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Model and parameter identification through Bayesian inference in solid mechanics Rappel, Hussein Doctoral thesis (2018) Predicting the behaviour of various engineering systems is commonly performed using mathematical models. These mathematical models include application-specific parameters that must be identified from ... [more ▼] Predicting the behaviour of various engineering systems is commonly performed using mathematical models. These mathematical models include application-specific parameters that must be identified from measured data. The identification of model parameters usually comes with uncertainties due to model simplifications and errors in the experimental measurements. Quantifying these uncertainties can effectively improve the predictions as well as the performance of the engineering systems. Bayesian inference provides a probabilistic framework for quantifying these uncertainties in parameter identification problems. In a Bayesian framework, the user's initial knowledge, which is represented by a probability distribution, is updated by measurement data through Bayes' theorem. In the first two chapters of this thesis, Bayesian inference is developed for the identification of material parameters in elastoplasticity and viscoelasticity. The effect of the user's prior knowledge is systematically studied with respect to the number of measurements available. In addition, the influence of different types of experiments on the uncertainty is studied. Since all mathematical models are simplifications of reality, uncertainties of the model itself may also be incorporated. The third chapter of this thesis presents a Bayesian framework for parameter identification in elastoplasticity in which not only the uncertainty of the experimental output is included (i.e. stress measurements), but also the uncertainty of the model and the uncertainty of the experimental input (i.e. strain). Three different formulations for describing the model uncertainty are considered: (1) a random variable which is taken from a normal distribution with constant parameters, (2) a random variable which is taken from a normal distribution with an input-dependent mean, and (3) a Gaussian random process with a stationary covariance function. In the fourth chapter of this thesis, a Bayesian scheme is proposed to identify material parameter distributions, instead of material parameters. The application in this chapter are random fibre networks, in which the set of material parameters of each fibre is assumed to be a realisation from a material parameter distribution. The fibres behave either elastoplastically or in a perfectly brittle manner. The goal of the identification scheme is to avoid the experimentally demanding task of testing hundreds of constituents. Instead, only 20 fibres are considered. In addition to their material randomness, the macroscale behaviours of these fibre networks are also governed by their geometrical randomness. Another question aimed to be answered in this chapter is therefore is `how precise the material randomness needs to be identified, if the geometrical randomness will also influence the macroscale behaviour of these discrete networks'. [less ▲] Detailed reference viewed: 202 (33 UL)Model and Solution Methods for the Mixed-Fleet Multi-Terminal Bus Scheduling Problem ; Rinaldi, Marco ; et al in Transportation Research Procedia (2019, September) Detailed reference viewed: 28 (2 UL)Model I cohesive zone models of different rank coals ; Lian, Haojie ; et al in International Journal of Rock Mechanics and Mining Sciences (2019), 115 The present work develops cohesive zone models (CZM), i.e. cohesion-separation laws, for mode I fractures in different rank coals, including weakly caking coals, gas coals, fat coals, meager-lean coals ... [more ▼] The present work develops cohesive zone models (CZM), i.e. cohesion-separation laws, for mode I fractures in different rank coals, including weakly caking coals, gas coals, fat coals, meager-lean coals and anthracite, through disk-shaped compact tension tests. Firstly, the experiments show that with the coal rank rising, the critical crack separation displacements and the degrees of the nonlinearity of the softening function decline gradually. By fitting the experimental data with the four commonly used cohesive zone models including the power law, the exponential law, the bilinear law and the linear law, the best-fitted model for each rank of coals was identified and the corresponding parameters were found. Secondly, to arrive at a general CZM formulation for the different rank coals, Karihaloo’s polynomial law was employed, which also gave better fit to the experimental data compared with the aforementioned four CZMs. After obtaining the CZM for coals, fracture energy was evaluated which is equal to the area under the softening curve. With the increase of the coal rank, the fracture energy reduces but its coefficient of variation increases. Thirdly, the geometric characteristics of fractures in different rank coals are studied. The lower rank coals have more tortuous crack propagation paths and larger roughness coefficients, whereas the higher rank coals possess wider average fracture apertures. Lastly, in order to further test the applicability of the obtained cohesion-separation laws, we implemented the Karihaloo’s polynomial CZM and the bilinear CZM into the cohesive elements of ABAQUS® using the user-subroutine VUMAT, and thereby simulated the crack propagation in single-edge notched beams made of weakly caking coals, fat coals, and meager-lean coals, respectively. It is found that the numerical results based on Karihaloo’s polynomial CZM have a better agreement with the experimental data than the bilinear CZM [less ▲] Detailed reference viewed: 37 (0 UL)Model order reduction accelerated Monte Carlo stochastic isogeometric method for the analysis of structures with high-dimensional and independent material uncertainties Ding, Chensen ; ; et al in Computer Methods in Applied Mechanics and Engineering (2019), 349 Structural stochastic analysis is vital to engineering. However, current material related uncertainty methods are mostly limited to low dimension, and they mostly remain unable to account for spatially ... [more ▼] Structural stochastic analysis is vital to engineering. However, current material related uncertainty methods are mostly limited to low dimension, and they mostly remain unable to account for spatially uncorrelated material uncertainties. They are not representative of realistic and practical engineering situations. In particular, it is more serious for composite structures comprised of dissimilar materials. Therefore, we propose a novel model order reduction via proper orthogonal decomposition accelerated Monte Carlo stochastic isogeometric method (IGA-POD-MCS) for stochastic analysis of exactly represented (composite) structures. This approach particularly enables high-dimensional material uncertainties wherein the characteristics of each element are independent. And the novelties include: (1) the structural geometry is exactly modeled thanks to isogeometric analysis (IGA), as well as providing more accurate deterministic and stochastic solutions, (2) we innovatively consider high-dimensional and independent material uncertainties by separating the stochastic mesh from the IGA mesh, and modeling different stochastic elements to have different (independent) uncertainty behaviors, (3) the classical Monte Carlo simulation (MCS) is employed to universally solve the high-dimensional uncertainty problem. However, to circumvent its computational expense, we employ model order reduction via proper orthogonal decomposition (POD) into the IGA coupled MCS stochastic analysis. In particular, we observe that this work decouples all IGA elements and hence permits independent uncertainty models easily, thereby the engineering problem is modeled to be more realistic and authentic. Several illustrative numerical examples verify the proposed IGA-POD-MCS approach is effective and efficient; and the larger the scale of the problem is, the more advantageous the method will become. [less ▲] Detailed reference viewed: 18 (0 UL)Model order reduction applied to ALE‐fluid dynamics Baroli, Davide ; Zilian, Andreas in Proceedings in Applied Mathematics and Mechanics (2019) Detailed reference viewed: 62 (4 UL)A model order reduction approach to construct efficient and reliable virtual charts in computational homogenisation ; ; et al in Proceedings of the 17th U.S. National Congress on Theoretical and Applied Mechanics (2014, June 15) Computational homogenisation is a widely spread technique to calculate the overall properties of a composite material from the knowledge of the constitutive laws of its microscopic constituents [1, 2 ... [more ▼] Computational homogenisation is a widely spread technique to calculate the overall properties of a composite material from the knowledge of the constitutive laws of its microscopic constituents [1, 2]. Indeed, it relies on fewer assumptions than analytical or semi-analytical homogenisation approaches and can be used to coarse-grain a large range of micro-mechanical models. However, this accuracy comes at large computational costs, which prevents computational homogenisation from being used routinely in optimisation, even in the context of linear elastic materials. Indeed, a unit cell problem has to be solved for each microscopic distribution of interest in order to obtain the corresponding homogenised material constants. In the context of nonlinear, time-dependant problem, the computational effort becomes even greater as computational homogenisation requires solving for the time-evolution of the microstructure at every point of the macroscopic domain. In this paper, we propose to address these two issues within the unified framework of projection-based model order reduction (see for instance [3, 4, 5, 6]). The smoothness of the solution of the unit cell problem with respect to parameter or time variations is used to create a reduced order model with very few degrees of freedom, hence reducing the computational burden by orders of magnitude. [1] Tarek J. Zohdi and Peter Wriggers. Introduction to Computational Micromechanics, volume 20 of lecture notes in applied and computational mechanics. Springer, 2005. [2] M.G.D. Geers, V.G. Kouznetsova, and W.A.M. Brekelmans. Multi-scale computational homogenization: Trends and challenges. J. Computational Applied Mathematics, 234(7):2175–2182, 2010. [3] D.B.P. Huynh G. Rozza and A.T. Patera. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations: Application to transport and continuum mechanics. Archives of Computational Methods in Engineering, 15(3):229–275, 2008. [4] D. Amsallem and C. Farhat. An Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity. AIAA Journal, 46(7):1803–1813, 2008. [5] P. Kerfriden, P. Gosselet, S. Adhikari, and S.P.-A. Bordas. Bridging proper orthogonal decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems. Computer Methods in Applied Mechanics and Engineering, 200(5- 8):850–866, 2011. [6] P. Kerfriden, J.-C. Passieux, and S.P.-A. Bordas. Local/global model order reduction strategy for the simulation of quasi-brittle fracture. International Journal for Numerical Methods in Engineering, 89(2):154–179, 2011. [7] M. Barrault, Y. Maday, N.C. Nguyen, and A.T. Patera. An ’empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus de Math´ematiques, 339(9):667–672, 2004. [less ▲] Detailed reference viewed: 328 (6 UL)Modellierung und Validierung von Simulationsansätzen für die aussenliegende Lufttemperierung ; Scholzen, Frank ; Maas, Stefan et al in Tagungsband BauSim 2018 (2018, September) Detailed reference viewed: 70 (1 UL)Modellierung und Validierung von Simulationsansätzen für die aussenliegende Lufttemperierung (-) Detailed reference viewed: 23 (1 UL)Modelling and analysis of flow-driven energy harvesting devices and associated reduced order models Zilian, Andreas ; Baroli, Davide Scientific Conference (2018, June) A specific class of energy harvester devices for renewable energy resources allows conversion of ambient fluid flow energy to electrical energy via flow-induced vibrations of a piezo-ceramic composite ... [more ▼] A specific class of energy harvester devices for renewable energy resources allows conversion of ambient fluid flow energy to electrical energy via flow-induced vibrations of a piezo-ceramic composite structure positioned in the flow field. This energy converter technology simultaneously involves the interaction of a composite structure and a surrounding fluid, the electric charge accumulated in the piezo-ceramic material and a controlling electrical circuit. In order to predict the efficiency and operational properties of such future devices and to increase their robustness and performance, a mathematical and numerical model of the complex physical system is required to allow systematic computational investigation of the involved phenomena and coupling characteristics. The presentation will discuss a monolithic modelling approach that allows simultaneous analysis of the harvester, which involves surface-coupled fluid-structure interaction, volume-coupled electro-mechanics and a controlling energy harvesting circuit. Based on a finite element discretisation of the weighted residual form of the governing equations, time- and frequency-domain analysis enables investigation of different types of structures (plate, shells) subject to exterior/interior flow with varying parameters, and attached electrical circuits with respect to the electrical power output generated. Consequently, options for parametric reduced-order modelling of flow-driven energy harvesters will be discussed. [less ▲] Detailed reference viewed: 127 (9 UL)Modelling Complex Systems: a primer - agent-based models, equation-based models, statistical models and Bayesian inference, digital twins Bordas, Stéphane Learning material (2019) Modelling Complex Systems: a primer - agent-based models, equation-based models, statistical models and Bayesian inference, digital twins Detailed reference viewed: 565 (24 UL)Modelling hydraulic fractures in porous media using flow cohesive interface elements ; ; et al in Engineering Geology (2017), 225 Detailed reference viewed: 117 (2 UL)Modelling interfacial cracking with non-matching cohesive interface elements Nguyen, Viet Ha ; ; Bordas, Stéphane et al in Computational Mechanics (2016), 58(5), 731-746 Interfacial cracking occurs in many engineering problems such as delamination in composite laminates, matrix/interface debonding in fibre reinforced composites etc. Computational modelling of these ... [more ▼] Interfacial cracking occurs in many engineering problems such as delamination in composite laminates, matrix/interface debonding in fibre reinforced composites etc. Computational modelling of these interfacial cracks usually employs compatible or matching cohesive interface elements. In this paper, incompatible or non-matching cohesive interface elements are proposed for interfacial fracture mechanics problems. They allow non-matching finite element discretisations of the opposite crack faces thus lifting the constraint on the compatible discretisation of the domains sharing the interface. The formulation is based on a discontinuous Galerkin method and works with both initially elastic and rigid cohesive laws. The proposed formulation has the following advantages compared to classical interface elements: (i) non-matching discretisations of the domains and (ii) no high dummy stiffness. Two and three dimensional quasi-static fracture simulations are conducted to demonstrate the method. Our method not only simplifies the meshing process but also it requires less computational demands, compared with standard interface elements, for problems that involve materials/solids having a large mismatch in stiffnesses. [less ▲] Detailed reference viewed: 95 (3 UL)Modelling of Fluid-Structure Interaction – Effects of Added Mass, Damping and Stiffness Zilian, Andreas in Irschik, Hans; Belyaev, Alexander K. (Eds.) Dynamics of Mechanical Systems with Variable Mass (2014) Fluid-flow around mechanical structures can sometimes lead to catastrophic failures. Improved modelling of fluid/structure interaction is required for safety and mechanical considerations. In this ... [more ▼] Fluid-flow around mechanical structures can sometimes lead to catastrophic failures. Improved modelling of fluid/structure interaction is required for safety and mechanical considerations. In this contribution, concepts for modelling the interaction of structures and fluids are presented. Starting from excitation mechanisms and associated classifications, various model depth approaches are compared. Among them, the use of added coefficients for quasi-steady problems is discussed. On the basis of potential flow theory, different approaches for determining fluid-induced additional mass are established and illustrated using an analytical example. Given the limitations of simplifying the engineering models, the second part of the paper provides a brief overview on computational methods for fluid-structure interaction and presents a monolithic modelling approach using space-time finite elements for discretisation of both fluid and structure. Applications from aero- and hydro-elasticity show the applicability of computational methods for problems involving flow-induced added mass, damping, and stiffness. [less ▲] Detailed reference viewed: 203 (17 UL)Modelling of residually stressed, extended and inflated cylinders with application to aneurysms ; ; Dehghani, Hamidreza et al in Mechanics Research Communications (2021), 111 The paper presents the localized bifurcation abnormal enlargement associated with certain human diseases such as abdominal aortic aneurysms (AAA), among others. The constitutive framework herewith ... [more ▼] The paper presents the localized bifurcation abnormal enlargement associated with certain human diseases such as abdominal aortic aneurysms (AAA), among others. The constitutive framework herewith proposed is constructed relying on the modelling of non-linear elastic materials under the action of residual stresses. The suitable incorporation on the mechanical response of residual stresses in the analysis is regarded important for the formation of aneurysms in soft tissues. From a mechanical perspective, the onset of aneurysms formation can be interpreted through bifurcation conditions, whose localization is relatively sensitive to different material and geometrical parameters as it is shown here. In order to reduce the risk and interpret aneurysm formation, we perform a thorough sensitivity analysis of the effect of design parameters such as tube diameter, length, thickness and strength of the residual stress field on bifurcation of a tube under inflation and extesion. A consistent residually stressed material model is formulated in terms of invariants for a general elastic strain-energy function. The dependence of applied pressure, axial stretch and different geometrical and constitutive parameters on bulging and bending bifurcation is illustrated. The numerical procedure to analyse the bifurcation of the finite deformation boundary-value problem at hand is developed based on the modified Riks method. The proposed formulation is implemented in the general-purpose finite element code ABAQUS using user-defined material subroutines.For a given material model, bulging bifurcation is expected for sufficiently large values of the axial stretch while the onset of bifurcation is found to be the bending mode for small values of the axial stretch. This transition zone from bending bifurcation to bulging bifurcation is analyzed for the different parameters considered. [less ▲] Detailed reference viewed: 87 (0 UL)Modelling of ultrasound therapeutic heating and numerical study of the dynamics of the induced heat shock response Mizera, Andrzej ; in Communications in Nonlinear Science & Numerical Simulation (2011), 16(5), 23422349 Detailed reference viewed: 86 (2 UL)Modelling Thermochemical Processes in Granular Media Hoffmann, Florian Presentation (2012, October 26) Detailed reference viewed: 69 (1 UL)Models and Technologies for Intelligent Transportation Systems: new challenges and metaheuristic solutions for large-scale network applications Viti, Francesco ; in Journal of Intelligent Transportation Systems (2014), 18(1), 1-4 Detailed reference viewed: 112 (7 UL)Les modes opéatoires de la cryptographie symétrique Schiltz, Jang Report (2003) Detailed reference viewed: 38 (0 UL)Modification of the Shear-Slip Mesh Update Method with Respect to Space-Time Finite Element Discretisation of Fluid Flows ; Zilian, Andreas Scientific Conference (2012, April 27) Space-time discretisations of physical problems involving moving and deforming bodies, boundaries and interfaces have been shown to offer advantageous properties while being methodologically uniform and ... [more ▼] Space-time discretisations of physical problems involving moving and deforming bodies, boundaries and interfaces have been shown to offer advantageous properties while being methodologically uniform and flexible. Well-known phenomena which are ideally suited to be analysed by space-time methods, are fluid-structure interaction problems in general as well as fluid flows with subdomain phase boundaries or immersed moving objects. In this contribution a short overview of existing mesh- moving techniques is given within the framework of finite element discretisations of the incompressible Navier-Stokes equations in space and time. The investigation is based on a SUPG/PSPG velocity-pressure formulation on the deforming space-time domain. A modification of the shear-slip mesh update method in the framework of space-time finite element discretisation is presented leading to a continuous space-time mesh in the shear-slip layer. The modified mesh moving technique is applied to engineering problems with rotating space-time fluid meshes. Its conservation properties and its quality regarding the approximated solutions on moving and deforming meshes are investigated. [less ▲] Detailed reference viewed: 98 (1 UL)Möglichkeiten und Grenzen generischer Ansätze als Beitrag zur Steigerung der Robustheit von Produktentwicklungsprojekten Gericke, Kilian ; ; Blessing, Lucienne in Proceedings of 18th Symposium Design for X (2007) Zur Darstellung des theoretischen Rahmens dieser Arbeit werden ein Modell zur Visualisierung der Vernetzung von Einflussfaktoren auf den Projekterfolg aus den Domänen Projekt-Management, Produkt und ... [more ▼] Zur Darstellung des theoretischen Rahmens dieser Arbeit werden ein Modell zur Visualisierung der Vernetzung von Einflussfaktoren auf den Projekterfolg aus den Domänen Projekt-Management, Produkt und Stakeholder und ein Verbesserungsprozess zur Steigerung der Robustheit von Produktentwicklungsprojekten vorgestellt. Vor diesem Hintergrund werden die Grenzen aber auch die Möglichkeiten generischer Lösungsansätze diskutiert. Anhand einer Fallstudie wird untersucht welche Barrieren die Durchführung des Verbesserungsprozesses und somit auch die Anwendung der Lösungsansätze in der Praxis erschweren. Die Analysen zeigen, dass die Kenntnis der Ursachen von Problemen, die zu Planungsabweichungen in Produktenwicklungsprojekten führen, und eine entsprechende Anpassung der Handlungsempfehlungen Voraussetzungen zur Implementierung daraus abgeleiteter Maßnahmen sind. Die domänenübergreifende Betrachtung möglicher Einflussfaktoren gemäß dem Konzept der Robustheit führt während der Ursachenanalyse zu einem fundierten Verständnis der Problemlage und ermöglicht eine bessere Anpassung der Lösungsansätze. Aus den theoretischen Vorüberlegungen und den Ergebnissen der Fallstudie werden Anforderungen an die Weiterentwicklung des Ansatzes zur Steigerung der Robustheit von Produktentwicklungsprojekten abgeleitet, der die Anwender unterstützen soll, den Transfer empirischer Erkenntnisse und Handlungsempfehlungen auf individuelle Problemstellungen zu vollziehen. [less ▲] Detailed reference viewed: 57 (0 UL) |
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