Robuste Berechnungsverfahren zur nichtlinearen dynamischen Analyse von Balken- und Schalenstrukturen

Gegenwärtige und zukünftige dynamisch beanspruchte, schlanke Strukturen aus mehrschichtig verbundenen, hyperelastischen Werkstoffen, z. B. Windenergieanlagen und Hubschrauber usw., sind sehr komplex. Eine genaue Untersuchung im Zeitbereich erfordert den Einsatz von Methoden, die kinematische, geometrische sowie, bis zu einem gewissen Grad, materielle Nichtlinearitäten berücksichtigen sollten. Daher könnten Simulationen mit Beachtung von großen Verschiebungen, Drehungen und Verzerrungen nötig sein, um das mechanische Verhalten akkurat zu vorhersagen zu vermögen. Zunächst werden die Bewegungsgleichungen räumlich diskretisiert. Dann werden die zum Teil diskretisierten Gleichungen mittels eines Integrationsverfahrens zeitlich diskretisiert. Solche diskreten Gleichungen sind sehr steif, sodass sich die Berechnung der langzeitigen Lösung erschwert. Darüber hinaus ist die Einführung von Nebenbedingungen oft nötig, um komplexere Strukturen aufstellen zu können, wodurch sich die Komplexität erhöht wird und unerwünschte Eigenschaften noch verschärft werden. Um Robustheit zu gewinnen, sollen Berechnungsverfahren hergeleitet werden, die die zugrunde legende Physik in gewissem Maße erhalten können und gleichzeitig den hochfrequenten Anteil der Lösung unterdrücken können. Die Erfüllung dieser Anforderungen stellt sich als sehr herausfordernd dar. Das Hauptziel dieser Arbeit liegt an der Entwicklung von Berechnungsverfahren zur Vertiefung des Verständnises des dynamischen Verhaltens von Balken- und Schalenstrukturen. Um dieses Ziel zu erreichen, wird ein umfassender Ansatz vorgeschlagen. Dieser besteht aus: i) Einer auf Direktoren basierenden, Finite-Elemente-Formulierung für den geometrisch exakten Balken mit allgemeinen Querschnittseigenschaften; ii) einer auf Direktoren basierenden, Finite-Elemente-Formulierung für die Kontinuumsmechanik-basierte Schale aus mehrschichtig verbundenen, hyperelastischen Werkstoffen; iii) einer vereinheitlichten Beschreibung von Starrkörpern, Balken und Schalen und deren Kopplung mittels kinematischer Nebenbedingungen; und, iv) einem robusten Integrationsverfahren basierend auf dem gemittelten Vektorfeld. Des Weiteren wird Folgendes ebenfalls vorgeschlagen: v) Die Partikularisierung der Hauptgeodätenanalyse zur nichtlinearen Identifikation von Bewegungsmoden an Balkenstrukturen; und, vi) ein neues konservatives/dissipatives Integrationsverfahren für allgemeine nichtlineare mechanische Systeme basierend auf optimierten Modifizierungen höherer Ordnung, die die Defizite der Mittelpunktsregel beheben. Die sehr gute Leistung des vorgeschlagenen Ansatzes wird durch mehrere Beispiele unterschiedlicher Komplexität nachgewiesen.Existing and new slender structures made of hyperelastic multilayer composite materials subject to highly dynamic loads, e.g., wind turbines, helicopters, cars, speedboats or submarines inter alia, are very complex. Their dynamic analysis requires fully nonlinear formulations, at least from the kinematic and geometric point of view, and also to some extent from the material point of view. Thus, simulations in time-domain involving large displacements, rotations and strains could be necessary to predict their mechanical behavior accurately. Numerical procedures to carry out such simulations rely firstly on the partial discretization in space of the governing equations, for instance with finite elements. These semi discrete equations are further discretized in time with an integration scheme. The resulting discrete equations are in fact very stiff and therefore, the computation of the long-term behavior could be problematic. In many applications, the introduction of constraints is also necessary for rendering more complex structures. Besides introducing a new level of complexity, this can sharpen conditioning problems already present in the fully discrete problem. Additionally, we also require procedures able to annihilate the unwanted unresolved high-frequency content without upsetting of the underlying physics. However, the simultaneous satisfaction of all these requirements is a very challenging task. The main objective of this work is to provide means intended for helping to understand further the nonlinear dynamics of beam and shell structures made of hyperelastic multilayer composite materials subject to highly dynamic loads. To accomplish this main goal, we propose a unifying computational approach that relies on: i) a director-based finite-element formulation for geometrically exact beams with general cross-section properties; ii) a director-based finite-element formulation for solid-degenerate shells made of hyperelastic multilayer composite materials; iii) a unifying description of rigid bodies, geometrically exact beams and solid-degenerate shells and their combination with kinematic pairs, which avoids inherently the necessity of rotational degrees of freedom; and, iv) a robust integration scheme based on the average vector field. Additionally, we propose: v) the particularization of the principal geodesic analysis to identify motion patters exhibited by beam structures in a purely nonlinear setting; and, vi) a new conservative/dissipative integration method for general nonlinear mechanical systems, which relies on high-order correction terms that optimally modify the midpoint rule. Moreover, the excellent numerical performance of the proposed unifying framework and procedures is illustrated by means of a good number of examples with different difficulty levels

Finite Element Analysis of Structures using a General Higher-Order Plate and One-Dimensional Theories for Classical and Cosserat Continuum Having Constrained Microrotation

In this study nonlinear finite element models for beams and plates considering general higher-order expansions of the displacement fields have been developed, The models account for Cosserat continuum having constrained micro-rotation. The models can be used to analyze solid continua with very small inclusions or small scale structures in which material length scales, that classical continuum mechanics fails to capture, play a role. The beam and plate models developed herein are used to study the effect of different length scale parameters and the orientation of small inclusions. Also, the classical plate theory for rotation gradient dependent potential energy (Cosserat continuum for constrained micro-rotation) is applied to model nano-indentation on a carbon nanotube (CNT)-reinforced hard coating on an elastic substrate to see the effect of CNT reinforcement, which is modeled by small material length scale parameters. A general higher-order one-dimensional theory has also been developed in cylindrical and curvilinear cylindrical coordinate systems by considering a very general displacement approximation of arbitrary cross-section of a body in polar coordinates. Based on this approximation, the governing equations of motion have been derived using the principle of virtual displacements for large deformation case. Further, a nonlinear finite element model is developed to determine nonlinear response using the theories presented. In the numerical examples, the finite element model is used to analyze shell and rod-like structures for large deformation. Also, these higher-order one-dimensional theories are very relevant for the analysis of shell and rod-like structures of Cosserat continuum for constrained micro rotation because all gradient elasticity theories require C1 or higher-order continuity of the displacement variables, which is hard to achieve in the case of two or three dimensions, especially for non-rectangular grids. The one-dimensional theory developed herein allows continuity of any desired order of the variables by general Hermite interpolation functions in the finite element model

A Numerical Investigation of Wellbore Stability Problems Using an Elastoplastic Model

Wellbore stability analysis acts an important role in the drilling design to avoid pipe-stuck, lost circulation and the other instability-induced problems. However, the conventional linear elastic model used by the industry is too conservative in predicting the mud weight window. This project is aimed at improving the accuracy of wellbore stability analysis. An elastoplastic model with Drucker-Prager yield criterion featured by strain hardening is proposed to characterize the rock behavior. Object-oriented finite element analysis simulator, NSMOOM, is programmed in MATLAB. The simulator is verified with the analytical solution in the elastic domain and with the commercial software ABAQUS in the elastoplastic domain. Upon the good verification results, the code is applied to an under-balanced-drilling case. For the case study, a good match is shown between the prediction of the proposed elastoplastic model and the actual wellbore response. On the other hand, no available mud weight window for under-balanced-drilling can be calculated by the pure elastic model. In conclusion, the proposed model provides a more realistic tool to predict wellbore stability

On the Statics, Dynamics, and Stability of Continuum Robots: Model Formulations and Efficient Computational Schemes

This dissertation presents advances in continuum-robotic mathematical-modeling techniques. Specifically, problems of statics, dynamics, and stability are studied for robots with slender elastic links. The general procedure within each topic is to develop a continuous theory describing robot behavior, develop a discretization strategy to enable simulation and control, and to validate simulation predictions against experimental results.Chapter 1 introduces the basic concept of continuum robotics and reviews progress in the field. It also introduces the mathematical modeling used to describe continuum robots and explains some notation used throughout the dissertation.The derivation of Cosserat rod statics, the coupling of rods to form a parallel continuum robot (PCR), and solution of the kinematics problem are reviewed in Chapter 2. With this foundation, soft real-time teleoperation of a PCR is demonstrated and a miniature prototype robot with a grasper is controlled.Chapter 3 reviews the derivation of Cosserat rod dynamics and presents a discretization strategy having several desirable features, such as generality, accuracy, and potential for good computational efficiency. The discretized rod model is validated experimentally using high speed camera footage of a cantilevered rod. The discretization strategy is then applied to simulate continuum robot dynamics for several classes of robot, including PCRs, tendon-driven robots, fluidic actuators, and concentric tube robots.In Chapter 4, the stability of a PCR is analyzed using optimal control theory. Conditions of stability are gradually developed starting from a single planar rod and finally arriving at a stability test for parallel continuum robots. The approach is experimentally validated using a camera tracking system.Chapter 5 provides closing discussion and proposes potential future work

Large displacements of FGSW beams in thermal environment using a finite element formulation

The large displacements of functionally graded sandwich (FGSW) beams in thermal environment  are studied using a finite element formulation. The beams are composed of three layers, a homogeneous core and two functionally graded face sheets with volume fraction of constituents following a power gradation law. The material properties of the beams are considered to be temperature-dependent.  Based on Antman beam model and the total Lagrange formulation, a two-node nonlinear beam element taking the effect of temperature rise into account  is formulated and employed in the study. The element with explicit expressions for the internal force vector and tangent stiffness matrix is derived using linear interpolations and reduced integration technique to avoid the shear locking. Newton-Raphson based iterative algorithm is employed in combination with the arc-length control method to compute the large displacement response of a cantilever FGSW beam subjected to end forces.  The accuracy of the formulated element is confirmed through a comparison study. The effects of the material inhomogeneity, temperature rise and layer thickness ratio on the large deflection response of the beam are examined and highlighted

\u201cMASONRY ARCH BRIDGES IN VENICE: EXPERIMENTAL AND NUMERICAL PROCEDURES FOR STRUCTURAL IDENTIFICATION\u201d

Masonry arch bridges are an important part of architectural historical heritage. Their presence is a characteristic feature of the Italian and European landscape. A large number of research and studies about. This theme have been produced in literature during time. Regarding Venetian bridges, except for the most famous architectures. Data are lacking given by research results are lacking. A procedure for structural identification and for the evaluation of the material mechanical characteristics for historical masonry bridges is here presented with the aim of their conservation and restoration. The procedure, based on experimental measurements and numerical analyses, requires, at first, the measurements of the bridge\u2019s fundamental frequencies, then, through the calibration of bridge FE Model, allows the estimation of the average materials characteristics. In particular, for the frequency acquisition data, the procedure proposes the use of a compact digital tromograph, a highly sophisticated measuring device, equipped with accelerometric and velocimetric transducers, that allows fast and low cost vibration measurements. Successive analyses, by means of fast Fourier transform, permit to estimate the fundamental frequency of the structure. For one study case the validity of the results obtained is confirmed by making a comparison with a measurement campaign performed using accelerometers as instruments

The Multiscale Damage Mechanics in Objected-oriented Fortran Framework

We develop a dual-purpose damage model (DPDM) that can simultaneously model intralayer damage (ply failure) and interlayer damage (delamination) as an alternative to conventional practices that models ply failure by continuum damage mechanics (CDM) and delamination by cohesive elements. From purely computational point of view, if successful, the proposed approach will significantly reduce computational cost by eliminating the need for having double nodes at ply interfaces. At the core, DPDM is based on the regularized continuum damage mechanics approach with vectorial representation of damage and ellipsoidal damage surface. Shear correction factors are introduced to match the mixed mode fracture toughness of an analytical cohesive zone model. A predictor-corrector local-nonlocal regularization scheme, which treats intralayer portion of damage as nonlocal and interlayer damage as local, is developed and verified. Two variants of the DPDM are studied: a single- and two- scale DPDM. For the two-scale DPDM, reduced-order-homogenization (ROH) framework is employed with matrix phase modeled by the DPDM while the inclusion phase modeled by the CDM. The proposed DPDM is verified on several multi-layer laminates with various ply orientations including double-cantilever beam (DCB), end-notch-flexure (ENF), mixed-mode-bending (MMB), and three-point-bending (TPB). The simulation is executed in the platform of FOOF (Finite element solver based on Object-Oriented Fortran). The objective of FOOF is to develop a new architecture of the nonlinear multiphysics finite element code in object oriented Fortran environment. The salient features of FOOF are reusability, extensibility, and performance. Computational efficiency stems from the intrinsic optimization of numerical computing intrinsic to Fortran, while reusability and extensibility is inherited from the support of object-oriented programming style in Fortran 2003 and its later versions. The shortcomings of the object oriented style in Fortran 2003 (in comparison to C++) are alleviated by introducing the class hierarchy and by utilizing a multilevel programming style

Physically-based 6-DoF Nodes Deformable Models: Application to Connective Tissues Simulation and Soft-Robots Control

The medical simulation is an increasingly active research field. Yet, despite the promising advance observed over the past years, the complete virtual patient’s model is yet to come. There are still many avenues for improvements, especially concerning the mechanical modeling of boundary conditions on anatomical structures.So far, most of the work has been dedicated to organs simulation, which are generally simulated alone. This raises a real problem as the role of the surrounding organs in the boundary conditions is neglected. However, these interactions can be complex, involving contacts but also mechanical links provided by layers of soft tissues. The latter are known as connective tissues or fasciae. As a consequence, the mutual influences between the anatomical structures are generally simplified, weakening the realism of the simulations.This thesis aims at studying the importance of the connective tissues, and especially of a proper modeling of the boundary conditions. To this end, the role of the ligaments during laparoscopic liver surgery has been investigated. In order to enhance the simulations’ realism, a mechanical model dedicated to the connective tissues has been worked out. This has led to the development of a physically-based method relying on material points that can, not only translate, but also rotate themselves. The goal of this model is to enable the simulation of multiple organs linked by complex interactions.In addition, the work on the connective tissues model has been derived to be used in soft robotics. Indeed, the principle of relying on orientable material points has been used to developed a reduced model that can reproduce the behavior of more complex structures. The objective of this work is to provide the means to control – in real-time – a soft robot made of a deformable arm.La simulation médicale est un domaine de recherche de plus en plus actif. Cependant, malgré les avancées prometteuses observées ces dernières années, le modèle complet du patient virtuel reste un objectif ambitieux. Il existe encore de nombreuses opportunités de recherche, notamment concernant la modélisation mécanique des conditions aux limites des organes.Jusqu'à présent, la majorité des travaux était consacrée à la simulation d'organes, ces derniers étant généralement simulés seuls. Cette situation pose un réel problème car l'influence qu'ont les organes environnants sur les conditions aux limites est négligée. Ces interactions peuvent être complexes, impliquant des contacts mais aussi des liaisons mécaniques dues à des couches de tissus connus sous le nom de tissus conjonctifs ou fasciae. Pour cette raison, les influences mutuelles entre les structures anatomiques sont généralement simplifiées, diminuant le réalisme des simulations.Cette thèse visé à étudier l'importance des tissus conjonctifs, et plus particulièrement d'une bonne modélisation des conditions aux limites. Dans ce but, le rôle des ligaments lors d'une intervention chirurgicale sur la foie par laparoscopie a été étudié. Afin d'améliorer le réalisme des simulations, un modèle mécanique dédié aux tissus conjonctifs a été mis au point. Ainsi, une méthode basée sur la mécanique des milieux continus et un ensemble de nœuds à 6 degrés de liberté a été développée. L'objectif de ce modèle étant de permettre la simulation simultanée de plusieurs organes liés par des interaction complexes.En outre, les travaux sur les tissus conjonctifs ont donné lieu à la mise au point d'une méthode de modélisation utilisée dans le cadre des robots déformables. Cette méthode permet un contrôle précis, et temps-réel, d'un bras robotisé déformable. En effet, l'utilisation de nœuds orientables a permis de développer un modèle a nombre de degrés de liberté réduit, qui permet de reproduire le comportement de structures plus complexes

Homogenization Methods for Problems with Multiphysics, Temporal and Spatial Coupling

There are many natural and man-made materials with heterogeneous micro- or nanostructure (fine-scale structure) which represent a great interest for industry. Therefore there is a great demand for computational methods capable to model mechanical behavior of such materials. Direct numerical simulation resolving all fine-scale details using very fine mesh often becomes very expensive. One of alternative effective group of methods is the homogenization methods allowing to model behavior of materials with heterogeneous fine-scale structure. The essence of homogenization is to replace heterogeneous material with some equivalent effectively homogeneous material. The homogenization methods are proven to be effective in certain classes of problems while there is need to improve their performance, which includes extension of the range of applicability, simplification, usage with conventional FE software and reducing computational cost. In this dissertation methods extending the range of applicability of homogenization are developed. Firstly, homogenization was extended of the case of full nonlinear electromechanical coupling with large deformations, which allows simulating effectively behavior of electroactive materials such as composites made of electroactive polymers. Secondly, homogenization was extended on wave problems where dispersion is significant and should be accounted for. Finally, the homogenization was extended on the case where the size of microstructure. The distinctive feature of the methods introduced in this dissertation is that they don't require higher order derivatives and can be implemented with conventional FE codes. The performance of methods is tested on various examples using Abaqus