Nos travaux se positionnent dans le cadre de l'algorithmique distribuée et plus particulièrement des réseaux ad hoc. Les réseaux ad hoc sont auto-organisés en permettant des échanges directs entre nœuds mobiles et ne reposent sur aucune infrastructure. Chaque nœud peut se déplacer librement et indépendamment des autres impliquant une modification perpétuelle de la topologie. Dans ce contexte, la probabilité que des défaillances surviennent dans le réseau est importante. Ces défaillances gênent le bon fonctionnement du réseau et peuvent même entrainer une paralysie de celui-ci. C'est pourquoi la conception de solutions pour de tels réseaux nécessitent des mécanismes de gestion de fautes. Parmi ceux-ci, l'approche d'auto-stabilisation permet à un système de gérer les fautes transitoires. Nous étendons cette approche pour répondre aux principaux problèmes liés à la mobilité des nœuds. Notre objectif est de répondre à un double besoin d'auto-organisation du réseau et d'optimisation du nombre de messages échangés. Notre approche consiste à découper le réseau en clusters afin de lui donner une structure hiérarchique. Cette dernière rend l'utilisation du réseau plus efficace et plus performante. L'algorithme que nous avons développé à cet effet est auto-stabilisant et n'est basé que sur des connaissances locales. Nous exploitons cette solution pour proposer deux utilisations efficaces : la diffusion d'informations dans le réseau et le routage. La diffusion d'informations exploite un arbre couvrant inter-clusters, construit sans surcoût, en parallèle de la clusterisation. Le routage quant à lui exploite cet arbre pour permettre à la fois d'optimiser le délai de bout en bout et le nombre de messages échangés. / Our work relies in the domain of distributed system, more preciselly ad hoc networks. Ad hoc networks are self-organized allowing direct exchanges between mobile nodes and do not rely on any infrastruture. Each node can move freely and independently of each others involving continuous topology variability. In this context, the probability that a failure occurs in the network is high. These failures hinder the proper functioning of the network and even causes its paralysis. Therefore, designing solutions for such networks requires fault management mechanisms. Among these, a self-stabilizating approach allows the system to withstand transient faults. We extend this approach to answer the problems induced by nodes mobility. We have two main objectives: a self-organizing network and optimizing number of exchanged messages. Our approach consists in dividing the network into clusters in order to give it a hierarchical structure. This solution allows a more efficient and effective network use. The algorithm that we developed for this purpose is a self-stabilizing algorithm based only on local informations. Based on this solution, we propose two efficient use cases: Information broadcast and a routing protocol. Information broadcast uses an inter-cluster spanning tree, generated without any overhead. In the same time as the clustering process. The routing protocol uses this tree for both round trip and number of exchanged messages optimization.

The objective of this thesis is to design and implement a velocity-stabilizing driver for permanent magnet synchronous motor. The research presents how to achieve high efficiency in stabilizing overall velocity for a permanent magnet synchronous motor. In order to drive the integral system, there are six steps square-wave starting device, sine-wave driver, estimation of magnetic angle, velocity feedback and current feedback control circuits designed. A test platform is built by Microchip-made dsPIC33FJ128MC804 digital signal processor used as a control core. ¡§Simulink¡¨ simulator is used during the laboratory test. The simulation results are compared with those of experiments in order to verify the achievement of excellent performance of Robust Integral Velocity-stabilizing Controller on Permanent Magnet Synchronous Motor Driver.

We consider the stabilized finite element method for solving the incompressible Navier-Stokes equations and the magnetohydrodynamic (MHD) equations in two dimensions. The well-known instabilities arising from the application of standard Galerkin finite element method are eliminated by using the stabilizing subgrid method (SSM), the streamline upwind Petrov-Galerkin (SUPG) method, and the two-level finite element method (TLFEM). The domain is discretized into a set of regular triangular elements. In SSM, the finite-dimensional spaces employed consist of piecewise continuous linear interpolants enriched with the residual-free bubble functions. To find the bubble part of the solution, a two-level finite element method with a stabilizing subgrid of a single node is described and its applications to the Navier-Stokes equations and MHD equations are displayed. This constitutes the main original contribution of this thesis. Numerical approximations employing the proposed algorithms are presented for some benchmark problems. The results show that the proper choice of the subgrid node is crucial to get stable and accurate numerical approximations consistent with the physical configuration of the problem at a cheap computational cost. The stabilized finite element method of SUPG type is applied to the unsteady Navier-Stokes equations together with a finite element discretization in the time domain. Thus, oscillations in the solution and the need of very small time increment are avoided in obtaining stable solutions.

Tyrimo problema: lėtinio nugaros juosmeninės dalies skausmo pasikartojimo tikimybė labai didelė, todėl svarbu ištirti ir įvertinti pratimų išliekamąjį poveikį gydant nugaros skausmą. Kol apatiniai stuburo segmentai yra nestabilūs, jokie pratimai, mažinantys nugaros juosmeninės dalies skausmą, nebus efektyvūs. Stuburą stabilizuojančių pratimų dozavimas, jų atlikimo trukmė ir išliekamasis poveikis vis dar kelia diskusijų ir reikalauja išsamesnių tyrimų. Tyrimo hipotezė: 12 savaičių 24 procedūrų stuburą stabilizuojančių pratimų programos išliekamasis poveikis yra nepakankamas, siekiant ilgalaikio gydomojo efekto 40–60 metų amžiaus moterims, kamuojamoms lėtinio nugaros juosmeninės dalies skausmo. Tyrimo tikslas: įvertinti 12 savaičių 24 procedūrų stuburą stabilizuojančių pratimų programos išliekamąjį poveikį 40–60 metų amžiaus moterims, kamuojamoms lėtinio nugaros juosmeninės dalies skausmo. Tyrimo uždaviniai: ištirti liemens lenkiamųjų ir tiesiamųjų raumenų izometrinę jėgą ir ištvermę prieš ir po stuburą stabilizuojančių pratimų programos bei praėjus 4 ir 8 savaitėms po jos; nustatyti tiriamųjų nugaros juosmeninės dalies skausmo lygį ir įvertinti funkcinę būklę prieš ir po stuburą stabilizuojančių pratimų programos bei praėjus 4 ir 8 savaitėms po jos; įvertinti liemens lenkiamųjų ir tiesiamųjų raumenų jėgos ir ištvermės pokyčio įtaką nugaros juosmeninės dalies skausmo intensyvumui bei funkcinei būklei. Tyrimo metodai: Biodex System 3 Pro izokinetinis dinamometras, pilvo ir... [toliau žr. visą tekstą] / The problem of the research: the probability that chronic low back pain will reoccur is very high. For this reason, it is important to examine and evaluate the lastingness of the effect of the exercises while treating back pain. To reduce low back pain spine stabilizing exercises are applied. Dosage of exercises, duration of their performance and lastingness of the effect are still generating discussions and require a more detailed research. The hypothesis of the research: lastingness of twelve-week, 24 procedures, spine stabilizing exercises programme is not sufficient for 40-60 year old women with chronic low back pain while seeking a long lasting healing effect. The aim of the research: to evaluate lastingness of twelve-week, 24 procedures, spine stabilizing exercises programme effect on 40-60 year old women with chronic low back pain. The objectives of the research: to examine isometric force and endurance of back bending and straightening muscles before and after spine stabilizing exercises programme as well as 4 and 8 weeks after it; to determine subjects’ level of low back pain and functional state before and after spine stabilizing exercises programme as well as 4 and 8 weeks after it; to determine the effect of change in strength and endurance of waist bending and straightening muscles on low back pain intensity and functional state. Methods applied in the research: Biodex System 3 Pro isokinetic dynamometer, tests on abdomen and back muscles endurance, Oswestry... [to full text]

La chirurgie minimalement invasive est aujourd’hui une thématique de recherche particulièrement active. Un traitement thérapeutique ciblé et la possibilité d’établir un diagnostic précis grâce à l’utilisation de systèmes miniaturisés peuvent considérablement améliorer de nombreuses pratiques médicales. Le recours à des microrobots actionnés à distance et naviguant dans le système cardiovasculaire ouvre de nouvelles perspectives. L’objectif de cette thèse est de proposer un socle théorique solide concernant i) la modélisation d’un microrobot naviguant dans le système cardiovasculaire, ii) l’élaboration de lois de commande et d’observateurs assurant un bon suivi de trajectoire depuis la zone d’injection jusqu’à une zone cible. La modélisation du système fait intervenir de nombreuses forces : forces hydrodynamiques, forces surfaciques (électrostatique, van der Waals, stériques), forces de contact et poids apparent du microrobot. Ce microrobot est contrôlé dans le système cardiovasculaire par l’application de champs ou de gradients de champ magnétique selon le design du microrobot. La prise en compte de l’ensemble des forces aboutit à une représentation d’état sous la forme d’un système non-linéaire affine en la commande avec dérive comportant de nombreux paramètres physiologiques incertains. Une trajectoire de référence optimisée est déduite du modèle. L’approche de commande adoptée est établie à partir de critères de stabilité du système. Le système étant non-linéaire, une commande de type Lyapunov stabilisante est développée suivant une approche de type backstepping. L’estimation de certains paramètres physiologiques est rendue possible par une commande de type backstepping adaptatif. Un observateur grand gain reconstruit l’état complet du système nécessaire au calcul de la commande. La stabilité et la robustesse de l’ensemble sont établies au travers de nombreuses simulations en présence de bruits de mesure et d’erreurs paramétriques. / Minimally invasive medical procedures are currently an active research aera. A drug targeted therapy and the possibility of establishing an accurate diagnosis through the use of miniaturized systems can greatly improve many medical practices. The use of untethered microrobots navigating in the cardiovascular system opens new perspectives. The objective of this PhD work is to provide a theoretical approach on i) the modeling of a microrobot navigating in the cardiovascular system, ii) the development of control laws and observers to ensure a fine tracking from the injection to a target area. Modeling such as system involves many forces : hydrodynamic forces, surface forces (electrostatic, van derWaals, steric), contact forces and apparent weight of the microrobot. This microrobot is controlled in the cardiovascular system by the application of magnetic fields or magnetic field gradients according to the design of the microrobot. The consideration of all the forces leads to a state representation in the form of a nonlinear system with many physiological uncertain parameters, but gives us sufficient informations to plan an optimal trajectory. The control approach is established based on stability consideration. A Lyapunov-stabilizing control is then developed using a backstepping approach. An adaptive backstepping control law estimates some physiological parameters. A high gain observer reconstructs the full state of the system required for implementing the control approach. Robustness and stability of the controller with respect to noise measurement, parameters variations and uncertainties are illustrated by simulations.

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2014-10-22T19:58:08Z No. of bitstreams: 2 Dissertação - Getúlio Henrique de Oliveira- 2013.pdf: 2643219 bytes, checksum: 04fc7d8dc87b43e20032d6e2cb521968 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2014-10-22T20:28:09Z (GMT) No. of bitstreams: 2 Dissertação - Getúlio Henrique de Oliveira- 2013.pdf: 2643219 bytes, checksum: 04fc7d8dc87b43e20032d6e2cb521968 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-10-22T20:28:09Z (GMT). No. of bitstreams: 2 Dissertação - Getúlio Henrique de Oliveira- 2013.pdf: 2643219 bytes, checksum: 04fc7d8dc87b43e20032d6e2cb521968 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-07-19 / The study aimed to assess the impact caused by the waste discharge from cesspools and septic tanks into an anaerobic pond, followed by aerated facultative. Anápolis wastewater treatment plant (WWTP) has two modules of anaerobic ponds followed by aerated facultative, but only one received the waste. By going through a basket retainer of course solids, they were driven directly to the receiver module ponds. The research was divided into three steps: first of all, the system receiving the waste in both modules was evaluated with the rate application volume (RAV) of 0.33%, then, the receiving pond received all of the waste volume disposed in WWTP (RAV = 1.2%), finally the receiving pond was operated with the maximum organic loading and RAV = 0,83%. Samples from different septic tank cleaning trucks were collected and analyzed. Sludge deposited bathymetry was conducted in the anaerobic pond before and after isolation of the modules. The surface scum bulk in the anaerobic pond was removed and quantified. Initially, simple samples were collected from the influent and effluent of anaerobic and facultative aerated ponds weekly, and then, when the receiver module received double flow, samples were collected twice a week. Parameters analyzed were: BOD, COD, Escherichia coli, pH, oil and grease, total phosphorus, amonniacal nitrogen, suspended solids and settleable solids. Data from qualitative characterization of waste cesspools and septic tanks were submitted to descriptive statistics, while referring to the ponds effluents were analyzed by t-test statistical tool. The results indicated the characteristics of the waste are in the range found by other authors, both in national and international literature. A negative impact was evidenced on the receiving anaerobic pond effluent only for the parameters ammonia and settleable solids with the RAV of 1.2%, however, with the rate of 0.82%, the difference was significant for the parameters BOD and BOD in anaerobic ponds. There was an increase in sludge generation of approximately 16% in the receiving anaerobic pond and only 2.3% in the control. As for the scum, the average removal was approximately 450 L in the receiving anaerobic pond and only 100 L in the control. The results showed no effect of the co-treatment on the quality of treated sewage or in the operation and maintenance of the WWTP. Furthermore, systems formed by an anaerobic pond followed by facultative aerated, operating under the same conditions that Anápolis WWTP can be used for co-treatment of waste from cesspools and septic tanks / O estudo teve como objetivo avaliar os impactos da codisposição de resíduos de fossas e tanques sépticos em sistemas de lagoas anaeróbias seguidas de facultativas aeradas. A ETE estudada é composta por dois módulos idênticos de lagoas anaeróbias seguidas de facultativas aeradas, porém apenas um deles recebeu os resíduos. Ao passar por um cesto retentor de sólidos grosseiros, os mesmos foram conduzidos diretamente ao módulo receptor de lagoas. A pesquisa foi dividida em três etapas; primeiramente foi avaliado o sistema recebendo os resíduos em ambos os módulos de lagoas, com taxa de aplicação volumétrica (TAV) de 0,33%, posteriormente, a lagoa receptora recebeu todo o volume de resíduos descartado na ETE (TAV = 1,2%), por fim, a lagoa receptora foi operada com a capacidade máxima de carga orgânica e TAV de 0,83%. Amostras provenientes de diferentes caminhões limpa-fossa foram coletadas e analisadas. Realizou-se a batimetria do lodo depositado nas lagoas anaeróbias antes e depois do isolamento dos módulos. A escuma formada na superfície das lagoas anaeróbias foi removida e quantificada. Inicialmente, coletou-se amostras simples do afluente e efluente das lagoas anaeróbias e facultativas aeradas em uma frequência semanal, posteriormente, quando o módulo receptor passou a receber o dobro de vazão, as coletas foram realizadas duas vezes na semana. Foram avaliados os parâmetros de DBO, DQO, Escherichia coli, pH, óleos e graxas, fósforo total, nitrogênio amoniacal, sólidos suspensos, sólidos sedimentáveis. Os dados de caracterização qualitativa dos resíduos de fossas e tanques sépticos foram submetidos à estatística descritiva, enquanto os referentes ao efluente das lagoas foram analisados pela ferramenta estatística teste t. Os resultados indicaram que as características dos resíduos estão na faixa encontrada por outros autores, tanto na literatura nacional, quanto internacional. Foi evidenciado impacto negativo no efluente da lagoa anaeróbia receptora somente para os parâmetros nitrogênio amoniacal e sólidos sedimentáveis com a TAR de 1,2%, entretanto, com a taxa de 0,82%, observou-se diferença significativa para os parâmetros DBO e DBO nas lagoas anaeróbias. Notou-se aumento na geração de lodo de aproximadamente 16% na lagoa anaeróbia receptora e de apenas 2,3% na testemunha. Quanto a escuma, a remoção média foi de aproximadamente 450 L na lagoa anaeróbia receptora e de apenas 100 L na testemunha. Os resultados mostraram que a codisposição não interferiu na qualidade do esgoto tratado nem na operação e manutenção da ETE. Além do mais, sistemas formados por lagoa anaeróbia, seguida de facultativa aerada, operando nas mesmas condições que a ETE - Anápolis, podem ser utilizadas para a codisposição de resíduos provenientes de fossa e tanques sépticos.

Cette thèse aborde la problématique de la restauration d’images 3D de noyaux cellulaires fluorescents issues de la microscopie 2-photons à balayage laser d’animaux observés in vivo et in toto au cours de leur développement embryonnaire. La dégradation originale de ces images provient des limitations des systèmes optiques, du bruit intrinsèque des systèmes de détection ansi que de l’absorption et la diffusion de la lumière dans la profondeur des tissus. A la différence des propositions de “débruitage” de l’état de l’art, nous proposons ici une méthode qui prend en compte les particularités des données biologiques. Cette méthode, adaptation à la troisième dimension d’un algorithme utilisé dans l’analyse d’image astronomique, tire parti de connaissances a priori sur les images étudiées. Les hypothèses émises portent à la fois sur la détérioration du signal par un bruit supposé Mixe Poisson Gaussien (MPG) et sur la nature des objets observés. Nous traitons ici le cas de noyaux de cellules embryonnaires que nous supposons quasi sphériques.L’implémentation en 3D doit prendre en compte les dimensions de la grille d’échantillonnage de l’image. En effet ces dimensions ne sont pas identiques dans les trois directions de l’espace et un objet sphérique échantillonné sur cette grille perd cette caractéristique. Pour adapter notre méthode à une telle grille, nous avons ré-interprété le processus de filtrage, au coeur de la théorie originale, comme un processus physique de diffusion. / In this this document, we present a method to denoise 3D images acquired by 2-photon microscopy and displaying cell nuclei of animal embryos. The specimens are observed in toto and in vivo during their early development. Image deterioration can be explained by the microscope optical flaws, the acquisition system limitations, and light absorption and diffusion through the tissue depth.The proposed method is a 3D adaptation of a 2D method so far applied to astronomical images and it also differs from state-of the of-the-art methods by the introduction of priors on the biological data. Our hypotheses include assuming that noise statistics are Mixed Poisson Gaussian (MPG) and that cell nuclei are quasi spherical.To implement our method in 3D, we had to take into account the sampling grid dimensions which are different in the x, y or z directions. A spherical object imaged on this grid loses this property. To deal with such a grid, we had to interpret the filtering process, which is a core element of the original theory, as a diffusion process.

This work reports the outdoor weathering performance of ultraviolet (UV)-stabilized polypropylene (PP) products (using PP resins from Encore Wire). Different hindered amine light stabilizers (HALSs) and nano-ZnO were used to stabilize PP-film-based formulations that were exposed under UV light for 6 weeks simulating for in harsh outdoor weather of Dallas, Texas, USA in 2016. Characterization of the exposed PP film products was done in terms of mechanical and friction spectroscopic properties. The PP film formulations were divided into 15 categories based on the type of HALS and nano-ZnO incorporated. This was done to derive meaningful comparison of the various film formulations. Following exposure under UV light, the lifetimes of certain formulations were determined. On the basis of the mechanical and friction properties, it was determined that generally, the HALS or nano-ZnO stabilized PP film give better properties and if those two kinds of UV stabilizers can work together.

This thesis deals with the reconstruction of the existing road arch bridge using free transverse prestressing cables. Cables are laid in holes drilled in the shape of strut. The holes routed diagonally across the front wall of the bottom edge of the arch. The work also includes the stability of long front wall. This is solved by means of spacer frames led across the road. The reconstruction can be done partially limited service.

Vid grundläggning av medelhöga hus på friktionsjord kan i många fall grundläggningen genomföras med betongfundament. I dessa fall är jordens kompressionsegenskaper av mycket stor betydelse. Jordars materialkurvor visar att elasticitetsmodulen för avlastning är större än den för pålastning. För ett momentbelastat fundament kommer ena sidan utsättas för pålastning och den andra för avlastning. Vanligen beräknas dock grundens rotationsstyvhet endast med hjälp av modulen för pålastning vilket leder till att rotationsstyvheten underskattas. Ytterligare antas även ofta att ett fundaments rotationsstyvhet kan beräknas med hjälp av jordens bäddmodul av centrisk last. Denna beräkning är baserad på en lastspridning i djupet och underskattar rotationsstyvheten jämfört med en beräkning baserad på plattans vinkeländring och tröghetsmoment. Denna underskattning beror på att spänningar i jorden avtar långsammare vid centrisk belastning än vid momentbelastning. En ökning av grundens rotationsstyvhet medför en ökning av byggnadens globala knäcklast. Momentbelastade fundament riskerar att lätta från marken då momentets dragspänningar når upp till normalspänningarna av byggnadens tyngd. Då fundamentet lättar från marken kan inte längre hela fundamentets yta utnyttjas. Risken för att detta sker kan minskas genom att använda sig av en platta med elastiskt mellanlägg i dess centrala delar I denna studie visas hur grundläggningens rotationsstyvhet förändras dels beroende på beräkningsmetod samt om hänsyn tas till skillnaden mellan jordens på- och avlastningsmodul. Det visas även hur rotationsstyvheten förändras beroende på hur stor skillnaden mellan på- och avlastningsmodul är. Rotationsstyvheter har framtagits för fem olika plattor varav två är kvadratiska och två rektangulära med konstant tjocklek samt en rektangulär med elastiskt mellanlägg. För att utföra studien har såväl handberäkning som finita element beräkningar genomförts. De mjukvaror som använts är Mathcad för handberäkningen samt Plaxis 2D och Ansys APDL för den finita element beräkningen. Den fullständiga analysen är dock genomförd i Ansys APDL  och Plaxis 2D har endast använts för att verifiera att den modell som skapats är tillförlitlig. Resultaten av denna studie visar att rotationsstyvheten blir mycket bättre om beräkningen baseras på plattans vinkeländring till följd av momentbelastning istället för den bäddmodul som avser fundamentets egenskaper vid centrisk belastning. Resultaten visar också att rotationsstyvheten blir bättre ju större avlastningsmodulen är i förhållande till pålastningsmodulen. Den finita elementberäkningen ger en ökning av rotationsstyvheten med en faktor 1.75 – 3.85 för det fall med en relativ styvhetsfaktor 4. Motsvarande handberäkning ger en ökning med en faktor 1.45 – 2.85. Resultaten visar också att rotationsstyvheten för en grundplatta som förses med elastiskt mellanlägg endast blir något lägre än motsvarande grundplatta utan elastiskt mellanlägg. Samtidigt visade sig grundplattan med elastiskt mellanlägg klara ett väsentligt högre moment innan den lättar från jordytan på avlastad sida av fundamentet. Resultaten från knäckningsberäkningen visar att antalet våningar för en byggnad grundlagt med betongfundament på friktionsjord kan höjas från 8 till som mest 12 för det fallet då en relativ styvhetsfaktor är 4 och då skivans längd är 8 meter. Antalet våningar för en stabiliserande skiva med längden 4 meter kan höjas som mest till 9. / When founding medium high buildings on friction soil, the foundation is often carried out as a concrete footing. In these cases the earth compression characteristics are of very great importance. The material curve for soils shows that the elastic modulus of unloading is greater than that of loading. In a moment-loaded foundation, one side will be subjected to loading and the other to unloading. The rotational stiffness is however usually calculated only based on the elastic modulus of loading which result in an underestimation of the rotational stiffness. The rotational stiffness is also often calculated based on the bedding modulus due to centric loading. This calculation is based on an increasing area of the stress distribution by the depth and is underestimating the rotational stiffness compared to a calculation based on the angular change of the slab and its moment of inertia. This underestimation is due to that the stresses caused by centric loading decreases less rapidly than those caused by moment loading. An increase of the foundations rotational stiffness leads to an increase of the buildings global buckling load. Moment-loaded foundations are likely to ease off the ground at high moments. This occurs when the tensile stress caused by the moment reaches the normal stress due to the building's weight. When the foundation is lifted from the ground, the entire foundation surface can no longer be utilized. The risk for this to occur can be reduced by using a slab with elastic inserts. In this thesis, it is shown how the rotational stiffness of the foundation changes depending on the calculation method as well as if the difference in loading and unloading modulus is taken into account. It is also shown how the rotational stiffness changes depending on the relation between the loading and unloading modulus. Rotational stiffness has been evaluated for five different slabs of which two are square and two rectangular with constant thickness and one rectangular with elastic inserts. In order to perform the study, both hand calculation as well as finite element calculations are carried out. The used software are Mathcad for the hand calculation and Plaxis 2D as well as Ansys APDL for the finite element calculation. The full analysis is, however, performed in Ansys APDL and Plaxis 2D has only been used to verify that the model created is reliable. The results shows that the rotational stiffness of the foundation with the elastic inserts only reduces a small amount compared with the corresponding foundation without elastic inserts. The results also shows that the foundation with the elastic inserts resists a substantially higher moment-load before it eases off the ground on the unloaded side of the foundation.