Coupled structural, thermal, phase-change and electromagnetic analysis for superconductors, volume 1

This research program has dealt with the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromagnetic subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase-change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements; (2) finite element modeling of the electromagnetic problem; (3) coupling of thermal and mechanical effects; and (4) computer implementation and solution of the superconductivity transition problem. The research was carried out over the period September 1988 through March 1993. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles; (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements; and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects; and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The grant has fully supported the thesis work of one doctoral student (James Schuler, who started on January 1989 and completed on January 1993), and partly supported another thesis (Carmelo Militello, who started graduate work on January 1988 completing on August 1991). Twenty-three publications have acknowledged full or part support from this grant, with 16 having appeared in archival journals and 3 in edited books or proceedings

Two-Way Fluid-Structure Coupling Methodology for Modeling 3D Flexible Hydrofoils in Viscous Flow

RÉSUMÉ Les surfaces portantes. telles que des pâles, ailes, et hydrofoil sont sujets à des instabilités comme la divergence, le battement et la résonnance qui peuvent provoquer la fatigue de la structure et réduire sa tenue en service. Par conséquent, il est important de comprendre et de prédire avec précision la réponse et la stabilité de telles structures afin d’en assurer la sécurité, et de faciliter la conception et optimisation de concepts nouveaux et existants. L’interaction entre un écoulement et une structure, nommée interaction fluide-structure (IFS), doit être prise en compte lors de l’étude la réponse élastique et des instabilités de surfaces portantes. Pour de telles applications, l’écoulement et la structure sont couplés au travers de la charge qui s’exerce sur la structure par le fluide, et la déformation qui en découle. Pour certaines applications IFS, le fluide et le solide peuvent être couplés par un transfert unidirectionnel de la charge. Dans ce cas, un champ donné peut fortement affecter l’autre sans l’être lui-même. Cependant, pour certaines applications en ingénierie, où il y a une relation forte et potentiellement non-linéaire entre ces champs, un couplage unidirectionnel n’est pas adéquat. Alors, les déplacements de la structure causés par l’écoulement accentuent les forces du fluide de telle sorte que le fluide et la structure intéragissent en boucle de façon complexe. Donc, une analyse bi-directionnelle doit être entreprise. Les structure légères et flexibles sont couramment utilisées grâce aux avancées récentes dans les technologies des matériaux afin d’améliorer les caractéristiques hydrodynamiques et structurelles par rapport aux matériaux lourds et rigides. Dans cette thèse, on cherche une meilleure compréhension de la phénomènologie hydroélastique d’hydrofoils hautement flexibles, qui subissent de grandes déformations sous de fortes charges. Ceci milite en faveur d’une méthodologie IFS bidirectionnelle fortement couplée, en plus de l’incorporation de techniques numériques avancées pour la modélisation de la déformation de maillages adaptés. Pour des nombres de Reynolds moyens à élevés, le développement d’un écoulement turbulent autour de l’hydrofoil provoque un transfert du mouvement perpendiculaire à la paroi et permet à l’écoulement de se rattacher, et ainsi former une bulle laminaire de séparation (Laminar Separation Bubble, LSB). Le décrochage de l’écoulement, la formation de tourbillons dans le sillage, la localisation et le mouvement de la bulle laminaire sont tous des phénomènes qui affectent les charges hydrodynamiques et les vibrations de la structure. Par conséquent, une méthodologie numérique avancée, avec une précision spatiale suffisamment élevée a été incorporée dans ce travail pour capturer finement ces phénomènes à l’interface fluide-structure, tels que l’apparition et l’étendue de la zone de séparation.----------ABSTRACT Lifting bodies, such as blades, wings, and hydrofoils, may be subject to instabilities, such as divergence, flutter, and resonance, which can fatigue the structure and reduce its operational longevity. Therefore, it is important to understand and accurately predict the response and stability of such structures to ensure their structural safety and facilitate the design and optimization of new and existing concepts. The interaction between fluid and structure, known as Fluid-Structure Interaction (FSI), should be taken into account in the study of elastic response and instabilities of flexible lifting bodies. In such applications, the fluid flow and structure are coupled through the loads exerted on the structure by the fluid, which results in the the structural deformation. In some FSI applications, fluid and solid can be coupled by one-way (unidirectional) load transfer. In this case, a given field may strongly affect, but not be affected significantly by the other field. However, for some practical engineering applications, in which there is a strong and potentially nonlinear relationship between the fields, one-way coupling is not adequate. In such cases, the structural displacement caused by the flow further enhances the fluid forces in such a way that both fluid and structure are interacting in a complex feedback fashion. Hence, two-way FSI analysis needs to be undertaken. Light-weight, flexible structures are widely used through recent advances in material technologies to improve hydrodynamic and structural performance compared to heavy and stiff materials. This project seeks to gain greater insight into the hydroelastic response of highly flexible hydrofoils, which undergo large deformation when subjected to high hydrodynamic loadings. This increases the necessity of incorporating strongly-coupled two-way FSI methodology in addition to the numerical challenges in mesh deformation modelling. At moderate to high Reynolds numbers, the development of turbulent flow around a hydrofoil causes a momentum transfer normal to the wall and allows the flow to re-attach, and form a Laminar Separation Bubble (LSB). Flow separation, formation of trailing edge vortices, location and movement of the LSB affect the hydrodynamic loading and structural vibration. Hence, an advanced numerical technique with sufficiently high spatial accuracy is incorporated in the present study to precisely capture these local interface phenomena, such as the onset and the amount of flow separation. The interaction between the foil and surrounding flow involve significant three-dimensional features that will not be neglected in the present study

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Modelling-based design of anisotropic piezocomposite transducers and multi-domain analysis of smart structures

Piezocomposites are attracting widespread interest since they can offer greater flexibility and better performances in specific applications with respect to traditional piezoelectric wafers. Design of piezocomposites requires accurate homogenisation models for the prediction of the equivalent electro-mechanical properties. In macro-scale models of structures with piezocomposite transducers, these properties are adopted in order to avoid the complexity of the piezocomposite microstructure. In the case of smart structures the accurate modelling of the actuation and the response of the structure is of primary importance. If classical structural finite elements are not sufficiently accurate, higher order or solid elements should be adopted. Thanks to adaptation or mixed-dimensional methods, it is possible to adopt computationally expensive higher order or solid elements only in some sub-domains of the structure. In this work, the modelling of smart structures equipped with thin piezoelectric transducers is considered in a multi-scale framework. Micromechanical homogenisation models are developed and employed for the prediction of the equivalent properties of piezocomposites. A micromechanical model based on the concept of inclusion is proposed to investigate the influence of the shape of the inclusions, of the constituent materials and of the polarisation on the equivalent properties. It has been found that fibre-shaped inclusions should be considered in order to obtain piezocomposites with strong piezoelectric effect and to have at the same time high direction-dependence. The equivalent properties of Macro Fiber Composites are determined via the Asymptotic Homogenisation Method (AHM) with an analytical solution and with a numerical solution via FEM which takes into account the effect of the electrodes. AHM analytical solution is adopted to investigate the effect of the material properties of the matrix on the overall piezocomposite. Results indicate that low values of the Young's modulus and of the Poisson's ratio yield high directional dependence in the piezoelectric properties. A laminated design with anisotropic layers and a piezocomposite layer is investigated via UFM. A configuration with maximum directional dependence in terms of equivalent piezoelectric strain constants is proposed, whereas maximum directional dependence in terms of piezoelectric stress constants is proved to be not achievable with such a design. Hierarchical finite elements for structural analyses based on a Unified Formulation (UF) by Carrera are developed and coupled via the Arlequin method proposed by Ben Dhia. Solid, plate and beam finite elements for mechanical and for piezoelectric problems are presented. Via UF, higher order and piezoelectric elements can be formulated straightforwardly. These elements are combined in variable kinematic solutions in the Arlequin framework. Higher-order elements are adopted locally where the stress field is three-dimensional, whereas the remaining parts of the structure are modelled with computationally cheap lower-order elements. Two electro-mechanical coupling operator for the Arlequin method in the context of piezoelectric analyses are proposed. Results are validated towards monomodel solutions and three-dimensional analytical and numerical reference solutions. Accurate solutions are obtained reducing the computational costs

Multivariate relationship specification and visualization

In this dissertation, we present a novel method for multivariate visualization that focuses on multivariate relationshipswithin scientific datasets. Specifically, we explore the considerations of such a problem, i.e. we develop an appropriate visualization approach, provide a framework for the specification of multivariate relationships and analyze the space of such relationships for the purpose of guiding the user toward desired visualizations. The visualization approach is derived from a point classification algorithm that summarizes many variables of a dataset into a single image via the creation of attribute subspaces. Then, we extend the notion of attribute subspaces to encompass multivariate relationships. In addition, we provide an unconstrained framework for the user to define such relationships. Althoughwe intend this approach to be generally applicable, the specification of complicated relationships is a daunting task due to the increasing difficulty for a user to understand and apply these relationships. For this reason, we explore this relationship space with a common information visualization technique well suited for this purpose, parallel coordinates. In manipulating this space, a user is able to discover and select both complex and logically informative relationship specifications