Calculs de plaques fissurées en flexion avec la méthode des éléments finis étendue (XFEM)

This thesis is devoted to the development of numerical methods for cracked plate and shell computations. For this issue, classical methods are based on the Finite Element Method (FEM). Due to the presence of a singularity near the crack tip, the FEM has several drawbacks. Its convergence rate is not optimal. Moreover, if the crack propagates, the domain must be remeshed. A new finite element method, introduced in 1999 and called XFEM, enables to avoid these drawbacks. In this method, the finite element base is enriched by specific shape functions which represent the discontinuity of the material and the crack tip singularity. In consequence, domain and crack are independent and the rate of convergence is optimal. In this thesis, we develop two XFEM formulations adapted to thin plates. These methods have been implemented in the finite element toolbox Getfem++, and tested on benchmark problems where the exact solution is known. The measure of the error shows that XFEM has an optimal rate of convergence, whereas the FEM shows a lower convergence. The other contribution of this thesis deals with the Stress Intensity Factors (SIF) : these variables indicate the risk of propagation of a crack.We propose two original computation methods, based on our XFEM formulations. The first uses the J-integral, and the other provides a direct estimation, without post-treatment.Cette thèse est consacrée au développement de méthodes numériques pour la simulation de plaques et coques fissurées. Pour ce problème, les méthodes classiques sont basées sur la Méthode des Elements Finis (MEF). En raison de la présence d'une singularité en fond de fissure, la MEF souffre de plusieurs défauts. Son taux de convergence n'est pas optimal. De plus, en cas de propagation de la fissure, le domaine doit être remaillé. Une nouvelle méthode d'éléments finis, introduite en 1999 et baptisée XFEM, permet de s'affranchir de ces inconvénients. Dans cette méthode, la base éléments finis est enrichie par des fonctions de forme spécifiques qui représentent la séparation du matériau et la singularité de fond de fissure. Ainsi, domaine et fissure sont indépendants et le taux de convergence est optimal. Dans cette thèse, on développe deux formulations XFEM adaptées à un modèle de plaques minces. Ces méthodes ont pu être implémentées dans la bibliothèque d'éléments finis Getfem++, et testées sur des exemples où la solution exacte est connue. L'étude d'erreur montre que la méthode XFEM possède un taux de convergence optimal, alors que la MEF montre une convergence plus lente. L'autre contribution de cette thèse concerne le calcul de Facteurs d'Intensité de Contraintes (FIC) : ces grandeurs indiquent le risque de propagation de la fissure. Nous proposons deux méthodes de calcul originales, basées sur nos formulations XFEM. La première méthode utilise l'intégrale-J, et la deuxième fournit une estimation directe, sans post-traitement

A numerical approach for modelling thin cracked plates with XFEM

The modelization of bending plates with through the thickness cracks is investigated. We consider the Kirchhoff-Love plate model which is valid for very thin plates. We apply the eXtended Finite Element Method (XFEM) strategy: enrichment of the finite element space with the asymptotic bending and with the discontinuity across the crack. We present two variants and their numerical validations and also a numerical computation of the stress intensity factors

Application de la méthode XFEM aux plaques fissurées en flexion

Dans cet article nous étudions les possibilités d'application de la méthode des éléments finis étendue (XFEM)au cas des plaques minces fissurées en flexion. Nous supposons le matériau homogène isotrope et la fissure traversante. La déformation de la plaque est réglé par le modèle de Kirchhoff-Love, pour lequel on utilise l'élément triangulaire HCT réduit ou son équivalent en quadrangle. Deux stratégies d'enrichissement sont présentées : ajout, dans une zone fixe, des singularités de fond de fissure soit sur tous les noeuds de cette zone, soit de façon globale avec raccord intégral à la frontière de la zone d'enrichissement. Des tests numériques montrent que la méthode conduit à une précision optimale, dans le sens où l'ordre de convergence de l'erreur numérique est comparable à celui d'une méthode d'éléments finis classique sur un problème régulier

eXtended finite element methods for thin plates

eXtended finite element methods for thin plates

Extended finite element methods for thin cracked plates with Kirchhoff-Love theory

International audienceA modelization of cracked plates under bending loads in the XFEM framework is addressed. The Kirchhoff–Love model is considered. It is well suited for very thin plates commonly used for instance in aircraft structures. Reduced HCT and FVS elements are used for the numerical discretization.Two kinds of strategies are proposed for the enrichment around the crack tip with, for both of them, an enrichment area of fixed size (i.e. independant of the mesh size parameter). In the first one, each degree of freedom inside this area is enriched with the nonsmooth functions that describe the asymptotic displacement near the crack tip. The second strategy consists in introducing these functions in the finite element basis with a single degree of freedom for each one. An integral matching is then used in order to ensure the C1 continuity of the solution at the interface between the enriched and the non-enriched areas. Finally, numerical convergence results for these strategies are presented and discussed

Long-term neurological symptoms after acute COVID-19 illness requiring hospitalization in adult patients: insights from the ISARIC-COVID-19 follow-up study

in this study we aimed to characterize the type and prevalence of neurological symptoms related to neurological long-COVID-19 from a large international multicenter cohort of adults after discharge from hospital for acute COVID-19

Paediatric COVID-19 mortality: a database analysis of the impact of health resource disparity

Background The impact of the COVID-19 pandemic on paediatric populations varied between high-income countries (HICs) versus low-income to middle-income countries (LMICs). We sought to investigate differences in paediatric clinical outcomes and identify factors contributing to disparity between countries.Methods The International Severe Acute Respiratory and Emerging Infections Consortium (ISARIC) COVID-19 database was queried to include children under 19 years of age admitted to hospital from January 2020 to April 2021 with suspected or confirmed COVID-19 diagnosis. Univariate and multivariable analysis of contributing factors for mortality were assessed by country group (HICs vs LMICs) as defined by the World Bank criteria.Results A total of 12 860 children (3819 from 21 HICs and 9041 from 15 LMICs) participated in this study. Of these, 8961 were laboratory-confirmed and 3899 suspected COVID-19 cases. About 52% of LMICs children were black, and more than 40% were infants and adolescent. Overall in-hospital mortality rate (95% CI) was 3.3% [=(3.0% to 3.6%), higher in LMICs than HICs (4.0% (3.6% to 4.4%) and 1.7% (1.3% to 2.1%), respectively). There were significant differences between country income groups in intervention profile, with higher use of antibiotics, antivirals, corticosteroids, prone positioning, high flow nasal cannula, non-invasive and invasive mechanical ventilation in HICs. Out of the 439 mechanically ventilated children, mortality occurred in 106 (24.1%) subjects, which was higher in LMICs than HICs (89 (43.6%) vs 17 (7.2%) respectively). Pre-existing infectious comorbidities (tuberculosis and HIV) and some complications (bacterial pneumonia, acute respiratory distress syndrome and myocarditis) were significantly higher in LMICs compared with HICs. On multivariable analysis, LMIC as country income group was associated with increased risk of mortality (adjusted HR 4.73 (3.16 to 7.10)).Conclusion Mortality and morbidities were higher in LMICs than HICs, and it may be attributable to differences in patient demographics, complications and access to supportive and treatment modalities

Respiratory support in patients with severe COVID-19 in the International Severe Acute Respiratory and Emerging Infection (ISARIC) COVID-19 study: a prospective, multinational, observational study

Background: Up to 30% of hospitalised patients with COVID-19 require advanced respiratory support, including high-flow nasal cannulas (HFNC), non-invasive mechanical ventilation (NIV), or invasive mechanical ventilation (IMV). We aimed to describe the clinical characteristics, outcomes and risk factors for failing non-invasive respiratory support in patients treated with severe COVID-19 during the first two years of the pandemic in high-income countries (HICs) and low middle-income countries (LMICs). Methods: This is a multinational, multicentre, prospective cohort study embedded in the ISARIC-WHO COVID-19 Clinical Characterisation Protocol. Patients with laboratory-confirmed SARS-CoV-2 infection who required hospital admission were recruited prospectively. Patients treated with HFNC, NIV, or IMV within the first 24 h of hospital admission were included in this study. Descriptive statistics, random forest, and logistic regression analyses were used to describe clinical characteristics and compare clinical outcomes among patients treated with the different types of advanced respiratory support. Results: A total of 66,565 patients were included in this study. Overall, 82.6% of patients were treated in HIC, and 40.6% were admitted to the hospital during the first pandemic wave. During the first 24 h after hospital admission, patients in HICs were more frequently treated with HFNC (48.0%), followed by NIV (38.6%) and IMV (13.4%). In contrast, patients admitted in lower- and middle-income countries (LMICs) were less frequently treated with HFNC (16.1%) and the majority received IMV (59.1%). The failure rate of non-invasive respiratory support (i.e. HFNC or NIV) was 15.5%, of which 71.2% were from HIC and 28.8% from LMIC. The variables most strongly associated with non-invasive ventilation failure, defined as progression to IMV, were high leukocyte counts at hospital admission (OR [95%CI]; 5.86 [4.83-7.10]), treatment in an LMIC (OR [95%CI]; 2.04 [1.97-2.11]), and tachypnoea at hospital admission (OR [95%CI]; 1.16 [1.14-1.18]). Patients who failed HFNC/NIV had a higher 28-day fatality ratio (OR [95%CI]; 1.27 [1.25-1.30]). Conclusions: In the present international cohort, the most frequently used advanced respiratory support was the HFNC. However, IMV was used more often in LMIC. Higher leucocyte count, tachypnoea, and treatment in LMIC were risk factors for HFNC/NIV failure. HFNC/NIV failure was related to worse clinical outcomes, such as 28-day mortality. Trial registration This is a prospective observational study; therefore, no health care interventions were applied to participants, and trial registration is not applicable