A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed preconditioners and include numerical examples that validate the theory and assess the performance of the preconditioners.

Modelització numèrica d’un sistema de descàrrega d’una columna de la catedral d Girona mitjançant el mètode dels elements finits (anàlisi no lineal)

Aquest projecte consisteix en aplicar el càlcul no lineal en la modelització volumètricanumèrica de l’estructura del sistema de descàrrega d’una columna del claustre de lacatedral de Girona mitjançant el mètode dels elements finits. A la Universitat de Gironas’ha fet diferents estudis del claustre de la catedral de Girona però sempre simulant uncomportament lineal de les característiques dels materials. El programa utilitzat és la versió docent del programa ANSYS disponible al Dept.d’EMCI i l’element emprat ha sigut el SOLID65. Aquest element permet introduircaracterístiques de no linealitat en els models i és adequat per a anàlisi no lineald’elements com la pedra de Girona

Anàlisi paramètrica de l'assaig a compressió d'un panell de material compost rigiditzat amb tres nervis

L’objectiu d’aquest treball és desenvolupar una metodologia per realitzar l’anàlisiparamètrica de l’assaig de compressió d’un panell de material compost rigiditzat ambtres nervis. En primer lloc és necessari desenvolupar un sistema automatitzat per generar i avaluar el conjunt de parametritzacions. A continuació, s’estudiaran quines variables d’estat són les més adequades per representar el vinclament local, la flexió global, la càrrega crítica de desestabilització i l’índex de fallada en l’anàlisi paramètrica. La modelització amb el mètode dels elements finits serveix per simular l’assaig a compressió del panell. La simulació es realitza mitjançant un càlcul no lineal, per estudiar la desestabilització i els fenòmens no lineals que pateix el panell. L’estudi es complementa amb una anàlisi modal i una anàlisi lineal

Simulated joint and muscle forces in reversed and anatomic shoulder prostheses.

Reversed shoulder prostheses are increasingly being used for the treatment of glenohumeral arthropathy associated with a deficient rotator cuff. These non-anatomical implants attempt to balance the joint forces by means of a semi-constrained articular surface and a medialised centre of rotation. A finite element model was used to compare a reversed prosthesis with an anatomical implant. Active abduction was simulated from 0 degrees to 150 degrees of elevation. With the anatomical prosthesis, the joint force almost reached the equivalence of body weight. The joint force was half this for the reversed prosthesis. The direction of force was much more vertically aligned for the reverse prosthesis, in the first 90 degrees of abduction. With the reversed prosthesis, abduction was possible without rotator cuff muscles and required 20% less deltoid force to achieve it. This force analysis confirms the potential mechanical advantage of reversed prostheses when rotator cuff muscles are deficient.

Failure mechanism under tensile loads in CFRP 0-90º cross-ply laminates containing voids

The failure mechanism of a voided CFRP 0-90° cross-ply laminate under tensile loads applied in one direction was studied in this Final Degree Project. For this purpose, voided coupons were manufactured for being tested and a FEA was done. In both investigations, voids were placed in 90º and 0º direction, in order to understand the void location influence. On the one hand, the behaviour of the voided laminates was investigated through a FEM in order to preview the stress distribution within the material. On the other hand, voided specimens where manufactured by applying blowing agent in between the inner layers. These specimens were tested by a quasi-static step wise tensile test where data showing its real behaviour was collected. Specimens were X-rayed after each step of the test in order to investigate the failure mechanism of the composite. Data from the test was studied so that relations such as strength of the laminates, crack density per stress, void length per first crack at the void and void area per first crack at the specimen could be characterized

Càlcul, disseny i fabricació d'una carrosseria autoportant en material compòsit per al vehicle de baix consum Àliga

El projecte és l’inici de la creació d’un nou prototip per a poder competir la temporada 2008 a la cursa de vehicles de baix consum Shell Eco-Marathon. El principal objectiu és aconseguir un xassís que redueixi, en la mesura del possible, el pes del prototip a la vegada que asseguri una millor rigidesa i millori l’ergonomia de tot el conjunt. Es dissenyarà tota la part estructural de la carrosseria, que serà sotmesa a càlcul mitjançant la tècnica dels elements finits i posteriorment es realitzarà una guia de producció per tal de guiar els membres de l’equip que en realitzin la producció

Orthotropic active strain models for the numerical simulation of cardiac biomechanics

An active strain formulation for orthotropic constitutive laws arising in cardiac mechanics modeling is introduced and studied. The passive mechanical properties of the tissue are described by the Holzapfel-Ogden relation. In the active strain formulation, the Euler-Lagrange equations for minimizing the total energy are written in terms of active and passive deformation factors, where the active part is assumed to depend, at the cell level, on the electrodynamics and on the specific orientation of the cardiac cells. The well-posedness of the linear system derived from a generic Newton iteration of the original problem is analyzed and different mechanical activation functions are considered. In addition, the active strain formulation is compared with the classical active stress formulation from both numerical and modeling perspectives. Taylor-Hood and MINI finite elements are employed to discretize the mechanical problem. The results of several numerical experiments show that the proposed formulation is mathematically consistent and is able to represent the main key features of the phenomenon, while allowing savings in computational costs.

Benefit of Cup Medialization in Total Hip Arthroplasty is Associated With Femoral Anatomy.

BACKGROUND: Medialization of the cup with a respective increase in femoral offset has been proposed in THA to increase abductor moment arms. Insofar as there are potential disadvantages to cup medialization, it is important to ascertain whether the purported biomechanical benefits of cup medialization are large enough to warrant the downsides; to date, studies regarding this question have disagreed. QUESTIONS/PURPOSES: The purpose of this study was to quantify the effect of cup medialization with a compensatory increase in femoral offset compared with anatomic reconstruction for patients undergoing THA. We tested the hypothesis that there is a (linear) correlation between preoperative anatomic parameters and muscle moment arm increase caused by cup medialization. METHODS: Fifteen patients undergoing THA were selected, covering a typical range of preoperative femoral offsets. For each patient, a finite element model was built based on a preoperative CT scan. The model included the pelvis, femur, gluteus minimus, medius, and maximus. Two reconstructions were compared: (1) anatomic position of the acetabular center of rotation, and (2) cup medialization compensated by an increase in the femoral offset. Passive abduction-adduction and flexion-extension were simulated in the range of normal gait. Muscle moment arms were evaluated and correlated to preoperative femoral offset, acetabular offset, height of the greater trochanter (relative to femoral center of rotation), and femoral antetorsion angle. RESULTS: The increase of muscle moment arms caused by cup medialization varied among patients. Muscle moment arms increase by 10% to 85% of the amount of cup medialization for abduction-adduction and from -35% (decrease) to 50% for flexion-extension. The change in moment arm was inversely correlated (R(2) = 0.588, p = 0.001) to femoral antetorsion (anteversion), such that patients with less femoral antetorsion gained more in terms of hip muscle moments. No linear correlation was observed between changes in moment arm and other preoperative parameters in this series. CONCLUSIONS: The benefit of cup medialization is variable and depends on the individual anatomy. CLINICAL RELEVANCE: Cup medialization with compensatory increase of the femoral offset may be particularly effective in patients with less femoral antetorsion. However, cup medialization must be balanced against its tradeoffs, including the additional loss of medial acetabular bone stock, and eventual proprioceptive implications of the nonanatomic center of rotation and perhaps joint reaction forces. Clinical studies should better determine the relevance of small changes of moment arms on function and joint reaction forces.

Steel Diaphragms in Prestressed Concrete Girder Bridges, September 2004

Over the years, bridge engineers have been concerned about the response of prestressed concrete (PC) girder bridges that had been hit by over-height vehicles or vehicle loads. When a bridge is struck by an over-height vehicle or vehicle load, usually the outside and in some instances one of the interior girders are damaged in a bridge. The effect of intermediate diaphragms in providing damage protection to the PC girders of a bridge is not clearly defined. This analytical study focused on the role of intermediate diaphragms in reducing the occurrence of damage in the girders of a PC-girder bridge that has been struck by an over-height vehicle or vehicle load. The study also investigated whether a steel, intermediate diaphragm would essentially provide the same degree of impact protection for PC girders as that provided by a reinforced-concrete diaphragm. This investigation includes the following: a literature search and a survey questionnaire to determine the state-of-the-art in the use and design of intermediate diaphragms in PC-girder bridges. Comparisons were made between the strain and displacement results that were experimentally measured for a large-scale, laboratory, model bridge during previously documented work and those results that were obtained from analyses of the finite-element models that were developed during this research for that bridge. These comparisons were conducted to calibrate the finite element models used in the analyses for this research on intermediate diaphragms. Finite-element models were developed for non-skewed and skewed PC-girder bridges. Each model was analyzed with either a reinforced concrete or two types of steel, intermediate diaphragms that were located at mid-span of an interior span for a PC-girder bridge. The bridge models were analyzed for lateral-impact loads that were applied to the bottom flange of the exterior girders at the diaphragms location and away from the diaphragms location. A comparison was conducted between the strains and displacements induced in the girders for each intermediate-diaphragm type. These results showed that intermediate diaphragms have an effect in reducing impact damage to the PC girders. When the lateral impact-load was applied at the diaphragm location, the reinforced-concrete diaphragms provided more protection for the girders than that provided by the two types of steel diaphragms. The three types of diaphragms provided essentially the same degree of protection to the impacted, PC girder when the lateral-impact load was applied away from the diaphragm location.

Deployment of self-expandable stents in aneurysmatic cerebral vessels: comparison of different computational approaches for interventional planning

In the last few years, there has been a growing focus on faster computational methods to support clinicians in planning stenting procedures. This study investigates the possibility of introducing computational approximations in modelling stent deployment in aneurysmatic cerebral vessels to achieve simulations compatible with the constraints of real clinical workflows. The release of a self-expandable stent in a simplified aneurysmatic vessel was modelled in four different initial positions. Six progressively simplified modelling approaches (based on Finite Element method and Fast Virtual Stenting – FVS) have been used. Comparing accuracy of the results, the final configuration of the stent is more affected by neglecting mechanical properties of materials (FVS) than by adopting 1D instead of 3D stent models. Nevertheless, the differencesshowed are acceptable compared to those achieved by considering different stent initial positions. Regarding computationalcosts, simulations involving 1D stent features are the only ones feasible in clinical context.

Total knee arthroplasty - a clinical and numerical study of the micromovements of the tibial implant

Introduction The importance of the micromovements in the mechanism of aseptic loosening is clinically difficult to evaluate. To complete the analysis of a series of total knee arthroplasties (TKA), we used a tridimensional numerical model to study the micromovements of the tibial implant.Material and Methods Fifty one patients (with 57 cemented Porous Coated Anatomic TKAs) were reviewed (mean follow-up 4.5 year). Radiolucency at the tibial bone-cement interface was sought on the AP radiographs and divided in 7 areas. The distribution of the radiolucency was then correlated with the axis of the lower limb as measured on the orthoradiograms.The tridimensional numerical model is based on the finite element method. It allowed the measurement of the cemented prosthetic tibial implant's displacements and the microvements generated at bone-ciment interface. A total load (2000 Newton) was applied at first vertically and asymetrically on the tibial plateau, thereby simulating an axial deviation of the lower limbs. The vector's posterior inclination then permitted the addition of a tangential component to the axial load. This type of effort is generated by complex biomechanical phenomena such as knee flexion.Results 81 per cent of the 57 knees had a radiolucent line of at least 1 mm, at one or more of the tibial cement-epiphysis jonctional areas. The distribution of these lucent lines showed that they came out more frequently at the periphery of the implant. The lucent lines appeared most often under the unloaded margin of the tibial plateau, when axial deviation of lower limbs was present.Numerical simulations showed that asymetrical loading on the tibial plateau induced a subsidence of the loaded margin (0-100 microns) and lifting off at the opposite border (0-70 microns). The postero-anterior tangential component induced an anterior displacement of the tibial implant (160-220 microns), and horizontal micromovements with non homogenous distribution at the bone-ciment interface (28-54 microns).Discussion Comparison of clinical and numerical results showed a relation between the development of radiolucent lines and the unloading of the tibial implant's margin. The deleterious effect of lower limbs' axial deviation is thereby proven. The irregular distribution of lucent lines under the tibial plateau was similar of the micromovements' repartition at the bone-cement interface when tangential forces were present. A causative relation between the two phenomenaes could not however be established.Numerical simulation is a truly useful method of study; it permits to calculate micromovements which are relative, non homogenous and of very low amplitude. However, comparative clinical studies remain as essential to ensure the credibility of results.

Limits on the validity of infinite length assumptions for modelling shallow landslides

The infinite slope method is widely used as the geotechnical component of geomorphic and landscape evolution models. Its assumption that shallow landslides are infinitely long (in a downslope direction) is usually considered valid for natural landslides on the basis that they are generally long relative to their depth. However, this is rarely justified, because the critical length/depth (L/H) ratio below which edge effects become important is unknown. We establish this critical L/H ratio by benchmarking infinite slope stability predictions against finite element predictions for a set of synthetic two-dimensional slopes, assuming that the difference between the predictions is due to error in the infinite slope method. We test the infinite slope method for six different L/H ratios to find the critical ratio at which its predictions fall within 5% of those from the finite element method. We repeat these tests for 5000 synthetic slopes with a range of failure plane depths, pore water pressures, friction angles, soil cohesions, soil unit weights and slope angles characteristic of natural slopes. We find that: (1) infinite slope stability predictions are consistently too conservative for small L/H ratios; (2) the predictions always converge to within 5% of the finite element benchmarks by a L/H ratio of 25 (i.e. the infinite slope assumption is reasonable for landslides 25 times longer than they are deep); but (3) they can converge at much lower ratios depending on slope properties, particularly for low cohesion soils. The implication for catchment scale stability models is that the infinite length assumption is reasonable if their grid resolution is coarse (e.g. >25?m). However, it may also be valid even at much finer grid resolutions (e.g. 1?m), because spatial organization in the predicted pore water pressure field reduces the probability of short landslides and minimizes the risk that predicted landslides will have L/H ratios less than 25. Copyright (c) 2012 John Wiley & Sons, Ltd.

Avaruusinstrumentin mekaniikkasuunnittelu

Tämän insinöörityön tarkoituksena on kehittää avaruusinstrumentti, joka on osa Euroopan avaruusjärjestön ESA:n ja Japanin avaruusjärjestön JAXA:n BepiColombo-yhteistyöhanketta. Satelliitti lähetetään Merkurius-planeetan kiertoradalle vuonna 2013. Avaruusaluksen matka Merkuriukseen kestää yhteensä kuusi vuotta ja on perillä vuonna 2019. Yksi BepiColombo-satelliitin tieteellisistä instrumenteista on Oxford Instruments Analytical Oy:n kehittämä SIXS-instrumentti (Solar Intensity X-ray and particle Spectrometer). Instrumentin tarkoituksena on mitata auringosta tulevaa röntgen- ja partikkelisäteilyä. Se toimii yhteistyössä Merkuriuksen pintaa mittaavan MIXS-instrumentin (Mercury Imaging X-ray Spectrometer) kanssa. Tuloksista pystytään analysoimaan ne alkuaineet, joista Merkuriuksen pinta koostuu. Työn alussa esitellään teoriataustaa alkuaineiden mittauksesta niiltä osin, kuin se tämän työn kannalta on tarpeellista. Työssä syvennytään tarkemmin auringosta tulevan säteilyn mittauksesta vastaavan instrumentin tekniikkaan ja mekaniikkasuunnitteluun. Instrumentin lämpöteknisestä suunnittelusta, värähtelymittauksista ja lujuusanalyysista on työhön sisällytetty pääasiat. Työn tuloksena on kehitetty instrumenttiin tulevan partikkelidetektorin prototyyppi sekä instrumenttikotelon malli. Lopullisen koon instrumenttikotelolle määrittää vaadittavan elektroniikan viemä tila. Mittalaitteen kehitystyö jatkuu Oxford Instruments Analytical Oy:ssä vuoteen 2011 saakka.

In vivo loading increases mechanical properties of scaffold by affecting bone formation and bone resorption rates.

A successful bone tissue engineering strategy entails producing bone-scaffold constructs with adequate mechanical properties. Apart from the mechanical properties of the scaffold itself, the forming bone inside the scaffold also adds to the strength of the construct. In this study, we investigated the role of in vivo cyclic loading on mechanical properties of a bone scaffold. We implanted PLA/β-TCP scaffolds in the distal femur of six rats, applied external cyclic loading on the right leg, and kept the left leg as a control. We monitored bone formation at 7 time points over 35 weeks using time-lapsed micro-computed tomography (CT) imaging. The images were then used to construct micro-finite element models of bone-scaffold constructs, with which we estimated the stiffness for each sample at all time points. We found that loading increased the stiffness by 60% at 35 weeks. The increase of stiffness was correlated to an increase in bone volume fraction of 18% in the loaded scaffold compared to control scaffold. These changes in volume fraction and related stiffness in the bone scaffold are regulated by two independent processes, bone formation and bone resorption. Using time-lapsed micro-CT imaging and a newly-developed longitudinal image registration technique, we observed that mechanical stimulation increases the bone formation rate during 4-10 weeks, and decreases the bone resorption rate during 9-18 weeks post-operatively. For the first time, we report that in vivo cyclic loading increases mechanical properties of the scaffold by increasing the bone formation rate and decreasing the bone resorption rate.

Total shoulder arthroplasty: downward inclination of the glenoid component to balance supraspinatus deficiency.

HYPOTHESIS: Supraspinatus deficiency associated with total shoulder arthroplasty (TSA) provokes eccentric loading and may induce loosening of the glenoid component. A downward inclination of the glenoid component has been proposed to balance supraspinatus deficiency. METHODS: This hypothesis was assessed by a numeric musculoskeletal model of the glenohumeral joint during active abduction. Three cases were compared: TSA with normal muscular function, TSA with supraspinatus deficiency, and TSA with supraspinatus deficiency and downward inclination of the glenoid. RESULTS: Supraspinatus deficiency increased humeral migration and eccentric loading. A downward inclination of the glenoid partly balanced the loss of stability, but this potential advantage was counterbalanced by an important stress increase within the glenoid cement. The additional subchondral bone reaming required to incline the glenoid component indeed reduced the bone support, increasing cement deformation and stress. CONCLUSION: Glenoid inclination should not be obtained at the expense of subchondral bone support.