Development of a three-dimensional nonlinear viscoelastic constitutive model of solid propellant

A three dimensional nonlinear viscoelastic constitutive model for the solid propellant is developed. In their earlier work, the authors have developed an isotropic constitutive model and verified it for one dimensional case. In the present work, the validity of the model is extended to three-dimensional cases. Large deformation, dewetting and cyclic loading effects are treated as the main sources of nonlinear behavior of the solid propellant. Viscoelastic dewetting criteria is used and the softening of the solid propellant due to dewetting is treated by the modulus decrease. The nonlinearities during cyclic loading are accounted for by the functions of the octahedral shear strain measure. The constitutive equation is implemented into a finite element code for the analysis of propellant grains. A commercial finite element package ‘ABAQUS’ is used for the analysis and the model is introduced into the code through a user subroutine. The model is evaluated with different loading conditions and the predicted values are in good agreement with the measured ones. The resulting model applied to analyze a solid propellant grain for the thermal cycling load.

Development of finite elements for analysis of biomechanical structures using flexible multibody formulations

The absolute nodal coordinate formulation was originally developed for the analysis of structures undergoing large rotations and deformations. This dissertation proposes several enhancements to the absolute nodal coordinate formulation based finite beam and plate elements. The main scientific contribution of this thesis relies on the development of elements based on the absolute nodal coordinate formulation that do not suffer from commonly known numerical locking phenomena. These elements can be used in the future in a number of practical applications, for example, analysis of biomechanical soft tissues. This study presents several higher-order Euler–Bernoulli beam elements, a simple method to alleviate Poisson’s and transverse shear locking in gradient deficient plate elements, and a nearly locking free gradient deficient plate element. The absolute nodal coordinate formulation based gradient deficient plate elements developed in this dissertation describe most of the common numerical locking phenomena encountered in the formulation of a continuum mechanics based description of elastic energy. Thus, with these fairly straightforwardly formulated elements that are comprised only of the position and transverse direction gradient degrees of freedom, the pathologies and remedies for the numerical locking phenomena are presented in a clear and understandable manner. The analysis of the Euler–Bernoulli beam elements developed in this study show that the choice of higher gradient degrees of freedom as nodal degrees of freedom leads to a smoother strain field. This improves the rate of convergence.

Développement d'une nouvelle méthode de caractérisation tissulaire basée sur l'élastographie ultrasonore : application pour le dépistage précoce du cancer du sein

Le cancer du sein est le cancer le plus fréquent chez la femme. Il demeure la cause de mortalité la plus importante chez les femmes âgées entre 35 et 55 ans. Au Canada, plus de 20 000 nouveaux cas sont diagnostiqués chaque année. Les études scientifiques démontrent que l'espérance de vie est étroitement liée à la précocité du diagnostic. Les moyens de diagnostic actuels comme la mammographie, l'échographie et la biopsie comportent certaines limitations. Par exemple, la mammographie permet de diagnostiquer la présence d’une masse suspecte dans le sein, mais ne peut en déterminer la nature (bénigne ou maligne). Les techniques d’imagerie complémentaires comme l'échographie ou l'imagerie par résonance magnétique (IRM) sont alors utilisées en complément, mais elles sont limitées quant à la sensibilité et la spécificité de leur diagnostic, principalement chez les jeunes femmes (< 50 ans) ou celles ayant un parenchyme dense. Par conséquent, nombreuses sont celles qui doivent subir une biopsie alors que leur lésions sont bénignes. Quelques voies de recherche sont privilégiées depuis peu pour réduire l`incertitude du diagnostic par imagerie ultrasonore. Dans ce contexte, l’élastographie dynamique est prometteuse. Cette technique est inspirée du geste médical de palpation et est basée sur la détermination de la rigidité des tissus, sachant que les lésions en général sont plus rigides que le tissu sain environnant. Le principe de cette technique est de générer des ondes de cisaillement et d'en étudier la propagation de ces ondes afin de remonter aux propriétés mécaniques du milieu via un problème inverse préétabli. Cette thèse vise le développement d'une nouvelle méthode d'élastographie dynamique pour le dépistage précoce des lésions mammaires. L'un des principaux problèmes des techniques d'élastographie dynamiques en utilisant la force de radiation est la forte atténuation des ondes de cisaillement. Après quelques longueurs d'onde de propagation, les amplitudes de déplacement diminuent considérablement et leur suivi devient difficile voir impossible. Ce problème affecte grandement la caractérisation des tissus biologiques. En outre, ces techniques ne donnent que l'information sur l'élasticité tandis que des études récentes montrent que certaines lésions bénignes ont les mêmes élasticités que des lésions malignes ce qui affecte la spécificité de ces techniques et motive la quantification de d'autres paramètres mécaniques (e.g.la viscosité). Le premier objectif de cette thèse consiste à optimiser la pression de radiation acoustique afin de rehausser l'amplitude des déplacements générés. Pour ce faire, un modèle analytique de prédiction de la fréquence de génération de la force de radiation a été développé. Une fois validé in vitro, ce modèle a servi pour la prédiction des fréquences optimales pour la génération de la force de radiation dans d'autres expérimentations in vitro et ex vivo sur des échantillons de tissu mammaire obtenus après mastectomie totale. Dans la continuité de ces travaux, un prototype de sonde ultrasonore conçu pour la génération d'un type spécifique d'ondes de cisaillement appelé ''onde de torsion'' a été développé. Le but est d'utiliser la force de radiation optimisée afin de générer des ondes de cisaillement adaptatives, et de monter leur utilité dans l'amélioration de l'amplitude des déplacements. Contrairement aux techniques élastographiques classiques, ce prototype permet la génération des ondes de cisaillement selon des parcours adaptatifs (e.g. circulaire, elliptique,…etc.) dépendamment de la forme de la lésion. L’optimisation des dépôts énergétiques induit une meilleure réponse mécanique du tissu et améliore le rapport signal sur bruit pour une meilleure quantification des paramètres viscoélastiques. Il est aussi question de consolider davantage les travaux de recherches antérieurs par un appui expérimental, et de prouver que ce type particulier d'onde de torsion peut mettre en résonance des structures. Ce phénomène de résonance des structures permet de rehausser davantage le contraste de déplacement entre les masses suspectes et le milieu environnant pour une meilleure détection. Enfin, dans le cadre de la quantification des paramètres viscoélastiques des tissus, la dernière étape consiste à développer un modèle inverse basé sur la propagation des ondes de cisaillement adaptatives pour l'estimation des paramètres viscoélastiques. L'estimation des paramètres viscoélastiques se fait via la résolution d'un problème inverse intégré dans un modèle numérique éléments finis. La robustesse de ce modèle a été étudiée afin de déterminer ces limites d'utilisation. Les résultats obtenus par ce modèle sont comparés à d'autres résultats (mêmes échantillons) obtenus par des méthodes de référence (e.g. Rheospectris) afin d'estimer la précision de la méthode développée. La quantification des paramètres mécaniques des lésions permet d'améliorer la sensibilité et la spécificité du diagnostic. La caractérisation tissulaire permet aussi une meilleure identification du type de lésion (malin ou bénin) ainsi que son évolution. Cette technique aide grandement les cliniciens dans le choix et la planification d'une prise en charge adaptée.

Thermo-Structural Analysis of 3D Composites

Three dimensional (3D) composites are strong contenders for the structural applications in situations like aerospace,aircraft and automotive industries where multidirectional thermal and mechanical stresses exist. The presence of reinforcement along the thickness direction in 3D composites,increases the through the thickness stiffness and strength properties.The 3D preforms can be manufactured with numerous complex architecture variations to meet the needs of specific applications.For hot structure applications Carbon-Carbon(C-C) composites are generally used,whose property variation with respect to temperature is essential for carrying out the design of hot structures.The thermomechanical behavior of 3D composites is not fully understood and reported.The methodology to find the thermomechanical properties using analytical modelling of 3D woven,3D 4-axes braided and 3D 5-axes braided composites from Representative Unit Cells(RUC's) based on constitutive equations for 3D composites has been dealt in the present study.High Temperature Unidirectional (UD) Carbon-Carbon material properties have been evaluated using analytical methods,viz.,Composite cylinder assemblage Model and Method of Cells based on experiments carried out on Carbon-Carbon fabric composite for a temparature range of 300 degreeK to 2800degreeK.These properties have been used for evaluating the 3D composite properties.From among the existing methods of solution sequences for 3D composites,"3D composite Strength Model" has been identified as the most suitable method.For thegeneration of material properies of RUC's od 3D composites,software has been developed using MATLAB.Correlaton of the analytically determined properties with test results available in literature has been established.Parametric studies on the variation of all the thermomechanical constants for different 3D performs of Carbon-Carbon material have been studied and selection criteria have been formulated for their applications for the hot structures.Procedure for the structural design of hot structures made of 3D Carbon-Carbon composites has been established through the numerical investigations on a Nosecap.Nonlinear transient thermal and nonlinear transient thermo-structural analysis on the Nosecap have been carried out using finite element software NASTRAN.Failure indices have been established for the identified performs,identification of suitable 3D composite based on parametric studies on strength properties and recommendation of this material for Nosecap of RLV based on structural performance have been carried out in this Study.Based on the 3D failure theory the best perform for the Nosecap has been identified as 4-axis 15degree braided composite.

How to save a bad element with weak boundary conditions

The P-1-P-1 finite element pair is known to allow the existence of spurious pressure (surface elevation) modes for the shallow water equations and to be unstable for mixed formulations. We show that this behavior is strongly influenced by the strong or the weak enforcement of the impermeability boundary conditions. A numerical analysis of the Stommel model is performed for both P-1-P-1 and P-1(NC)-P-1 mixed formulations. Steady and transient test cases are considered. We observe that the P-1-P-1 element exhibits stable discrete solutions with weak boundary conditions or with fully unstructured meshes. (c) 2005 Elsevier Ltd. All rights reserved.

Chapter 4: Simulation of reaction injection moulding

Reaction Injection Moulding is a technology that enables the rapid production of complex plastic parts directly from a mixture of two reactive materials of low viscosity. The reactants are mixed in specific quantities and injected into a mould. This process allows large complex parts to be produced without the need for high clamping pressures. This chapter explores the simulation of the complex processes involved in reaction injection moulding. The reaction processes mean that the dynamics of the material in the mould are in constant evolution and an effective model which takes full account of these changing dynamics is introduced and incorporated in to finite element procedures, which are able to provide a complete simulation of the cycle of mould filling and subsequent curing.

Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model

We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen–Cahn/Cahn–Hilliard/Navier–Stokes–Korteweg type which allows for phase transitions. We show that the scheme is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to discrete equivalents of those effects already causing dissipation on the continuous level, that is, there is no artificial numerical dissipation added into the scheme. In this sense the methods are consistent with the energy dissipation of the continuous PDE system.

Impact of atmospheric forcing data on simulations of the Laptev Sea polynya dynamics using the sea-ice ocean model FESOM

The polynyas of the Laptev Sea are regions of particular interest due to the strong formation of Arctic sea-ice. In order to simulate the polynya dynamics and to quantify ice production, we apply the Finite Element Sea-Ice Ocean Model FESOM. In previous simulations FESOM has been forced with daily atmospheric NCEP (National Centers for Environmental Prediction) 1. For the periods 1 April to 9 May 2008 and 1 January to 8 February 2009 we examine the impact of different forcing data: daily and 6-hourly NCEP reanalyses 1 (1.875° x 1.875°), 6-hourly NCEP reanalyses 2 (1.875° x 1.875°), 6-hourly analyses from the GME (Global Model of the German Weather Service) (0.5° x 0.5°) and high-resolution hourly COSMO (Consortium for Small-Scale Modeling) data (5 km x 5 km). In all FESOM simulations, except for those with 6-hourly and daily NCEP 1 data, the openings and closings of polynyas are simulated in principle agreement with satellite products. Over the fast-ice area the wind fields of all atmospheric data are similar and close to in situ measurements. Over the polynya areas, however, there are strong differences between the forcing data with respect to air temperature and turbulent heat flux. These differences have a strong impact on sea-ice production rates. Depending on the forcing fields polynya ice production ranges from 1.4 km3 to 7.8 km3 during 1 April to 9 May 2011 and from 25.7 km3 to 66.2 km3 during 1 January to 8 February 2009. Therefore, atmospheric forcing data with high spatial and temporal resolution which account for the presence of the polynyas are needed to reduce the uncertainty in quantifying ice production in polynyas.

Modelagem numérica de estruturas de contenção atirantadas em areia

A numerical study on the behavior of tied-back retaining walls in sand, using the finite element method (FEM) is presented. The analyses were performed using the software Plaxis 2D, and were focused on the development of horizontal displacements, horizontal stresses, shear forces and bending moments in the structure during the construction process. Emphasis was placed on the evaluation of wall embedment, tie-back horizontal spacing, wall thickness, and free anchor length on wall behavior. A representative soil profile of a specific region at the City of Natal, Brazil, was used in the numerical analyses. New facilities built on this region often include retaining structures of the same type studied herein. Soil behavior was modeled using the Mohr-Coulomb constitutive model, whereas the structural elements were modeled using the linear elastic model. Shear strength parameters of the soil layers were obtained from direct shear test results conducted with samples collected at the studied site. Deformation parameters were obtained from empirical correlations from SPT test results carried out on the studied site. The results of the numerical analyses revealed that the effect of wall embedment on the investigated parameters is virtually negligible. Conversely, the tie-back horizontal spacing plays an important role on the investigated parameters. The results also demonstrated that the wall thickness significantly affects the wall horizontal displacements, and the shear forces and bending moments within the retaining structure. However, wall thickness was not found to influence horizontal stresses in the structure

Determination of the numerical parameters of a continuous damage model for the structural analysis of clay brick masonry

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Two-dimensional modeling of material failure in reinforced concrete by means of a continuum strong discontinuity approach

The paper presents a new methodology to model material failure, in two-dimensional reinforced concrete members, using the Continuum Strong Discontinuity Approach (CSDA). The mixture theory is used as the methodological approach to model reinforced concrete as a composite material, constituted by a plain concrete matrix reinforced with two embedded orthogonal long fiber bundles (rebars). Matrix failure is modeled on the basis of a continuum damage model, equipped with strain softening, whereas the rebars effects are modeled by means of phenomenological constitutive models devised to reproduce the axial non-linear behavior, as well as the bondslip and dowel effects. The proposed methodology extends the fundamental ingredients of the standard Strong Discontinuity Approach, and the embedded discontinuity finite element formulations, in homogeneous materials, to matrix/fiber composite materials, as reinforced concrete. The specific aspects of the material failure modeling for those composites are also addressed. A number of available experimental tests are reproduced in order to illustrate the feasibility of the proposed methodology. (c) 2007 Elsevier B.V. All rights reserved.

Application of a model updating technique for health condition monitoring and damage detection of flexible structures

This paper discusses the application of a damage detection methodology to monitor the location and extent of partial structural damage. The methodology combines, in an iterative way, the model updating technique based on frequency response functions (FRF) with monitoring data aiming at identifying the damage area of the structure. After the updating procedure reaches a good correlation between the models, it compares the parameters of the damage structure with those of the undamaged one to find the deteriorated area. The influence of the FEM mesh size on the evaluation of the extent of the damage has also been discussed. The methodology is applied using real experimental data from a spatial frame structure.

Pressure field in the cathode-anode region of a high-power klystron amplifier

The pressure field of a high-power klystron amplifier in the cathode and anode region was investigated. The investigation was performed using a 1.3 GHz, 100 A and 240 kV high-power klystron with five reentrant coaxial cavities, assembled in cylindrical drift tube 1.2 m long. The diffusion equation in mathematical model was also solved by using a 3-D finite element method code, in order to obtain pressure profile in region of interest. The results show that density profile of molecules between cathode-anode region was determined, where cathode pressure is approximately 10% higher than anode pressure.

Tilted and Short Implants Supporting Fixed Prosthesis in an Atrophic Maxilla: A 3D-FEA Biomechanical Evaluation

Purpose: This study compared the biomechanical behavior of tilted long implant and vertical short implants to support fixed prosthesis in an atrophic maxilla. Materials and Methods: The maxilla model was built based on a tomographic image of the patient. Implant models were based on micro-computer tomography imaging of implants. The different configurations considered were M4S, four vertical anterior implants; M4T, two mesial vertical implants and two distal tilted (45°) implants in the anterior region of the maxilla; and M6S, four vertical anterior implants and two vertical posterior implants. Numerical simulation was carried out under bilateral 150N loads applied in the cantilever region in axial (L1) and oblique (45°) (L2) direction. Bone was analyzed using the maximum and minimum principal stress (σmax and σmin), and von Mises stress (σvM) assessments. Implants were analyzed using the σvM. Results: The higher σmax was observed at: M4T, followed by M6S/L1, M6S/L2, M4S/L2, and M4S/L1 and the higher σvM: M4T/L1, M4T/L2 and M4S/L2, M6S/L2, M4S/L1, and M6S/L1. Conclusions: The presence of distal tilted (all-on-four) and distal short implants (all-on-six) resulted in higher stresses in both situations in the maxillary bone in comparison to the presence of vertical implants (all-on-four). © 2013 Wiley Periodicals, Inc.

A model for computing vibration induced stresses of electronic components in a general flexible mounting

This paper develops a novel full analytic model for vibration analysis of solid-state electronic components. The model is just as accurate as finite element models and numerically light enough to permit for quick design trade-offs and statistical analysis. The paper shows the development of the model, comparison to finite elements and an application to a common engineering problem. A gull-wing flat pack component was selected as the benchmark test case, although the presented methodology is applicable to a wide range of component packages. Results showed very good agreement between the presented method and finite elements and demonstrated the usefulness of the method in how to use standard test data for a general application. © 2013 Elsevier Ltd.