Modelling and numerical analysis of thin-walled silos under discharge

Ziel der vorliegenden Arbeit ist ein Modell für die numerische Analyse von Verformungen und Spannungen während der Entleerung von Behältern und Silos, die mit Flüssigkeiten oder Schüttgütern befüllt sind. Das Verformungsverhalten dünnwandiger Siloschalen aus Stahl ist mit einem kontinuumsmechanischen Modell für große Rotationen und elastisch-viskoplastischem Materialverhalten beschrieben. Das mechanische Verhalten von Flüssigkeiten und Schüttgütern ist mit den Navier-Stokes-Gleichungen für kompressible Fluide modelliert, um Verdichtungs- und Auflockerungszonen berücksichtigen zu können. Der Phasenübergang zwischen ruhendem und strömendem Schüttgut ist mit einem Modell für viskoplastische Fluide nach Bingham formuliert. Die Beschreibung von freien Oberflächen erfolgt mit der Level-Set-Methode. Mit Berücksichtigung der Wandreibung liegt ein Gesamtmodell vor, mit dem das Zusammenwirken der Verformung von Siloschalen mit dem Strömungszustand von Schüttgütern numerisch untersucht werden kann. Die Modellgleichungen sind mit dem Prinzip der virtuellen Leistung angegeben. Die Diskretisierung erfolgt mit der Raum-Zeit-Finite-Elemente-Methode. So ist das Verformungsverhalten der Struktur innerhalb gemischt-hybrider Elemente mit quadratischen Ansätzen für die Geschwindigkeiten und abgestimmten Ansätzen für die Spannungen formuliert. Mit einer Pseudo-Struktur ist das Gebiet des Fluids an die Verformung der nachgiebigen Struktur entlang des gemeinsamen Randes angepasst. Die fragmented finite element method wird für die Bewegung von Fluiden eingesetzt, die nur in einem Teil des Raum-Zeit-Gebietes präsent sind. So wird das Raum-Zeit-Gebiet von aktiven und passiven Elementen bedeckt. Die Auswertung der Elemente mit freier Oberfläche erfordert Integrationsformeln, die mit einem Algorithmus für die Parkettierung von Teilgebieten vierdimensionaler Elemente bestimmt sind. Die Güte der Näherungslösung für die Bewegung der freien Oberfläche wird mit einer Extrapolation der Geschwindigkeiten verbessert. Die gleiche Methodik wird auch für die Extrapolation der Dichte kompressibler Fluide eingesetzt, um in neu aktivierten Elementen gültige Startwerte für eine Näherungslösung zu erhalten. Die Beanspruchung und das Verformungsverhalten von Siloschalen ist für ruhende und strömende Schüttgüter untersucht. Die Entwicklung der freien Oberfläche von Flüssigkeiten und Schüttgütern wird während zentrischer und exzentrischer Entleerungen analysiert.A monolithic approach to fluid-structure interactions based on the space-time finite element method is presented. The method is applied to investigate the stress states in silos during discharge. Adapting the continuum approach, a thin-walled silo-shell is modelled as an elastic-viscoplastic solid under large deformations, whereas the flowing liquid material is described by a model for viscoplastic and compressible fluids. Between the fluid and solid, advanced slip boundary conditions incorporating friction are taken into account. In order to solve the governing equations of the multi-field problem, the weighted residual method is applied, which is discretized by time-discontinuous space-time finite elements. Within the simultaneous solution procedure for the coupled problem, the kinematics of both solid and fluid is described using velocities as primary variables. A mesh-moving scheme based on a pseudo-structure is used to adapt the coordinates of the nodes in the fluid domain to the structural deformations. The non-linear system of equations composed of physical unknowns and velocities of the fluid mesh is solved iteratively applying the Newton-Raphson scheme. For the investigation of stress states inside thin-walled structures, isoparametric finite elements with quadratic approximation of the velocities are used, whereas the stresses are described by lower-order shape functions on element-level leading to mixed-hybrid finite elements. The motion of the free surface between the liquid and air above is described by the level-set method and the finite element approximation is enhanced by the XFEM in space and time. For applying the XFEM, an algorithm for tesselation intersected tesseracts defining the geometry of four-dimensional space-time finite elements is developed. Furthermore, the fragmented finite element method is implemented, where the finite elements related to the air are deactivated. In this case a pde-based extrapolation for the velocity-field is used to ensure an accurate transport of the free surface. The same method is applied to extrapolate the density of a compressible liquid into reactivated neighboring finite elements in order to get valid initial values for the Newton-Raphson scheme. The proposed methodology is applied to dynamic behavior of silos under changing loading conditions during discharge

Bayesian parameter identification in plasticity

To evaluate the cyclic behaviour under different loading conditions using the kinematic and isotropic hardening theory of steel a Chaboche visco-plastic material model is employed. The parameters of a constitutive model are usually identified by minimization of the distance between model response and experimental data. However, measurement errors and differences in the specimens lead to deviations in the determined parameters. In this article the Choboche model is used and a stochastic simulation technique is applied to generate artificial data which exhibit the same stochastic behaviour as experimental data. Then the model parameters are identified by applying a variaty of Bayes’s theorem. Identified parameters are compared with the true parameters in the simulation and the efficiency of the identification method is discussed

Finite element method for strongly-coupled systems of fluid-structure interaction with application to granular flow in silos

A monolithic approach to fluid-structure interactions based on the space-time finite element method (STFEM) is presented. The method is applied to the investigation of stress states in silos filled with granular material during discharge. The thin-walled siloshell is modeled in a continuum approach as elastic solid material, whereas the flowing granular material is described by an enhanced viscoplastic non-Newtonian fluid model. The weak forms of the governing equations are discretized by STFEM for both solid and fluid domain. To adapt the matching mesh nodes of the fluid domain to the structural deformations, a mesh-moving scheme using a neo-Hookean pseudo-solid is applied. The finite element approximation of non-smooth solution characteristics is enhanced by the extended finite element method (XFEM). The proposed methodology is applied to the 4D (space-time) investigation of deformation-dependent loading conditions during silo discharge

Comparison of Bayesian Methods on Parameter Identification for a Viscoplastic Model with Damage

The state of materials and accordingly the properties of structures are changing over the period of use, which may influence the reliability and quality of the structure during its life-time. Therefore, identification of the model parameters of the system is a topic which has attracted attention in the content of structural health monitoring. The parameters of a constitutive model are usually identified by minimization of the difference between model response and experimental data. However, the measurement errors and differences in the specimens lead to deviations in the determined parameters. In this article, the focus is on the identification of material parameters of a viscoplastic damaging material using a stochastic simulation technique to generate artificial data which exhibit the same stochastic behavior as experimental data. It is proposed to use Bayesian inverse methods for parameter identification and therefore the model and damage parameters are identified by applying the Transitional Markov Chain Monte Carlo Method (TMCMC) and Gauss-Markov-Kalman filter (GMKF) approach. Identified parameters by using these two Bayesian approaches are compared with the true parameters in the simulation and with each other, and the efficiency of the identification methods is discussed. The aim of this study is to observe which one of the mentioned methods is more suitable and efficient to identify the model and damage parameters of a material model, as a highly non-linear model, using a limited surface displacement measurement vector and see how much information is indeed needed to estimate the parameters accuratel

Bayesian Parameter Determination of a CT-Test Described by a Viscoplastic-Damage Model Considering the Model Error

The state of materials and accordingly the properties of structures are changing over the period of use, which may influence the reliability and quality of the structure during its life-time. Therefore identification of the model parameters of the system is a topic which has attracted attention in the content of structural health monitoring. The parameters of a constitutive model are usually identified by minimization of the difference between model response and experimental data. However, the measurement errors and differences in the specimens lead to deviations in the determined parameters. In this article, the Choboche model with a damage is used and a stochastic simulation technique is applied to generate artificial data which exhibit the same stochastic behavior as experimental data. Then the model and damage parameters are identified by applying the sequential Gauss-Markov-Kalman filter (SGMKF) approach as this method is determined as the most efficient method for time consuming finite element model updating problems among filtering and random walk approaches. The parameters identified using this Bayesian approach are compared with the true parameters in the simulation, and further, the efficiency of the identification method is discussed. The aim of this study is to observe whether the mentioned method is suitable and efficient to identify the model and damage parameters of a material model, as a highly non-linear model, for a real structural specimen using a limited surface displacement measurement vector gained by Digital Image Correlation (DIC) and to see how much information is indeed needed to estimate the parameters accurately even by considering the model error and whether this approach can also practically be used for health monitoring purposes before the occurrence of severe damage and collaps

Finite element methods for strongly-coupled systems of fluid-structure interaction with application to granular flow in silos

A monolithic approach to fluid-structure interactions based on the space-time finite element method is presented to investigate stress states in silos filled with granular material during discharge. The thin-walled silo-shell is discretized by continuum based, mixed-hybrid finite elements, whereas the flowing granular material is described by an enhanced viscoplastic non-Newtonian fluid model. To adapt the mesh nodes of the fluid domain to the structural deformations, a mesh-moving scheme using a pseudo-solid is applied. The level-set-method involving XFEM is used, including a 4D split algorithm for the space-time finite elements, in order to describe free surfaces. The method is applied to 3D silo discharges. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Comparison of Bayesian methods on parameter identification for a viscoplastic model with damage

The state of materials and accordingly the properties of structures are changing over the period of use, which may influence the reliability and quality of the structure during its life-time. Therefore, identification of the model parameters of the system is a topic which has attracted attention in the content of structural health monitoring. The parameters of a constitutive model are usually identified by minimization of the difference between model response and experimental data. However, the measurement errors and differences in the specimens lead to deviations in the determined parameters. In this article, the focus is on the identification of material parameters of a viscoplastic damaging material using a stochastic simulation technique to generate artificial data which exhibit the same stochastic behavior as experimental data. It is proposed to use Bayesian inverse methods for parameter identification and therefore the model and damage parameters are identified by applying the Transitional Markov Chain Monte Carlo Method (TMCMC) and Gauss–Markov–Kalman filter (GMKF) approach. Identified parameters by using these two Bayesian approaches are compared with the true parameters in the simulation and with each other, and the efficiency of the identification methods is discussed. The aim of this study is to observe which one of the mentioned methods is more suitable and efficient to identify the model and damage parameters of a material model, as a highly non-linear model, using a limited surface displacement measurement vector and see how much information is indeed needed to estimate the parameters accurately