a model with a finite d.o.f.. Thus, for arbitrary loadings, the beam will always deform according to the adopted kinematics. The objective of this thesis, is to completely overcome all the hypothesis behind the classical beam models, to develop a new higher order beam model, able to represent precisely the global and local deformations. This kind of element will also allow the derivation of the transversal bending of the beam, to capture the local effects due to anchor or prestressing cables, or to treat the shear lag phenomenon in large width spans. After a brief review of some classical beam theories, we will develop in the two first articles a new method to obtain a basis for the transverse deformation and warping modes. The method is based on an eigenvalue analysis of a mechanical model of the cross section, to obtain the transverse deformation modes basis, and an iterative equilibrium scheme, to obtain the warping modes basis. The kinematic being defined, the virtual work principle will be used to derive the equilibrium equations of the beam, then the stiffness matrix will be assembled from their analytical solution. In the third article, a new method is proposed for the derivation of a more appropriate kinematic, where the transverse deformation and warping modes are obtained in function of the external loadings. The method is based on the application of the asymptotic expansion method to the strong form of the equilibrium equations describing the beam equilibrium

L'objectif principal visé par cette thèse est de modéliser les poutres gonflables en textiles techniques orthotropes. Les approches statiques font l'objet de ce rapport. Avant d'aborder ce problème, nous avons été amenés à identifier tous les paramètres qui ont un effet direct sur les propriétés mécaniques effectives de ces composites. Ainsi, nous avons développé un modèle micro mécanique de prédiction de ces propriétés mécaniques. Le modèle proposé est basé sur l’analyse d'un volume élémentaire représentatif (VER) prenant en compte non seulement les propriétés mécaniques et la. fraction de volume de chaque phase dans le VER mais également leur géométrie et leur architecture. Chaque fil dans le VER a été modélisé comme un matériau isotrope transverse (contenant les fibres et la résine). La méthode dite d’assemblage de cylindres a été utilisée pour l’homogénéisation au niveau des fils. Une deuxième homogénéisation est ensuite réalisée. Elle prend en compte la fraction de volume de chaque constituant (fils de chaîne, fils de trame et résine non prise en compte dans les fils). Le modèle a été validé par des résultats expérimentaux existant dans la littérature. Une élude paramétrique a été menée afin d'étudier les effets des divers paramètres géométriques et mécaniques sur ces propriétés mécaniques. Dans l'analyse structurale, un modèle poutre gonflable 3D de Timoshenko en tissu orthotrope a été proposé. Il prend en compte les non-linéarités géométriques et l'effet de la force suiveuse générée par la pression de gonflage. Les équations d'équilibre non-linéaires dérivent du principe des travaux virtuels en configuration lagrangienne totale. Dans une première approche, une linéarisation a été faite autour de la configuration de référence précontrainte pour obtenir les équations adaptées aux problèmes linéaires. A titre d'exemple, le problème de flexion plane a été abordé. Quatre cas de conditions aux limites ont été traités et les résultats obtenus améliorent les modèles existants dans le cas de tissu isotrope. Les charges de plissage ont été également proposées dans chaque cas traité. Dans une deuxième approche, les équations non-linéaires ont été discrétisées par la méthode des éléments finis. Deux types de solutions ont été alors proposées : les solutions aux problèmes éléments finis linéaires obtenues par une linéarisation des équations discrétisées autour de la configuration de référence précontrainte et les solutions aux problèmes éléments finis non-linéaires réalisées en adoptant une méthode Quasi-Newton sous sa forme incrémentale. A titre d’exemple, la flexion d’une poutre encastrée-libre a été étudiée et les résultats améliorent les modèles théoriques. Le modèle éléments finis non-linéaire a été comparé favorablement à un modèle éléments finis coque mince 3D. Une étude paramétrique a été ensuite effectuée. Elle a porté sur l'influence des propriétés mécaniques et sur de la pression de gonflage sur la réponse de la poutre. Les solutions éléments finis linéaires se sont avérées proches des résultats théoriques linéarisés d'une part et les résultats du modèle éléments finis non-linéaire se sont avérés proches des résultats du modèle linéaire dans le cas des propriétés mécaniques élevées alors que le modèle éléments finis non-linéaire est indispensable pour modéliser ces poutres lorsque les propriétés mécaniques du tissu sont faibles<br>The main objective of this thesis was to model inflatable beams made frorn orthotropic woven fabric composites. The static aspects were investigated in this report. Before planning to develop these models, it was necessary to know all the parameters which have a direct effect on the effective mechanical properties these composites. Thus, a micro­ mechanical model was performed for predicting the effective mechanical properties. The proposed model was based on the analysis of the representative volume element (RVE). The model took into account not only the mechanical properties and volume fraction of each components in the RVE but also their geometry and architecture. Each yarn in the RVE was modelled as a transversely isotropic material (containing fibres and resin) using the concentric cylinders model (CCIVI). A second volumetric averaging which took into account the volume fraction of each constituent (warp yarn, weft yarn and resin), was performed. The model was validated favorably against experimental available data. A parametric study was conducted in order to investigate the effects of various geometrical and mechanical parameters on the elastic properties of these composites. ln the structural analysis, a 3D Timoshenko airbeam with a homogeneous orthotropic woven fabric (OWF) was addressed. The model took into account the geometrical nonlinearities and the inflation pressure follower force effect. The analytical equilibrium equations were performed using the total Lagrangian form of the virtual work principle. As these equations were nonlinear, in a first approach, a linearization was performed at the prestressed reference configuration to obtain the equations devoted to linearized problems. As example, the bending problem was investigated. Four cases of boundary conditions were treated and the deflections and rotations results improved the existing models in the case of isotropic fabric. The wrinkling load in every case was also proposed. In a second approach, the nonlinear equilibrium equations of the 3DTimoshenko airbeam were discretized by the finite element method. Two finite element solutions were then investigated : finite element solutions for linearized problems which were obtained by the means of the linearization around the prestressed reference configuration of the nonlinear equations and nonlinear finite element solutions which were performed by the use of an optimization algorithm based on the Qua.si-Newton method. As an example, the bending problem of a cantilever inflated beam under concentrated load was considered and the deflection results improve the theoretical models. As these beams are made from fabric, the beam models were validated through their comparison with a 3D thin-shell finite element model. The influence of the material effective properties and the inflation pressure on the beam response was also investigated through a parametric study. The finite element solutions for linearized problems were found to be close to the theoretical linearized results. On the other hand, the results for the nonlinear finite element model were shown to be close to the results for the linearized finite element model in the case of high mechanical properties and the non linear finite element model was used to improve the linearized model when the mechanical properties of the fabric are low

This paper is intended to present wavelet Galerkin schemes for the boundary element method. Wavelet Galerkin schemes employ appropriate wavelet bases for the discretization of boundary integral operators. This yields quasisparse system matrices which can be compressed to O(N_J) relevant matrix entries without compromising the accuracy of the underlying Galerkin scheme. Herein, O(N_J) denotes the number of unknowns. The assembly of the compressed system matrix can be performed in O(N_J) operations. Therefore, we arrive at an algorithm which solves boundary integral equations within optimal complexity. By numerical experiments we provide results which corroborate the theory.

La presente tesi tratta dello studio di concetti volti all'ottenimento di strutture meccaniche a rigidezza variabile per applicazioni in ambito di ricerca scientifica, in particolare per una futura applicazione in un robot aereo ad ala battente, al fine di studiare l'interazione tra ala elastica ed aria. Vengono riassunti i metodi per ottenere rigidezza variabile ed, in seguito ad una fase di confronto basato su requisiti ed obiettivi di progetto, vengono scelte due soluzioni. Il lavoro mostra che il concetto "sliding segments" funziona bene per una trave composta da un'asta interna ed un tubo esterno, entrambi formati da segmenti rigidi e flessibili alternati, di due materiali differenti. La rigidezza flessionale della trave varia grazie ad una traslazione dell'asta interna. Viene inoltre mostrato come un'asta ed un tubo possono essere combinati per ottenere una trave rotante con diversi livelli di rigidezza flessionale in una direzione, riducendo gli effetti della flessione deviata.

Les poutres à parois minces à sections ouvertes sont des éléments de base des ouvrages courants en génie civil, de l'automobile et de l'aéronautique. En raison de leur élancement et la forme des sections, elles sont très sensibles à la torsion et aux instabilités aussi bien en statique qu’en dynamique. En dynamique, les modes de vibration en torsion sont plus dominants par rapport au modes de flexion classiques. Pour ces raisons, les défaillances planaires de telles structures sont connues pour être une exception plutôt qu'une règle. Dans ce travail de thèse, on s’intéresse au comportement dynamique de poutres à parois minces et à section ouvertes arbitraires. En se basant sur le modèle de Vlasov qui prend en compte de la torsion et du gauchissement, les équations de mouvement 3D sont dérivées à partir du principe d’Hamilton. Des solutions analytiques originales pour différentes conditions aux limites sont dérivées pour des modes supérieurs en vibrations libres. Dans ces solutions, les effets des termes de rotation inertiels en flexion et torsion sont pris en compte. Pour des cas généraux, un modèle élément fini de poutre 3D est décrit et implémenté. Dans le modèle, un degré de liberté (ddl) est affecté au gauchissement. Toutes les matrices de rigidité masse de base sont calculées par intégration numérique (intégration de Gauss). Dans le modèle, les calculs en vibrations libres et forcées sont possibles. Le modèle est validé par comparaison aux solutions numériques et expérimentaux de la littérature. Une comparaison aux simulations des codes commerciaux est aussi suivie. Afin de valider le modèle théorique et numérique utilisé, une campagne d’essais a été suivie au LEM3 à Metz. Des essais de vibration libre et forcée sont effectués sur des poutres à parois minces avec différentes conditions aux limites. Les solutions analytiques, numériques et les mesures expérimentales sont comparées et validées. Un bon accord entre les différentes solutions est constaté. Le modèle est étendu aux poutres 3D retenues latéralement par des entretoises. Des ressorts élastiques et visqueux 3D sont ajoutés dans le modèle numérique. L'effet des entretoises est étudié dans le but d’améliorer le comportement des poutres à parois minces vis-à-vis des modes indésirables de type flexion latérale et torsion<br>Thin-walled beams with open section constitute main elements in engineering applications fields as in civil engineering, automotive and aerospace construction. Due to slenderness and cross section shapes, these elements are very sensitive to torsion and instabilities in both statics and dynamics. In dynamics, the torsional and flexural-torsional modes of vibration are often lower frequencies compared to the classical plane pure bending modes. Thus, planar failures of such structures are known to be an exception rather than a rule. In torsion, warping is important and governs the behavior. In this thesis work, we are interested with the dynamic behavior of thin-walled beams with arbitrary open cross sections. Based on the Vlasov’s model accounting for warping, the 3D motion equations are derived from the Hamilton’s principle. Original analytical solutions for different boundary conditions are derived for higher free vibration modes. In these solutions, the effects of the inertial rotation terms in bending and torsion are taken into consideration. For more general cases, a 3D beam finite element model is described and implemented. Compared to conventional 3D beams, warping is considered as an additional Degree Of Freedom (DOF). The mass and stiffness matrices are obtained by numerical integration (Gauss method). In the model, free and forced vibration analyses are possible. The model is validated by comparison with benchmark solutions available in the literature and other numerical results obtained from simulation on commercial codes. In order to validate the present model, laboratory test campaign is undertaken at the LEM3 laboratory in Metz. Tests are carried out on thin-walled beams with different boundary conditions. Free and forced vibration tests are performed using impact hammer and shaker machine. In the presence of arbitrary sections, flexural-torsional vibration modes are observed. The analytical, the numerical and the experimental solutions are compared and validated. Moreover, the numerical and experimental dynamic response spectra are compared. A good agreement between the various solutions is remarked. The model is extended to 3D beams in presence of lateral braces. 3D elastic and viscous springs are added in the finite element model. The effect of the springs is studied in order to improve the behavior of thin-walled beams against undesirable lateral bending and torsion modes

In Printed Circuit Board (PCB) manufacturing. making the conductive tracks 3D and embedding the electronic components in substrate can effectively reduce the circuit board volume, and improve the power delivery performance. Laser based additive manufacturing has been developed for many years but currently it is still used to create non-functional product. This PhD work will combine the two technologies together to generate a complete 3D embedded circuit system. hi addition. the laser beam will be reconstructed using Holographic Optical Elements (HOE) to control the microstructure of the product.

O presente trabalho tem como objetivo desenvolver um processo de fabricação de elementos micro-ópticos utilizando-se litografia por feixe de elétrons, empregando o resiste SU-8, negativo e amplificado quimicamente, sobre substrato de Si. Para tanto, é realizado o estudo dos parâmetros do efeito de proximidade a, b e h para se modelar e controlar os efeitos do espalhamento dos elétrons no resiste e no substrato, e se altera o processamento convencional do SU-8 para se obter um processo com baixo contraste. A determinação dos parâmetros do efeito de proximidade para o sistema de escrita direta e amostra SU-8 / Si é feita experimentalmente e por simulação de Monte Carlo. Particularmente, verifica-se a dependência dos mesmos com a profundidade do resiste. Primeiramente utilizando o software PROXY, obtêm-se a, b e h da observação de padrões de teste revelados. Chega-se a 4m para o parâmetro () que mede o retroespalhamento dos elétrons pelo substrato e 0,7 para a relação (h) entre a intensidade destes com aquela dos elétrons diretamente espalhados pelo resiste (alcance dado por a). Ainda, com esses dados, estima-se o diâmetro do feixe do microscópio eletrônico de varredura a partir da equação de aproximação de espalhamento direto para pequenos ângulos (a = 128nm na superfície do resiste) e se determina a resolução lateral do processo (a = 800nm na interface resiste/ substrato, para um filme de 2,4m). Em seguida, usa-se o software CASINO para se calcular os parâmetros de proximidade a partir da curva de densidade de energia dissipada no resiste obtida pela simulação da trajetória de espalhamento dos elétrons. Confrontam-se, finalmente, os valores obtidos pelos dois métodos. Em relação ao processamento do resiste SU-8, são determinadas as condições experimentais para a fabricação de estruturas tridimensionais por litografia de feixe de elétrons. Especificamente, busca-se desenvolver um processo com características (espessura, contraste, sensibilidade e rugosidade) adequadas para a fabricação de micro-dispositivos ópticos. Inicia-se com o levantamento das curvas de contraste e da sensibilidade do SU-8 para determinadas temperaturas de aquecimento pós-exposição. Obtém-se contraste abaixo de 1 para aquecimento pós-exposição abaixo da temperatura de transição vítrea do resiste, mantendo-se sensibilidade elevada (2C/cm2). Em seguida, mede-se a rugosidade da superfície do filme revelado para diferentes doses de exposição. Para finalizar, submete-se a amostra a um processo de cura e escoamento térmico, para melhorar a dureza e a rugosidade do resiste a ser utilizado como dispositivo final Consegue-se um valor de rugosidade (40nm) inferior a 20 vezes o comprimento de onda de diodo laser de eletrônica de consumo. Por fim, é produzido um dispositivo com perfil discretizado em 16 níveis como prova de conceito.<br>This work aims at developing an electron-beam lithography process for the fabrication of microoptical elements using the negative tone chemically amplified resist SU-8 on Si substrate. A study of the proximity effect parameters a, b and h is carried out to model and control the electron scattering both in the resist and in the substrate, and the SU-8 standard processing conditions are changed to achieve a low contrast process. The determination of the SU-8 / Si proximity effect parameters and its dependence with resist depth is done employing an experimental method and through Monte Carlo simulations. First, a, b and h are obtained comparing exposed patterns calculated by the software PROXY. b, the parameter which measures the backscattering of the electrons by the substrate, is equal to 4m and the value of h, the ratio of the dose contribution of backscattered electrons to that of the forward scattered (related to a), is 0.7. The extrapolation of exposed patterns data is used to estimate the scanning electron microscope beam diameter through the equation for low angle scattering (a = 128nm at the resist surface) and the lateral resolution of the process is determined (a = 800nm at the resist/ substrate interface, for a 2.4m film). With aid of the software CASINO, Monte Carlo simulations of the scattering trajectories of electrons in substrate and resist materials are calculated, recording the energy that they dissipate through collisions along their path. The results obtained representing the profile of the energy dissipated in the resist are used to determine the proximity effect parameters. The experimental method results are compared to that obtained by simulation. Regarding the SU-8 processing, the process parameters for the fabrication of three-dimensional structures by electron-beam lithography are determined. The process is designed to have specifications (thickness, contrast, sensitivity and surface roughness) suitable for microoptical elements fabrication. It begins with the determination of the SU-8 contrast curve and its sensitivity for specific post-exposure bake temperatures. A below the unit contrast process with high sensitivity (2C/cm2) is achieved postannealing the sample below the resist glass transition temperature. The film surface roughness is measured after resist development for different exposure doses, and a controlled hardbake (cure) and reflow is carried to enhance both the mechanical properties and the surface roughness of the structures that will remain as part of the final device. A RMS roughness of 40nm, lower than 20 times the wavelength of consumer electronics laser diode, is obtained. The electron-beam process designed is applied to the fabrication of a microelement with a 16-level profile discretization.

Humanitarian clearance of minefields is most often carried out by hand, conventionally using a a metal detector and a probe. Detection is a very slow process, as every piece of detected metal must treated as if it were a landmine and carefully probed and excavated, while many of them are not. The process can be safely sped up by use of Ground-Penetrating Radar (GPR) to image the subsurface, to verify metal detection results and safely ignore any objects which could not possibly be a landmine. In this thesis, we explore the possibility of using Full Wave Inversion (FWI) to improve GPR imaging for landmine detection. Posing the imaging task as FWI means solving the large-scale, non-linear and ill-posed optimisation problem of determining the physical parameters of the subsurface (such as electrical permittivity) which would best reproduce the data. This thesis begins by giving an overview of all the mathematical and implementational aspects of FWI, so as to provide an informative text for both mathematicians (perhaps already familiar with other inverse problems) wanting to contribute to the mine detection problem, as well as a wider engineering audience (perhaps already working on GPR or mine detection) interested in the mathematical study of inverse problems and FWI.We present the first numerical 3D FWI results for GPR, and consider only surface measurements from small-scale arrays as these are suitable for our application. The FWI problem requires an accurate forward model to simulate GPR data, for which we use a hybrid finite-element boundary-integral solver utilising first order curl-conforming N\'d\'{e}lec (edge) elements. We present a novel `line search' type algorithm which prioritises inversion of some target parameters in a region of interest (ROI), with the update outside of the area defined implicitly as a function of the target parameters. This is particularly applicable to the mine detection problem, in which we wish to know more about some detected metallic objects, but are not interested in the surrounding medium. We may need to resolve the surrounding area though, in order to account for the target being obscured and multiple scattering in a highly cluttered subsurface. We focus particularly on spatial sensitivity of the inverse problem, using both a singular value decomposition to analyse the Jacobian matrix, as well as an asymptotic expansion involving polarization tensors describing the perturbation of electric field due to small objects. The latter allows us to extend the current theory of sensitivity in for acoustic FWI, based on the Born approximation, to better understand how polarization plays a role in the 3D electromagnetic inverse problem. Based on this asymptotic approximation, we derive a novel approximation to the diagonals of the Hessian matrix which can be used to pre-condition the GPR FWI problem.

碩士<br>國立成功大學<br>土木工程學系<br>89<br>The main purpose of this study is to develop a three-dimensional nonlinear beam element for the NSP program. The NSP program is a general purpose nonlinear finite element software for static and dynamic analyses of structures. The concept behind the program has been developed at the National Cheng-Kung University for a project from the National Science Council. In this report, extensions made to the NSP are described. And all the extensions are included in a subroutine, vbeam.for, of the NSP program. This subroutine mainly deals with the biaxial moment interaction and the loading behavior of beam-column elements. It can help NSP to analyze three-dimension inelastic structures subjected to earthquake motions.

碩士<br>國立成功大學<br>土木工程學系碩博士班<br>90<br>The main purpose of this study is to improve the 3D beam element formulations for the NSP program and design the membrane element to simulate shear walls and floor slabs for modeling the inelastic behavior of reinforced concrete (RC) structures. The NSP program is a general purpose nonlinear finite element software for static and dynamic analyses of structures. In this report, all improvements were included in a subroutine, nbeam.for. It simplifies the input data of the 3D beam and adds the shear force yielding surface and elastic loading-unloading behavior. For three-dimensional (3D) building analyses, floor slabs are often assumed to be rigid in their planes. This assumption was demonstrated to be adequate for buildings without shear walls. However, it can cause errors for buildings with shear walls. Most of the above conclusion was obtained from the linear-elastic analysis. Thus, analyzing the behavior of buildings using inelastic structural analyses is necessary. Therefore, comparing the difference between inelastic rigid-floor and flexible-floor structural analysis was investigated in this study.

碩士<br>國立臺北科技大學<br>土木與防災技術研究所<br>92<br>Now, the key point of the civil engineering is the strengthening of reinforced concrete structures. In the developed countries, every kind of materials is used in the strengthening of reinforced concrete structures, actively. The strengthening of external steel plates is the most common way. The bond of interface between the reinforced concrete structures and external steel plates is three-dimension of the thin elements, and there is not the analytic solution of three-dimension stresses after strengthening now. Therefore, the key point of this study is the finite element analysis of three-dimension stress of the bond. The program of the nonlinearing finite element analysis － ANSYS－ is used to analyze, and set proper model of the material by the different elements such as the reinforcing, the concrete, the bond, and the steel plate, and the arc-length method is used to analyze the nonlinear problem. Then, they are discussed that the form of the fissure in the conditions of the no strengthening, the wings, or the jacket, the conditions of stresses, sliding, and debonding of the bonds. 　　The results of the tests （Wen-Shan Lin，2001） can be verified from this analytic results, the way of the jacket is the best way of strengthening. Some bonds fell off at the interface of the external steel plates, but the reinforced concrete beam still supply to decrease the failed velocity. In the analysis of ANSYS program, the analytic results of the bonds can be discussed, the mechanical behavior of the reinforced concrete beam that the force applied can be simulated, and these can supply to determine preliminary for engineers.

碩士<br>國立臺北科技大學<br>土木與防災研究所<br>94<br>Now, the key point of the civil engineering is the strengthening of reinforced concrete structures. In the developed countries, every kind of materials is used in the strengthening of reinforced concrete structures, actively. The strengthening of Glass Fiber Reinforcement Plastics is the most common way. The key point of this study is the finite element analysis of three-dimension stress of the bond. The goal of the present research is to analyze and predict the behavior and failure mechanism of reinforced concrete beams and use the nonlinear finite element program-ANSYS.Also, the present research discusses the effect of element type, material parameters, meshing density, and retrofitted type used in the analysis on stiffness and ultimate load capacity. And the arc-length method is used to analyze the nonlinear problem. Then, they are discussed that the form of the fissure in the conditions of the no strengthening, or the jacket, the conditions of stresses, sliding, and debonding of the bonds. The results of the tests can be verified from this analytic results, but the reinforced concrete beam still supply to decrease the failed velocity. In the analysis of ANSYS program, the analytic results can be discussed, the mechanical behavior of the reinforced concrete beam that the force applied can be simulated, and these can supply to determine preliminary for engineers.

In many engineering structures, the effects of shear and torsional loads are an important aspect of both the analysis and the design process. These effects are usually neglected in typical framed structures. However, in some relevant cases, such as bridges, shear walls or thin-walled frames, it is essential to account for the shear and torsional loads and their interaction with the other loading conditions to correctly reproduce the structural response. In this framework, the main task is to accurately describe the nonlinear structural response in terms of global behavior and local stress-strain distributions, reproducing the coupling of the stress components and its influence on the global response. This results even more important in large scale structures made of cementitious and/or innovative composite materials, widely adopted in nowadays professional practice. Indeed, these structures usually show degrading mechanisms and softening behavior. Hence, they require sophisticated computational models and ad hoc analysis strategies to predict the structure capacity under severe loading conditions. A standard approach to analyze these structures is the adoption of beam-column finite element (FE) models, which are often preferred with respect to two-dimensional (2D) plate/shell or three-dimensional (3D) FEs, because of their efficiency and low computational cost. However, most beam-column FE formulations are based on theclassical Euler-Bernoulli or Timoshenko theory, assuming the cross-sections to remain plane during the loading process. This assumption requires specific corrective measures, when the shear and torsion and the related warping effects are pronounced. This work discusses the simulation of RC members with a 3D 2-node beam FE that includes warping effects. The FE formulation in [1] is extended to allow the description of structural members with softening material behavior. The governing equations are derived from a four-field Hu-Washizu variational principle, with independent interpolation of the warping displacement field from the rigid section displacements, the generalized section deformations and the material stress fields. In particular, the warping of the cross-section is described by interpolating the out-of-plane displacement with the addition of a variable number of local degrees of freedom to those commonly used for the beam FE. The global nonlinear response and the local distributions of strains and stresses are described introducing a fiber cross-section discretization. Hence, the coupling of axial, flexural, shear and torsional effects in terms of material response is automatically taken into account. Focusing on RC structures, the damaging mechanisms of the concrete material is described by adopting a new 3D nonlinear constitutive relationship with plasticity and damage. This is an enhanced version of that proposed in [2] and introduces the description of the unilateral effects typically appearing in concrete-like materials, due to the crack opening and closure. A Drucker-Prager type plastic model is coupled with a two-parameter isotropic damage model, where two scalar variables are used to describe the damage in tension and compression, respectively. The localization problems and the related mesh-dependency, due to the softening material behavior, are controlled through a regularization technique based on a properly modified nonlocal integral procedure. For beam-column FEs, the nonlocal strain measures are evaluated performing the integration of the local generalized section deformations along the element axis, whereas for 2D FEs the nonlocal integration is performed considering the generalized membrane/plate deformations. The proposed model is implemented and validated through some correlation studies. These consider the numerical analysis of a series of plain concrete and RC beams subjected to torsional loads and of two RC shear walls. The results are compared with experimental measurements and with those of standard FE beam models.

Three 3D nonlinear finite-element (FE) models are developed to study the behavior of concrete beams and plates with and without externally reinforcement of fibre reinforced polymer (FRP). Ramtekkar’s mixed layer-wise 3 dimensional (3D) 18-node FE model (108 degrees-of-freedom, DOFs) is modified to accommodate the nonlinear concrete and elasto-plastic steel behaviour. Saenz’s stress-strain equation is used for material nonlinearity of concrete. As in any 3D mixed FE analysis, the run time using the model can be computationally expensive. Two additional layer-wise 18-node FE models: Displacement FE model (54 DOF) and transitional FE model (81 DOF) are developed. The displacement FE model is based on purely displacement field, i.e. only displacement components are enforced throughout the thickness of the structures. The transitional FE model has six DOF (three displacement components in the coordinate axis direction and three transverse stress components - where z is the thickness direction) per node in the upper surface and only three DOF (three displacement components in the coordinate axis direction) per node in the bottom surface.The analysis of reinforced concrete (RC) beam strengthened with FRP and composite plate using these models are verified against the experimental results and the results from the commercial software, ANSYS respectively. Several parametric studies are done on composite RC beam and composite plate.<br>May 2006

This work was supported by Fundação para a Ciência e a Tecnologia, through the scholarship SFRH/BD/35821/2007<br>Tese de doutoramento. Engenharia Mecânica. Faculdade de Engenharia. Universidade do Porto. 2012

This work was supported by Fundação para a Ciência e a Tecnologia, through the scholarship SFRH/BD/35821/2007<br>Tese de doutoramento. Engenharia Mecânica. Faculdade de Engenharia. Universidade do Porto. 2012

Tese de Doutoramento em Engenharia Civil, no ramo de Construções, apresentada ao Departamento de Engenharia Civil da Faculdade de Ciências e Tecnologia da Universidade de Coimbra<br>Os difusores acústicos são correntemente utilizados no condicionamento acústico de espaços com maiores exigências acústicas (estúdios, salas de espectáculos, etc.), servindo, sobretudo, para garantir uma acústica adequada, sem absorções excessivas e espalhando o som mais uniformemente pela sala, eliminando ao mesmo tempo defeitos acústicos como ecos ou zonas sombra. Apesar da optimização de difusores ser um tema de pesquisa intensa nos últimos anos, grande parte dos difusores existentes no mercado ainda correspondem a soluções do tipo Schröeder, QRD ou MLS, ou derivadas dessas, com geometrias angulosas, baseados em sub-elementos paralelepipédicos e associados numa dada sequência numérica mas cujo aspecto muitas vezes não é do agrado dos arquitectos. Deste modo, o principal objectivo deste trabalho é apresentar uma metodologia de desenvolvimento de superfícies mais orgânicas (i.e., curvilíneas), que potencialmente sejam esteticamente mais apreciadas e melhor aceites e que estejam optimizadas para dispersar uniformemente o som nelas incidente. Assim, neste documento demonstra-se a possibilidade de desenvolver soluções inovadoras de difusores acústicos com desempenho acústico maximizado, cuja forma é gerada pelo uso de funções de base radial (RBF) e que são baseadas nas mais modernas técnicas de modelação numérica, alicerçadas no método dos elementos de fronteira (BEM) e de optimização (Algoritmos Genéticos). Embora já existam algumas metodologias de desenvolvimento, modelação e optimização de difusores, julga-se que a metodologia proposta, bem como as ferramentas desenvolvidas baseadas no método dos elementos de fronteira, complementadas por algoritmos genéticos para a optimização, possam contribuir para o surgimento de novos produtos no mercado.<br>Acoustic diffusers are commonly used in acoustic conditioning of spaces with higher acoustic requirements (studio control rooms, concert halls, theaters, etc.), acting mainly to ensure proper acoustics without excessive absorption, by scattering the sound evenly around the room and eliminating acoustic defects, such as echoes or shadow zones. Most of the existing diffuser solutions presently available in the market correspond to Schröeder QRD, PRD or MLS diffusers, with sharp geometries and based on rectangular wells or sub-elements determined by a given numeric sequence and whose appearance is often not appreciated by architects. Therefore, the main objective of this work is to present a methodology for the development of more organic surfaces (i.e., curvilinear), which are potentially more aesthetically pleasing and better accepted and which are optimized to uniformly disperse the sound impinging them. Thus, this work demonstrates the possibility of developing innovative solutions of acoustic diffusers with maximized acoustic performance, whose shape is generated by the use of radial-based functions (RBF) and which are based on the most modern numerical modeling techniques such as the Boundary Element Method (BEM) and Genetic Algorithms for optimization. Although there are some already developed methodologies, modeling and optimization of diffusers, it is believed that the proposed methodology and the tools to be implemented (including the Boundary Elements Method, associated with recent techniques, complemented by genetic algorithms for optimization) can contribute to the emergence of new products on the market.

Realistic and real-time computational simulation of biological organs (e.g., human kidneys, human liver) is a necessity when one tries to build a quality surgical simulator that can simulate surgical procedures involving these organs. Currently deformable models, spring-mass models, or finite element models are widely used to achieve the realistic simulations and/or the real-time performance. It is widely agreed that continuum mechanics based numerical techniques are preferred over deformable models or spring-mass models, but those techniques are computationally expensive and hence the higher accuracy offered by those numerical techniques come at the expense of speed. Hence there is a need to study the speed of different numerical techniques, while keeping an eye on the accuracy offered by those numerical techniques. Such studies are available for the Finite Element Method (FEM) but rarely available for the Boundary Element Method (BEM). Hence the present work aims to conduct a study on the viability of BEM for the real-time simulation of biological organs, and the present study is justified by the fact that BEM is considered to be inherently efficient when compared to mesh based techniques like FEM. A significant portion of literature on the real-time simulation of biological organs suggests the use of BEM to achieve better simulations. When one talks about the simulation of biological organs, one needs to have the geometry of a biological organ in hand. Geometry of biological organs of interest is not readily available many a times, and hence there is a need to extract the three dimensional (3D) geometry of biological organs from a stack of two dimensional (2D) scanned images. Software packages that can readily reconstruct 3D geometry of biological organs from 2D images are expensive. Hence, a novel procedure that requires only a few free software packages to obtain the geometry of biological organs from 2D image sequences is presented. The geometry of a pig liver is extracted from CT scan images for illustration purpose. Next, the three dimensional geometry of human kidney (left and right kidneys of male, and left and right kidneys of female) is obtained from the Visible Human Dataset (VHD). The novel procedure presented in this work can be used to obtain patient specific organ geometry from patient specific images, without requiring any of the many commercial software packages that can readily do the job. To carry out studies on the speed and accuracy of BEM, a source code for BEM is needed. Since the BEM code for 3D elasticity is not readily available, a BEM code that can solve 3D linear elastostatic problems without accounting for body forces is developed from scratch. The code comes in three varieties: a MATLAB version, a Fortran version (sequential version), and a Fortran version (parallelized version). This is the first free and open source BEM code for 3D elasticity. The developed code is used to carry out studies on the viability of BEM for the real-time simulation of biological organs, and a few representative problems involving kidneys and liver are found to give accurate solutions. The present work demonstrates that it is possible to simulate linear elastostatic behaviour in real-time using BEM without resorting to any type of precomputations, on a computer cluster by fully parallelizing the simulations and by performing simulations on different number of processors and for different block sizes. Since it is possible to get a complete solution in real-time, there is no need to separately prove that every type of cutting, suturing etc. can be simulated in real-time. Future work could involve incorporating nonlinearities into the simulations. Finally, a BEM based simulator may be built, after taking into account details like rendering.