Nonlinear vibration and Supersonic Flutter of Conical Shells

Résumé Les coques coniques sont utilisées dans la conception d’une variété de composants de véhicules aérospatiaux, allant des réservoirs de carburant externes des avions de chasse aux lanceurs de satellites. Par conséquent, l’analyse de leurs comportements dynamique et aéroélastique est de grande importance pour la conception de ces structures. Depuis que des études expérimentales ont rapporté que le flottement supersonique se produit à des amplitudes ayant le même ordre de grandeur que l’épaisseur de la coque, les théories géométriques non-linéaires des coques sont de plus en plus utilisées. Ces dernières permettent une meilleure compréhension du phénomène et des résultats plus précis. Plusieurs théories des coques basées sur différentes hypothèses simplificatrices de la cinématique non linéaire ont été développées au cours des dernières décennies, y compris les théories des coques de Donnell, de Sanders et de Novozhilov. Ces théories se distinguent principalement par leurs différentes hypothèses dans le développement des relations de déplacements à la surface moyenne de la coque. La théorie de Donnell a introduit l’effet non linéaire du second ordre du déplacement normal à la surface moyenne lors du développement de la déformation dans le plan. La théorie de Sanders utilise la forme exacte des équations de « petites déformations » pour les déformations membranaires et un ensemble d’équations linéarisées pour les changements des courbures et des torsions de la surface de référence. Plus récemment, Nemeth a développé une théorie qui utilise les relations exactes non linéaires de déformation-déplacement avec des hypothèses de rotations modérées et de petites déformations. Cette théorie peut reproduire la théorie de Donnell et celle de Sanders en tant que cas particuliers, tout en offrant la possibilité de mener une étude comparative entre les prédictions de ces deux théories. Les relations déformation-déplacement peuvent être utilisées pour obtenir les équations d’équilibre et du mouvement des coques. La discrétisation de ces équations est faite en utilisant la méthode des éléments finis (MEF). Un avantage attrayant de cette méthode est sa flexibilité supérieure dans la gestion de différentes conditions aux limites. L’objectif de cette thèse est d’étudier les vibrations non linéaires et le flottement supersonique des coques coniques tronquées. Une formulation par la MEF hybride est d’abord développée sur la base de la solution exacte de la théorie améliorée de la première approximation de Sanders pour les coquilles minces. Par la suite, les équations non linéaires du mouvement des coques ont été obtenues en utilisant la méthode des coordonnées généralisées et des théories de coques non linéaires. Les coordonnées généralisées ont été choisies en fonction du déplacement nodaux de la coque. L’interaction fluide-structure induite par l’écoulement supersonique a été modélisée en utilisant la théorie de piston. Les effets de raidissement dus aux charges axiales et à la pression interne ont également été modélisés en les exprimant en termes des déplacements nodaux. Pour obtenir la réponse non linéaire de la vibration de la coque sans fluide, un algorithme a été développé basé sur la méthode de réponse harmonique modifiée et sur l’approche de Galerkin dans le domaine temporel. Cet algorithme peut fournir la fréquence de vibration non linéaire en fonction de la variation de l’amplitude de vibration. Une version améliorée du ce même algorithme a également été utilisée pour obtenir la réponse de flottement supersonique. Le modèle développé et l’outil numérique ont la capacité d’effectuer les analyses suivantes: i) Prédiction des vibrations naturelles linéaires des coques coniques tronquées sous pression et/ou sous charges axiales. Différents schémas de conditions aux limites ont pu être étudiés et les prédictions obtenues sont en bon accord avec les résultats expérimentaux rapportés dans la littérature. ii) Prédiction du début de divergence et du flottement linéaire des coques coniques tronquées sous pression et/ou sous charges axiales pour différentes conditions aux limites. Les prédictions de cette méthode ont été validées positivement par des expériences sélectionnées dans la littérature. Les réservoirs sous pression se sont révélés déstabilisés à des pressions dynamiques plus élevées. iii) Prédiction des vibrations non linéaires des coques coniques tronquées à vide prédite par les théories de Donnell, Sanders et Nemeth. La réponse axisymétrique des coques coniques tronquées étudiées a démontré un comportement de durcissement selon des courbes de l’épine dorsale. Dans les cas étudiés, bien que de légères différences entre la force des prédictions de la cinématique non linéaire de Donnell et deux autres théories aient pu être identifiées, il a été constaté que les différences entre les prédictions des théories de Sanders et de Nemeth sont négligeables. Par conséquent, en raison de son coût de calcul moins cher, la coniques tronquées. Une formulation par la MEF hybride est d’abord développée sur la base de la solution exacte de la théorie améliorée de la première approximation de Sanders pour les coquilles minces. Par la suite, les équations non linéaires du mouvement des coques ont été obtenues en utilisant la méthode des coordonnées généralisées et des théories de coques non linéaires. Les coordonnées généralisées ont été choisies en fonction du déplacement nodaux de la coque. L’interaction fluide-structure induite par l’écoulement supersonique a été modélisée en utilisant la théorie de piston. Les effets de raidissement dus aux charges axiales et à la pression interne ont également été modélisés en les exprimant en termes des déplacements nodaux. Pour obtenir la réponse non linéaire de la vibration de la coque sans fluide, un algorithme a été développé basé sur la méthode de réponse harmonique modifiée et sur l’approche de Galerkin dans le domaine temporel. Cet algorithme peut fournir la fréquence de vibration non linéaire en fonction de la variation de l’amplitude de vibration. Une version améliorée du ce même algorithme a également été utilisée pour obtenir la réponse de flottement supersonique. Le modèle développé et l’outil numérique ont la capacité d’effectuer les analyses suivantes: i) Prédiction des vibrations naturelles linéaires des coques coniques tronquées sous pression et/ou sous charges axiales. Différents schémas de conditions aux limites ont pu être étudiés et les prédictions obtenues sont en bon accord avec les résultats expérimentaux rapportés dans la littérature. ii) Prédiction du début de divergence et du flottement linéaire des coques coniques tronquées sous pression et/ou sous charges axiales pour différentes conditions aux limites. Les prédictions de cette méthode ont été validées positivement par des expériences sélectionnées dans la littérature. Les réservoirs sous pression se sont révélés déstabilisés à des pressions dynamiques plus élevées. iii) Prédiction des vibrations non linéaires des coques coniques tronquées à vide prédite par les théories de Donnell, Sanders et Nemeth. La réponse axisymétrique des coques coniques tronquées étudiées a démontré un comportement de durcissement selon des courbes de l’épine dorsale. Dans les cas étudiés, bien que de légères différences entre la force des prédictions de la cinématique non linéaire de Donnell et deux autres théories aient pu être identifiées, il a été constaté que les différences entre les prédictions des théories de Sanders et de Nemeth sont négligeables. Par conséquent, en raison de son coût de calcul moins cher, la théorie de Sanders peut être utilisée pour les classes de coques étudiées dans les travaux en cours. iv) Prédiction du comportement de flottement supersonique non linéaire de cônes tronqués sous pression et/ou sous charges axiales pour les trois théories non linéaires susmentionnées. Pour les cas étudiés, la cinématique non linéaire a diminué la stabilité de la coque lorsqu’elle est exposée au champ d’écoulement supersonique. Les vibrations non linéaires et le flottement ont été validés par les cas rapportés de coques cylindriques, qui ont été simulées via un cône tronqué avec un angle de cône très petit. L’application de la MEF permet la modélisation de différentes conditions aux limites et géométries des coques coniques tronquées. Ce programme, en comparaison avec les logiciels commerciaux, est moins coûteux en termes de calcul et il capable de modéliser comportement non linéaire qui reste une tâche difficile pour beaucoup de logiciel. ----------Abstract Conical shells have important applications in the design of a variety of aerospace vehicles, ranging from external fuel tanks of fighter jets to satellite launch vehicles. Hence, vibrational and aeroelastic analyses are important criteria in the design of these structures. Since experimental studies have reported that supersonic flutter occurs at amplitudes with the same order of magnitude as the thickness of the shell, geometrically nonlinear shell theories can provide a better and more accurate understanding of these problems. Different shell theories with different levels of approximation and simplifying assumptions for nonlinear kinematics have been developed in past decades, including Donnell’s, Sanders’ and Novozhilov’s shell theories. The differences between these theories mostly can be attributed to their different assumptions in the development of the strain-displacement relationship on the middle surface of the shell. Donnell’s theory introduced the secondorder nonlinear effect of normal-to-surface displacement in developing the in-plane strain. Sanders’ theory employed the exact form of the “small-strain” equations for the membrane strains and a set of linearized equations for the changes in the reference-surface curvature and torsions. More recently, Nemeth developed a theory that employed the exact nonlinear strain-displacement relations with presumptions of moderate rotations and small strains. This theory can reproduce Donnell’s and Sanders’ theories as an explicit subset while providing an opportunity to conduct a comparative study between the predictions of those theories. The strain-displacement relationships can be employed to obtain the equilibrium and equations of motion for shells.One important family of discretization of these equations is the finite elements method (FEM). One attractive advantage of the FEM is its superior flexibility in handling different boundary conditions. The objective of this thesis is to investigate the nonlinear vibration and supersonic flutter of truncated conical shells. In this thesis, a hybrid FEM formulation is first developed based on the exact solution of Sanders’ improved first-approximation theory for thin shells. Then, utilizing the generalized coordinates method and nonlinear shell theories, the nonlinear equations of motion for shells were obtained. The generalized coordinates were chosen in terms of the nodal displacement of the shell. Fluid structure interaction as a result of exposure to the supersonic flow was modeled using the piston theory. The effects of axial loads and internal pressure were also modeled in terms of nodal displacements. To obtain the nonlinear response of the shell’s vibration in vacuo, an algorithm was developed based on the modified harmonic response method that employed Galerkin’s approach in the time domain. This algorithm can provide the nonlinear vibration frequency as a result of the variation in vibration amplitude. An improved version of the same algorithm was also used to obtain the supersonic flutter response. The developed model and numerical tool have the capability to perform the following analyses: i) Prediction of linear natural vibration of pressurized truncated conical shells under axial loads. Different schemes for boundary conditions could be studied and the predictions found to be in good accordance with the experimental results reported in literature. ii) Prediction of linear flutter onset and divergence of pressurized truncated conical shells under axial loads under different boundary conditions. The predictions of this method were validated against selected experiments in the literature with good agreement. The pressurized shells were found to be destabilized at higher dynamic pressures. iii) Prediction of nonlinear vibration of truncated conical shells in vacuo predicted by Donnell’s, Sanders’ and Nemeth’s theories. The axisymmetric response of the studied truncated conical shells demonstrated a hardening behavior in the backbone curves. In the studied cases, while slight differences between the strength of predictions of Donnell’s nonlinear kinematics and two other theories could be identified, it was found that the differences between the predictions of Sanders’ and Nemeth’s theories were negligible. Hence, due to its less expensive computational cost, Sanders’ theory can be used for the classes of shells investigated in the current work. iv) Prediction of nonlinear supersonic flutter behavior of pressurized truncated conical shells under axial loads for three selected nonlinear theories. For the studied cases, the nonlinear kinematics decreased the shell’s stability when it was exposed to the supersonic flow field. Both nonlinear vibration and flutter were validated against reported cases of cylindrical shells, which were simulated via a truncated cone with a very small cone angle. The developed FEM application can be used to model different boundary conditions and geometries of truncated conical shells. Both nonlinear vibration and flutter were validated against reported cases of cylindrical shells which were simulated via a truncated cone with a very small cone angle. The developed FEM application can be used to model different boundary conditions and geometries of truncated conical shells. This program in comparison to general application commercial applications is computationally less expensive and can model nonlinear behaviors that are difficult to model with them

Conflict resolution in the multi-stakeholder stepped spillway design under uncertainty by machine learning techniques

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Fatigue behaviour of load-bearing polymeric bone scaffolds: A review

Bone scaffolds play a crucial role in bone tissue engineering by providing mechanical support for the growth of new tissue while enduring static and fatigue loads. Although polymers possess favourable characteristics such as adjustable degradation rate, tissue-compatible stiffness, ease of fabrication, and low toxicity, their relatively low mechanical strength has limited their use in load-bearing applications. While numerous studies have focused on assessing the static strength of polymeric scaffolds, little research has been conducted on their fatigue properties. The current review presents a comprehensive study on the fatigue behaviour of polymeric bone scaffolds. The fatigue failure in polymeric scaffolds is discussed and the impact of material properties, topological features, loading conditions, and environmental factors are also examined. The present review also provides insight into the fatigue damage evolution within polymeric scaffolds, drawing comparisons to the behaviour observed in natural bone. Additionally, the effect of polymer microstructure, incorporating reinforcing materials, the introduction of topological features, and hydrodynamic/corrosive impact of body fluids in the fatigue life of scaffolds are discussed. Understanding these parameters is crucial for enhancing the fatigue resistance of polymeric scaffolds and holds promise for expanding their application in clinical settings as structural biomaterials. Statement of Significance: Polymers have promising advantages for bone tissue engineering, including adjustable degradation rates, compatibility with native bone stiffness, ease of fabrication, and low toxicity. However, their limited mechanical strength has hindered their use in load-bearing scaffolds for clinical applications. While prior studies have addressed static behaviour of polymeric scaffolds, a comprehensive review of their fatigue performance is lacking. This review explores this gap, addressing fatigue characteristics, failure mechanisms, and the influence of parameters like material properties, topological features, loading conditions, and environmental factors. It also examines microstructure, reinforcement materials, pore architectures, body fluids, and tissue ingrowth effects on fatigue behaviour. A significant emphasis is placed on understanding fatigue damage progression in polymeric scaffolds, comparing it to natural bone behaviour

Nonlinear vibration of truncated conical shells : Donnell, Sanders and Nemeth theories

The formulation of nonlinear kinematics of shells in three different shell theories namely Donnell, Sanders and Nemeth including shear deformation for anisotropic materials is presented. A finite element solution for the equilibrium equations of Sander’s improved first-approximation theory is developed and has been used to develop the nonlinear finite element amplitude equation of vibration of conical shells of Donnell, Sanders and Nemeth theories using generalized coordinates methods and Lagrange equations of motions. The amplitude equation of nonlinear vibration of conical shell has been solved for multiple cases of isotropic materials with neglecting the shear deformation. Linear vibration frequencies for different conical shells with different materials, geometry and boundary conditions are validated against the existing experimental data in the literature and show excellent agreement. The nonlinear vibration results have been validated against the existing data for cylindrical shells and demonstrate good accordance. The validated model has been used to investigate effect of different parameters including circumferential mode number, cone-half angle, length to radius ratio, thickness to radius ratio and boundary conditions

Effect of oral tizanidine on prolongation of intrathecal lidocaine

Objective: In order to prolong the duration of intrathecal lidocaine, various drugs are used along with it. Due to the promising effects of tizanidine on central nervous system, it can be assumed that tizanidine can have a positive effect on increasing the anesthesia duration too. Thus, we aimed to investigate the effect of oral tizanidine on the duration of lidocaine spinal anesthesia. Methods: This double blind clinical trial was conducted on 40 male patients waiting for elective leg surgery with the age range of 20-60 years in one of the educational hospitals of Kerman University of Medical Sciences, Iran. We used simple random sampling and our participants were assigned into 2 groups (placebo and oral tizanidine receivers). Spinal anesthesia with 1 mg/kg of hyperbaric lidocaine 5% was performed in both groups. In tizanidine group, patients received 4 mg of oral tizanidine one hour before spinal anesthesia. Sensory block was examined by pin prick test and all anesthetic duration including start block until reduction of sensory level was calculated at 2 lower dermatomes. Results: Findings showed that oral tizanidine compared to placebo can cause a 10-15 minute increase in patients’ lidocaine spinal anesthesia. Therefore, the average anesthesia time for tizanidine group increased meaningfully (P = 0.03). In addition, tizanidine can sedate patients during surgery (P = 0.00) or in recovery (P = 0.003). Conclusion: Based on the results, tizanidine increased the duration of lidocaine so oral tizanidine can be used to prolong the duration of lidocaine spinal anesthesia

First evidence of the presence of adenovirus type 8 in myocardium of patients with severe idiopathic dilated cardiomyopathy

Previous studies have detected adenovirus and cytomegalovirus (CMV) in cardiac tissue of patients with myocarditis. Therefore, in this study, we investigated the frequency of these viruses, which may be involved in the development of severe dilated cardiomyopathy (DCM). Myocardial tissue from of 23 cardiac transplant candidates with acute idiopathic DCM below the age of 40 years were analyzed by amplification of adenovirus and CMV DNA and subsequent sequencing. Adenovirus was detected in four (17.4%) and CMV in one (4.3%) of the patients. All controls were negative for the presence of both viruses. Our study shows that myocardial infection with adenovirus may play an important role in the pathogenesis of severe DCM and suggests that vaccination against adenovirus might be helpful in decreasing the prevalence of severe idiopathic DCM. This is the first study in which adenovirus type 8 has been detected in the hearts of patients with DCM

Identifying the favored mutation in a positive selective sweep.

Most approaches that capture signatures of selective sweeps in population genomics data do not identify the specific mutation favored by selection. We present iSAFE (for "integrated selection of allele favored by evolution"), a method that enables researchers to accurately pinpoint the favored mutation in a large region (∼5 Mbp) by using a statistic derived solely from population genetics signals. iSAFE does not require knowledge of demography, the phenotype under selection, or functional annotations of mutations

Computational Methods to Study Tandem Repeats in Human Genome and Complex Diseases

A central goal in genomics is to identify genetic variations and their impact on underlying molecular changes that lead to disease. With the advances in whole genome sequencing, many studies have been able to identify thousands of genetic loci associated with human traits. These studies mainly focus on single-nucleotide variants (SNVs) and novel insertion and deletions in the genome, while ignoring more complex variants. Here, I consider the problem of genotyping Variable Number Tandem Repeats (VNTRs), composed of inexact tandem duplications of short (6-100 bp) repeating units that span 3% of the human genome.While some VNTRs are known to play a role in complex disorders (e.g. Alzheimer’s, Myoclonus epilepsy, and Diabetes), the majority of them have not been studied well due to computational difficulty in genotyping VNTRs on a large scale. Here, I will present our progress on developing efficient computational algorithms to profile VNTRs from high throughput sequencing data and identify possible variations within them. I applied our method to generate the largest catalog of VNTR genotypes to this date, which provides insights into the landscape of VNTR variations in different populations. I show the contribution of tandem repeats in mediating expression levels of key genes with known associations to neurological disorders and familial cancers, and argue the causality of this relation. Finally, I will describe our efforts to directly understand the impact of these variations on human phenotypes, which improves our understanding of genetic architecture of complex diseases

Computational Methods to Study Tandem Repeats in Human Genome and Complex Diseases

A central goal in genomics is to identify genetic variations and their impact on underlying molecular changes that lead to disease. With the advances in whole genome sequencing, many studies have been able to identify thousands of genetic loci associated with human traits. These studies mainly focus on single-nucleotide variants (SNVs) and novel insertion and deletions in the genome, while ignoring more complex variants. Here, I consider the problem of genotyping Variable Number Tandem Repeats (VNTRs), composed of inexact tandem duplications of short (6-100 bp) repeating units that span 3% of the human genome.While some VNTRs are known to play a role in complex disorders (e.g. Alzheimer’s, Myoclonus epilepsy, and Diabetes), the majority of them have not been studied well due to computational difficulty in genotyping VNTRs on a large scale. Here, I will present our progress on developing efficient computational algorithms to profile VNTRs from high throughput sequencing data and identify possible variations within them. I applied our method to generate the largest catalog of VNTR genotypes to this date, which provides insights into the landscape of VNTR variations in different populations. I show the contribution of tandem repeats in mediating expression levels of key genes with known associations to neurological disorders and familial cancers, and argue the causality of this relation. Finally, I will describe our efforts to directly understand the impact of these variations on human phenotypes, which improves our understanding of genetic architecture of complex diseases