Dissertations / Theses on the topic 'Spectral stochastic finite element'
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Fink, Sebastian [Verfasser]. "Simulation of elastic-plastic material behaviour with uncertain material parameters : a spectral stochastic finite element method approach / Sebastian Fink." Hannover : Technische Informationsbibliothek (TIB), 2015. http://d-nb.info/1095501860/34.
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Adam, Alexandros. "Finite element, adaptive spectral wave modelling." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/45307.
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The ability to predict the wave climate has a great impact on a wide range of sectors, including coastal and offshore engineering, marine renewable energy and shipping. The state of the art in wave prediction is called spectral wave modelling and is based on a phase-averaged, spectral description of the sea-surface elevation. The governing equation, called the action balance equation, is five-dimensional and describes the generation, propagation and evolution of action density in geographic space, spectral space and time. Due to the multidimensional nature of the equation the feasible resolutions are restricted by the computational costs. The aim of this work is to propose schemes which can increase the range of possible resolutions in spectral wave modelling, with the use of adaptivity in space and angle. Thus, this work focuses on the development of an unstructured, adaptive finite element spectral wave model (Fluidity-SW). A sub-grid scale model for the spatial discretisation is used, which retains the stability of discontinuous systems, with continuous degrees of freedom. Then, a new framework for angular adaptivity is developed, with results in dynamic angular and spatial anisotropy of the angular mesh. Finally a spatially h−adaptive scheme is implemented, which can dynamically treat the spatial gradients of the solution fields. The resulting framework is thoroughly verified and validated in a wide range of test cases and realistic scenarios, against analytical solutions, wave measurements and the results obtained with the widely used SWAN model. Thus, the overall ability of the code to simulate surface gravity wind-waves in fixed and adaptive spatial and angular meshes is demonstrated.
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Bakhtiari, Siamak. "Stochastic finite element slope stability analysis." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/stochastic-finite-element-slope-stability-analysis(c1b451d9-8bf6-43ff-9c10-7b5209fb45c1).html.
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In this thesis, the failures that occurred during the construction of the Jamuna Bridge Abutment in Bangladesh have been investigated. In particular, the influence of heterogeneity on slope stability has been studied using statistical methods, random field theory and the finite element method. The research is divided into three main parts: the statistical characterization of the Jamuna River Sand, based on an extensive in-situ and laboratory database available for the site; calibration of the laboratory data against a double-hardening elastoplastic soil model; and stochastic finite element slope stability analyses, using a Monte Carlo simulation, to analyse the slope failures accounting for heterogeneity. The sand state has been characterised in terms of state parameter, a meaningful quantity which can fully represent the mechanical behaviour of the soil. It was found that the site consists of predominantly loose to mildly dilative material and is very variable. Also, a Normal distribution was found to best represent the state parameter and a Lognormal distribution was found to best represent the tip resistance.The calibration of the constitutive model parameters was found to be challenging, as alternative approaches had to be adopted due to lack of appropriate test results available for the site. Single-variate random fields of state parameter were then linked to the constitutive model parameters based on the relationships found between them, and a parametric study of the abutment was then carried out by linking finite elements and random field theory within a Monte Carlo framework.It was found that, as the degree of anisotropy of the heterogeneity increases, the range of structural responses increases as well. For the isotropic cases, the range of responses was relatively smaller and tended to result in more localised failures. For the anisotropic cases, it was found that there are two different types of deformation mechanism. It was also found that, as the vertical scale of fluctuation becomes bigger, the range of possible structural responses increases and failure is more likely. Finally, it was found that the failed zones observed during the excavation of the West Guide Bund of the Jamuna Bridge Abutment could be closely predicted if heterogeneity was considered in the finite element analyses. In particular, it was found that, for such a natural deposit, a large degree of anisotropy (in the range of 20) could account for the deformation mechanisms observed on site.
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Ullmann, Elisabeth. "Solution strategies for stochastic finite element discretizations." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2009. http://nbn-resolving.de/urn:nbn:de:bsz:105-8042820.
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The discretization of the stationary diffusion equation with random parameters by the Stochastic Finite Element Method requires the solution of a highly structured but very large linear system of equations. Depending on the stochastic properties of the diffusion coefficient together with the stochastic discretization we consider three solver cases. If the diffusion coefficient is given by a stochastically linear expansion, e.g. a truncated Karhunen-Loeve expansion, and tensor product polynomial stochastic shape functions are employed, the Galerkin matrix can be transformed to a block-diagonal matrix. For the solution of the resulting sequence of linear systems we study Krylov subspace recycling methods whose success depends on the ordering and grouping of the linear systems as well as the preconditioner. If we use complete polynomials for the stochastic discretization instead, we show that decoupling of the Galerkin matrix with respect to the stochastic degrees of freedom is impossible. For a stochastically nonlinear diffusion coefficient, e.g. a lognormal random field, together with complete polynomials serving as stochastic shape functions, we introduce and test the performance of a new Kronecker product preconditioner, which is not exclusively based on the mean value of the diffusion coefficient.
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Savvides, Abraham. "Application of two-dimensional spectral/finite-difference and spectral/hp finite-element methods to cylinder flows." Thesis, Imperial College London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.264204.
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Xiao, Dong Wen. "Efficiency analysis on element decomposition method for stochastic finite element analysis." Thesis, University of Macau, 2000. http://umaclib3.umac.mo/record=b1636334.
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Starkloff, Hans-Jörg. "Stochastic finite element method with simple random elements." Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800596.
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We propose a variant of the stochastic finite element method, where the random
elements occuring in the problem formulation are approximated by simple random
elements, i.e. random elements with only a finite number of possible values.
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Parvini, Mehdi. "Pavement deflection analysis using stochastic finite element method." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0014/NQ42757.pdf.
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Zheng, Yuquan. "Stochastic finite element analysis of continuous elastic systems." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0002/MQ42231.pdf.
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Parvini, Mehdi. "Pavement deflection analysis using stochastic finite element method /." *McMaster only, 1997.
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Sachdeva, Sachin K. "Subspace projection schemes for stochastic finite element analysis." Thesis, University of Southampton, 2006. https://eprints.soton.ac.uk/72061/.
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This research is concerned with the development of subspace projection schemes for efficiently solving large systems of random algebraic equations obtained by finite element discretizations of stochastic partial differential equations. Reduced basis projections schemes employing the preconditioned stochastic Krylov subspace are compared with the polynomial chaos approach in terms of their accuracy and computational efficiency. For the class of problems considered, it is shown that stochastic reduced basis methods can be up to orders of magnitude faster, while providing results of comparable accuracy. Reduced basis projections schemes are further improved by hybridizing them with polynomial chaos expansions. The hybrid formulation ensures better accuracy by enabling the efficient application of reduced basis schemes even when a large number of basis vectors is used to approximate the response process. It also extends the application of reduced basis methods to non-Gaussian uncertainty models. A new scheme referred to as the strong Galerkin projection scheme is introduced which imposes orthogonality in a more strict sense compared to the conventional Galerkin projection scheme. It is shown that the proposed formulation is a generalization of stochastic reduced basis projection schemes and gives more accurate results than the polynomial chaos projection scheme, while incurring significantly lower computational cost. Finally, a software framework which utilizes existing deterministic finite element codes is developed for stochastic analysis of linear elastic problems. Numerical studies are presented for two-dimensional and three-dimensional problems to illustrate the capabilities of this framework.
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Li, Chenfeng. "Stochastic finite element modelling of elementary random media." Thesis, Swansea University, 2006. https://cronfa.swan.ac.uk/Record/cronfa42770.
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Following a stochastic approach, this thesis presents a numerical framework for elastostatics of random media. Firstly, after a mathematically rigorous investigation of the popular white noise model in an engineering context, the smooth spatial stochastic dependence between material properties is identified as a fundamental feature of practical random media. Based on the recognition of the probabilistic essence of practical random media and driven by engineering simulation requirements, a comprehensive random medium model, namely elementary random media (ERM), is consequently defined and its macro-scale properties including stationarity, smoothness and principles for material measurements are systematically explored. Moreover, an explicit representation scheme, namely the Fourier-Karhunen-Loeve (F-K-L) representation, is developed for the general elastic tensor of ERM by combining the spectral representation theory of wide-sense stationary stochastic fields and the standard dimensionality reduction technology of principal component analysis. Then, based on the concept of ERM and the F-K-L representation for its random elastic tensor, the stochastic partial differential equations regarding elastostatics of random media are formulated and further discretized, in a similar fashion as for the standard finite element method, to obtain a stochastic system of linear algebraic equations. For the solution of the resulting stochastic linear algebraic system, two different numerical techniques, i.e. the joint diagonalization solution strategy and the directed Monte Carlo simulation strategy, are developed. Original contributions include the theoretical analysis of practical random medium modelling, establishment of the ERM model and its F-K-L representation, and development of the numerical solvers for the stochastic linear algebraic system. In particular, for computational challenges arising from the proposed framework, two novel numerical algorithms are developed: (a) a quadrature algorithm for multidimensional oscillatory functions, which reduces the computational cost of the F-K-L representation by up to several orders of magnitude; and (b) a Jacobi-like joint diagonalization solution method for relatively small mesh structures, which can effectively solve the associated stochastic linear algebraic system with a large number of random variables.
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Antypas, Dionyssios. "Structural response modelling using the stochastic finite element method." Thesis, Imperial College London, 2002. http://hdl.handle.net/10044/1/8314.
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Mahadevan, Sankaran. "Stochastic finite element-based structural reliability analysis and optimization." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/19517.
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Valenciano, Rubio Jose L. "Adaptive spectral element methods for swirling Newtonian flows." Thesis, Edinburgh Napier University, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.285227.
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Khodaparast, Hamed Haddad. "Stochastic finite element model updating and its application in aeroelasticity." Thesis, University of Liverpool, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.548785.
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Nešpůrek, Lukáš. "STOCHASTIC CRACK PROPAGATION MODELLING USING THE EXTENDED FINITE ELEMENT METHOD." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2010. http://www.nusl.cz/ntk/nusl-233900.
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Tato disertační práce vychází z výzkumu v rámci francouzsko-českého programu doktorátu pod dvojím vedením na pracovišti Institut français de mécanique avancée v Clermont-Ferrand a na Ústavu fyziky materiálu AV v Brně. Úvodní výzkumný úkol na brněnském pracovišti se zabýval numerickou analýzou pole napětí v okolí čela trhliny v tenké kovové fólii. Zvláštní pozornost byla zaměřena na vliv speciálního typu singularity v průsečíku čela trhliny s volným povrchem. Těžiště disertační práce spočívá v numerickém modelování a stochastické analýze problémů šíření trhlin se složitou geometrií v dvojrozměrném prostoru. Při analýze těchto problémů se dříve zřídka používaly numerické metody, a to z důvodu vysoké náročnosti na výpočtový čas. V této disertaci je ukázáno, že aplikací moderních metod numerické mechaniky a vhodných technik v analýze spolehlivosti lze tyto problémy řešit s pomocí numerických metod i na PC. Ve spolehlivostní analýze byla využita lineární aproximační metoda FORM. Pro rychlost šíření trhlin se vycházelo z Parisova-Erdoganova vztahu. Pro parametry tohoto vztahu byl použit dvourozměrný statistický model, který postihuje vysokou citlivost na korelaci obou parametrů. Mechanická odezva byla počítána rozšířenou metodou konečných prvků (XFEM), která eliminuje výpočetní náročnost a numerický šum související se změnou sítě v klasické metodě konečných prvků. Prostřednictvím přímé diferenciace bylo odvozeno několik vztahů pro derivace funkce odezvy, čímž se dosáhlo lepší numerické stability a konvergence spolehlivostní analýzy a výrazného zkrácení doby výpočtu. Problém zatížení s proměnou amplitudou byl řešen aplikací transformace zatížení metodou PREFFAS. Využití distribuce výpočtů v síti PC umožnilo další zrychlení analýzy.
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Weber, Marc Anton. "Stochastic structural analysis of engineering components using the finite element method." Doctoral thesis, University of Cape Town, 1993. http://hdl.handle.net/11427/8476.
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Bibliography: p. 113-123.This thesis investigates probabilistic and stochastic methods for structural analysis which can be integrated into existing, commercially available finite element programs. It develops general probabilistic finite element routines which can be implemented within deterministic finite element programs without requiring major code development. These routines are implemented in the general purpose finite element program ABAQUS through its user element subroutine facility and two probabilistic finite elements are developed: a three-dimensional beam element limited to linear material behaviour and a two-dimensional plane element involving elastic-plastic material behaviour. The plane element incorporates plane strain, plane stress and axisymmetric formulations. The numerical accuracy and robustness of the routines are verified and application of the probabilistic finite element method is illustrated in two case studies, one involving a four-story, two-bay frame structure, the other a reactor pressure vessel nozzle. The probabilistic finite element routines developed in this thesis integrate point estimate methods and mean value first order methods within the same program. Both methods require a systematic sequence involving the perturbation of the random parameters to be evaluated, although the perturbation sequence of the methods differ. It is shown that computer-time saving techniques such as Taylor series and iterative perturbation schemes, developed for mean value based methods, can also be used to solve point estimate method problems. These efficient techniques are limited to linear problems; nonlinear problems must use full perturbation schemes. Finally, it is shown that all these probabilistic methods and perturbation schemes can be integrated within one program and can follow many of the existing deterministic program structures and subroutines. An overall strategy for converting deterministic finite element programs to probabilistic finite element programs is outlined.
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Breakah, Tamer M. "Stochastic finite element analysis of moisture damage in hot mix asphalt." [Ames, Iowa : Iowa State University], 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3389089.
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Oliver, Robin. "A stochastic finite element model for the dynamics of globular proteins." Thesis, University of Leeds, 2013. http://etheses.whiterose.ac.uk/5555/.
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This thesis concerns a novel coarse graining method for the simulation of the globular proteins. Conventional simulation methods such as molecular dynamics cannot generate sufficient times to reach the important timescales that govern the biology of large biological systems like molecular motors. To address this, I have developed a new coarse graining algorithm drawing on the techniques of continuum mechanics and finite element analysis to build a new simulation technique. The novel part of this algorithm is that the fluctuation dissipation relation for the system can be derived and solved locally. This avoids the need to invert a global resistance matrix to solve for the thermal noise component of the system and reduces the computational expense of the algorithm per time step. I have validated this coarse grained model by performing a variety of tests on the numerical code including spatial and temporal convergence tests using Fourier analysis and beam bending theory. In addition compliance with the equipartition theorem has been confirmed. One key advantage of this method over atomistic techniques is that the coarse grained method does not require any atomic information ab intio. Thus, this method can interface with low resolution imaging techniques such as Small Angle X-Ray Scattering and Cryo-Electron Microscopy. In this thesis, I show how to construct a finite element mesh from both of these sources and run simulations to replicate the results from Small Angle X-Ray Scattering and Cryo-Electron Microscopy experiments. In more detail, I have taken a structure obtained using Small Angle X-ray Scattering, ran simulations and checked that the dynamics do not affect the average X-Ray scattering curve. Furthermore, using experimentally obtained structures and dynamics of the molecular motor dynein I have run simulations to find the elastic parameters that match the experimental data to map the overall dynamics of the dynein motor.
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Huh, Jungwon. "Dynamic reliability analysis for nonlinear structures using stochastic finite element method." Diss., The University of Arizona, 1999. http://hdl.handle.net/10150/289087.
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An efficient and accurate algorithm is developed to evaluate reliability in the time domain for nonlinear structures subjected to short duration dynamic loadings, including earthquake loading. The algorithm is based on the nonlinear stochastic finite element method (SFEM). Uncertainties in the dynamic and seismic excitation, and resistance-related parameters are incorporated by modeling them as realistically as possible. The uncertainty in them is explicitly addressed. The proposed algorithm intelligently integrates the concepts of response surface method (RSM), finite element method (FEM), first-order reliability method (FORM), and an iterative linear interpolation scheme. This leads to the stochastic finite element concept. It has the potential to estimate the risk associated with any linear or nonlinear structure that can be represented by a finite element algorithm subjected to seismic loading or any short duration dynamic loadings. In the context of the finite element method, the assumed stress-based finite element algorithm is used to increase its efficiency. Two iterative response surface schemes consisting of second order polynomials (with and without cross terms) are proposed. A mixture of saturated and central composite designs is used to assure both efficiency and accuracy of the algorithm. Sensitivity analysis is used to improve the efficiency further. The unique feature of the algorithm is that it is capable of calculating risk using both serviceability and strength limit states and actual earthquake loading time histories can be used to excite structures, enabling a realistic representation of the loading condition. The uncertainty in the amplitude of the earthquake is successfully considered in the context of RSM. Uncertainty in the frequency content of an earthquake is considered indirectly by conducting a parametric study to quantify the effect of uncertainty in the frequency content of earthquakes on the overall reliability of structures. The algorithm has been extensively verified using the Monte Carlo simulation technique. The verified algorithm is used to study the reliability of structures excited by actual earthquake time histories. The results of the numerical examples show that the proposed algorithm can be used accurately and efficiently to estimate the risk for nonlinear structures subjected to short duration time-variant loadings including seismic loading.
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Citrain, Aurélien. "Hybrid finite element methods for seismic wave simulation : coupling of discontinuous Galerkin and spectral element discretizations." Thesis, Normandie, 2019. http://www.theses.fr/2019NORMIR28.
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Pour résoudre des équations d’ondes posées dans des milieux hétérogènes avec des éléments finis et un coût numérique raisonnable, nous couplons la méthode Discontinue de Galerkine (DGm) avec des éléments finis spectraux (SEm). Nous utilisons des maillages hybrides composés de tétraèdres et d’hexaèdres structurés. Le couplage est réalisé en partant d’une formulation DG mixte primale posée dans un maillage hybride composé d’un macro-élément hexaédrique et d’un sous-maillage composé de tétraèdres. La SEm est appliquée dans le macro-élément découpé en hexaèdres structurés et le couplage est assuré par les flux numériques de la DGm appliqués sur les faces internes du macro-élément communes avec le maillage tétraédrique. La stabilité de la méthode couplée est démontrée quand l’intégration en temps est effectuée avec un schéma Saute-Mouton. Les performances de la méthode couplée sont étudiées numériquement et on montre que le couplage permet de réduire les coûts numériques avec un très bon niveau de précision. On montre aussi que la formulation couplée peut stabiliser la méthode DG appliquée dans des domaines incluant des couches parfaitement adaptéesTo solve wave equations in heterogeneous media with finite elements with a reasonable numerical cost, we couple the Discontinuous Galerkin method (DGm) with Spectral Elements method (SEm). We use hybrid meshes composed of tetrahedra and structured hexahedra. The coupling is carried out starting from a mixed-primal DG formulation applied on a hybrid mesh composed of a hexahedral macro-element and a sub-mesh composed of tetrahedra. The SEm is applied in the macro-element paved with structured hexahedrons and the coupling is ensured by the DGm numerical fluxes applied on the internal faces of the macro-element common with the tetrahedral mesh. The stability of the coupled method is demonstrated when time integration is performed with a Leap-Frog scheme. The performance of the coupled method is studied numerically and it is shown that the coupling reduces numerical costs while keeping a high level of accuracy. It is also shown that the coupled formulation can stabilize the DGm applied in areas that include Perfectly Matched Layers
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Klenow, Bradley. "Finite and Spectral Element Methods for Modeling Far-Field Underwater Explosion Effects on Ships." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/37648.
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The far-field underwater explosion (UNDEX) problem is a complicated problem dominated by two phenomena: the shock wave traveling through the fluid and the cavitation in the fluid. Both of these phenomena have a significant effect on the loading of ship structures subjected to UNDEX.
An approach to numerically modeling these effects in the fluid and coupling to a structural model is using cavitating acoustic finite elements (CAFE) and more recently cavitating acoustic spectral elements (CASE). The use of spectral elements in CASE has shown to offer the greater accuracy and reduced computational expense when compared to traditional finite elements. However, spectral elements also increase spurious oscillations in both the fluid and structural response.
This dissertation investigates the application of CAFE, CASE, and a possible improvement to CAFE in the form of a finite element flux-corrected transport algorithm, to the far-field UNDEX problem by solving a set of simplified UNDEX problems. Specifically we examine the effect of increased oscillations on structural response and the effect of errors in cavitation capture on the structural response which have not been thoroughly explored in previous work.
The main contributions of this work are a demonstration of the problem dependency of increased oscillations in the structural response when applying the CASE methodology, the demonstration of how the sensitivity of errors in the structural response changes with changes in the structural model, a detailed explanation of how error in cavitation capture influences the structural response, and a demonstration of the need to accurately capture the shape and magnitude of cavitation regions in the fluid in order to obtain accurate structural response results.Ph. D.
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Guo, Xiu Xiu. "Finite element analysis of nonlinear stochastic oscillators with Poisson white noise excitation." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2182943.
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Kundu, Abhishek. "Efficient uncertainty propagation schemes for dynamical systems with stochastic finite element analysis." Thesis, Swansea University, 2014. https://cronfa.swan.ac.uk/Record/cronfa42292.
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Efficient uncertainty propagation schemes for dynamical systems are investigated here within the framework of stochastic finite element analysis. Uncertainty in the mathematical models arises from the incomplete knowledge or inherent variability of the various parametric and geometric properties of the physical system. These input uncertainties necessitate the use of stochastic mathematical models to accurately capture their behavior. The resolution of such stochastic models is computationally quite expensive. This work is concerned with development of model order reduction techniques for obtaining the dynamical response statistics of stochastic finite element systems. Efficient numerical methods have been proposed to propagate the input uncertainty of dynamical systems to the response variables. Response statistics of randomly parametrized structural dynamic systems have been investigated with a reduced spectral function approach. The frequency domain response and the transient evolution of the response of randomly parametrized structural dynamic systems have been studied with this approach. An efficient discrete representation of the input random field in a finite dimensional stochastic space is proposed here which has been integrated into the generic framework of the stochastic finite element weak formulation. This framework has been utilized to study the problem of random perturbation of the boundary surface of physical domains. Truncated reduced order representation of the complex mathematical quantities which are associated with the stochastic isoparametric mapping of the random domain to a deterministic master domain within the stochastic Galerkin framework have been provided. Lastly, an a-priori model reduction scheme for the resolution of the response statistics of stochastic dynamical systems has also been studied here which is based on the concept of balanced truncation. The performance and numerical accuracy of the methods proposed in this work have been exemplified with numerical simulations of stochastic dynamical systems and the convergence behavior of various error indicators.
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Lee, Jangwoon. "Analysis and finite element approximations of stochastic optimal control problems constrained by stochastic elliptic partial differential equations." [Ames, Iowa : Iowa State University], 2008.
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Nizamiev, Kamil. "Stochastic Galerkin Model Updating of Randomly Distributed Parameters." University of Akron / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302884328.
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Mousavi, Nezhad Mohaddeseh. "Stochastic finite element modelling of flow and solute transport in dual domain system." Thesis, University of Exeter, 2010. http://hdl.handle.net/10036/111704.
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Hydrological processes are greatly influenced by the characteristics of the domain through which the process occurs. It is generally accepted that earth materials have extreme variations from point to point in space. Consequently this heterogeneity results in high variation in hydraulic properties of soil. In order to develop a reliable predictive model for transport processes in soil, the effects of this variability must be considered. Soil heterogeneity due to presence of macropores (micro-) and to spatial variability in hydraulic properties (macro-heterogeneity) coexists in the real field conditions. The challenge is to incorporate the effects of both types of soil heterogeneity in simulation models. This thesis presents development and application of a 2D/3D numerical model for simulation of advection and diffusion-dispersion contaminant transport considering both types of soil heterogeneity. Stochastic finite element approach is used to incorporate the effects of the spatial variability of soil hydraulic properties on contaminant fate. The soil micro heterogeneity effects are modelled with a dual domain concept in which a first order kinetic expression is used to describe the transfer of the solute between the two domains. Also, the capability of the model in 3D simulation of field problems improves the accuracy of the results, since it is possible to avoid the generally applied assumption in 2D simulations. From comparison of the model results with experimental and analytical results, it is concluded that the model performs well in predicting contaminant fate and the incorporation of the both types of micro- and macro- heterogeneity in the simulation models improves the accuracy of the prediction. Also, capability of the model in evaluation of the concentration variation coefficient as an index of reliability of the model outputs makes it possible to estimate a probable interval (mean concentration minus and plus standard deviation) for the range of oscillations of possible realizations of solute distribution. Moreover, comparison of the results of the proposed method with the results obtained using the Monte Carlo approach yields a pronounced reduction in the computation cost while resulting in virtually the same response variability as the Monte Carlo technique.
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Zhang, Wu. "Adaptive stochastic finite element procedure of electronic packaging problems using disturbed state concept." Diss., The University of Arizona, 1997. http://hdl.handle.net/10150/282373.
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Complex engineering problems need appropriate constitutive laws such as Disturbed State Concept (DSC), as well as robust accurate computational analysis methods such as adaptive and stochastic finite element methods (FEM). DSC provides a unified basis for constitutive modeling including elastic, plastic and creep deformations, microcracking, damage and softening, stiffening, and cyclic fatigue under thermomechanical loading. It includes intrinsical regularization, localization, characteristic dimension and avoidance of spurious mesh dependence. It also leads to new procedures for adaptive FEM and stochastic FEM. Adaptive FEM is a method to adapt or guide itself to better subsequent computation by use of previous computational information so as to achieve prescribed accuracy. It's a powerful procedure for analyzing deformation of special problems such as interfaces and joints and shear bands, and complex materials with both hardening and softening. An adaptive finite element procedure with combined Disturbance-Hybrid stress error estimator/remeshing indicator is proposed and tested by comparing with some published results, and the corresponding user-interactive unified DSC finite element program with more than 10 options is developed and applied to thermal analysis of electronic packaging problems. Unlike deterministic analysis methods, stochastic FEM approach further considers the random variations of involved parameters to further make the deterministic constitutive and numerical modeling more realistic in a statistical manner. Traditional stochastic FEM is reviewed and a new efficient DSC stochastic FEM is formulated for reliability analysis of electronic packaging problems. The computer visualization and animation are applied to display the computed results for the purpose of easier use and interpretation of the results, which will be one of major trends for engineering application of computational methods. In this dissertation, combined study is carried out from a comprehensive (computational and constitutive) viewpoint, and the practical and academic values of the adaptive and stochastic DSC finite element procedures for electronic packaging problems will be demonstrated.
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Zhou, Yiguang. "Efficient stochastic finite element method for the reliability analysis of nonlinear frame structures." Diss., The University of Arizona, 1992. http://hdl.handle.net/10150/185746.
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An efficient stochastic finite element-based procedure is proposed for the reliability analysis of frame and truss structures with geometrical and material nonlinearities under static loading condition. The material properties, geometry and external loads of the structure are considered as random variables. The failure criteria of the structure are expressed in terms of limit-state functions. The method is based on the advanced first order second moment reliability analysis procedure. The assumed stress field approach is used in the finite element formulation to compute nonlinear structural responses and the corresponding response gradients. The proposed method is suitable for the reliability analysis of geometrically nonlinear frame structures with flexible connections. The mechanical properties of the nonlinear flexible connections can be deterministic or random. A random index parameter is introduced as a basic random variable to consider the uncertainties in the modeling of the connections. Structures with different types of connections can be handled by this method. An efficient method is also proposed for the reliability analysis of highly redundant elastic-perfectly-plastic frame structures with large deformations under proportional loading. The proposed method avoids dealing with the complicated failure mechanisms and stable configurations in the structure system reliability analysis, and has several advantages over the other available methods.
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Wang, Donghai. "Gaussian Finite Element Closure of Steady State Unsaturated Flow in Randomly Heterogeneous Soils." Diss., Tucson, Arizona : University of Arizona, 2005. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu%5Fetd%5F1331%5F1%5Fm.pdf&type=application/pdf.
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Carella, Alfredo Raúl. "Spectral Finite Element Methods for solving Fractional Differential Equations with applications in Anomalous Transport." Doctoral thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for energi- og prosessteknikk, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-17656.
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Quantifying species transport rates is a main concern in chemical and petrochemical industries. In particular, the design and operation of many large-scale industrial chemical processes is as much dependent on diffusion as it is on reaction rates. However, the existing diffusion models sometimes fail to predict experimentally observed behaviors and their accuracy is usually insufficient for process optimization purposes. Fractional diffusion models offer multiple possibilities for generalizing Fick’s law in a consistent manner in order to account for history dependence and nonlocal effects. These models have not been extensively applied to the study of real systems, mainly due to their computational cost and mathematical complexity. A least squares spectral formulation was developed for solving fractional differential equations. The proposed method was proven particularly well-suited for dealing with the numerical difficulties inherent to fractional differential operators. The practical implementation was explained in detail in order to enhance reproducibility, and directions were specified for extending it to multiple dimensions and arbitrarily shaped domains. A numerical framework based on the least-squares spectral element method was developed for studying and comparing anomalous diffusion models in pellets. This simulation tool is capable of solving arbitrary integro-differential equations and can be effortlessly adapted to various problems in any number of dimensions. Simulations of the flow around a cylindrical particle were achieved by extending the functionality of the developed framework. A test case was analyzed by coupling the boundary condition yielded by the fluid model with two families of anomalous diffusion models: hyperbolic diffusion and fractional diffusion. Qualitative guidelines for determining the suitability of diffusion models can be formulated by complementing experimental data with the results obtained from this approach.
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Mardyanto, Mas Agus. "A solution to an inverse problem of groundwater flow using stochastic finite element method." Thesis, University of Ottawa (Canada), 2004. http://hdl.handle.net/10393/29139.
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In this study, a stochastic finite element method is used to solve an inverse problem in groundwater flow. The adjoint states method combined with cokriging method is used to estimate the distribution of hydraulic conductivities in an area where hydraulic heads and hydraulic conductivities are measured at some locations. This method starts with obtaining the expected hydraulic heads in the entire study domain at different times. Then, the adjoint states at different times are calculated. Using both calculated values as input, the Jacobians that are needed for the development of covariance matrices of hydraulic heads at different times and the cross-covariance matrices between hydraulic heads at different times and hydraulic conductivities in the aquifer are calculated. Using the maximum likelihood estimate method (MLE), which utilizes all covariance and cross-covariance matrices obtained from the previous step, the statistical parameters (mean, variance, and correlation scale) of the model are estimated. Using the statistical parameter values and all observed values of hydraulic heads at different times and all measured hydraulic conductivities, the distribution of hydraulic conductivity in the entire study domain is estimated.
An attempt is made in this thesis to verify the computer program by utilizing two hypothetical problems as verification cases. In some parts of the aquifer, mostly at locations around the observation wells, the resulting hydraulic conductivity distributions have the same pattern with the "true" distribution patterns in both cases of verification. The values of L2-norms calculated by using the "true" and estimated values of log hydraulic conductivity are 0.18 and 0.57 for Case 1 and 2, respectively.
Data from two field problems are analyzed as an application of the computer program. The estimated values of hydraulic conductivity are found to be within the range of the observed values given in the original reports. These applications can be considered as a part of the validation of the method.
Considering the results of both case studies, it appears that the computer program developed in this study can be used with reasonable success to estimate the hydraulic conductivity distribution in real aquifers. As will be explained in the discussion of the results, however, the effect of zonation needs to be investigated further. (Abstract shortened by UMI.)
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Gao, Liwei. "Stochastic finite element method for the reliability analysis of nonlinear frames with PR connections." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186898.
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A nonlinear stochastic finite element-based procedure is developed for reliability analyses of structures. The procedure is based on the First Order Reliability Method. The failure criteria of structures are expressed in terms of the ultimate and serviceability state functions. The adjoint variable method is used to formulate the computation of the gradient vector. The assumed stress-based finite element method is used to compute nonlinear structural responses and the corresponding response gradients for steel frames. Nonlinearities due to geometry, material and partially restrained connections are considered in the procedure. A computational model based on the Richard model is developed to address the uncertain properties of partially restrained connections. The material properties, geometric properties, connections parameters and external loads are considered as random variables. Several observations with design implications are made from numerical examples. Frames designed considering strength may not be acceptable when serviceability is considered. The presence of partially restrained connections changes the stress distribution in frames and makes frames more flexible so that serviceability could become the governing limit state. It is essential to properly consider the presence of partially restrained connections in the analysis and design of frames. The proposed method can be used as an alternative to the currently available methods to design a structure and evaluate the corresponding reliability. As an extended study, an efficient finite element-based procedure is also developed for estimating nonlinear responses of complex two or three dimensional steel frames with partially restrained connections under dynamic and seismic excitations. The hysteretic behavior of partially restrained connections are modeled by using the Masing rule combined with the Richard model to describe the loading, unloading and reverse loading paths for connections. Numerical examples show that this procedure is accurate and efficient compared with other existing nonlinear methods.
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Jeisman, Joseph Ian. "Estimation of the parameters of stochastic differential equations." Thesis, Queensland University of Technology, 2006. https://eprints.qut.edu.au/16205/1/Joseph_Jesiman_Thesis.pdf.
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Stochastic di®erential equations (SDEs) are central to much of modern finance theory and have been widely used to model the behaviour of key variables such as the instantaneous short-term interest rate, asset prices, asset returns and their volatility. The explanatory and/or predictive power of these models depends crucially on the particularisation of the model SDE(s) to real data through the choice of values for their
parameters. In econometrics, optimal parameter estimates are generally considered to be those that maximise the likelihood of the sample. In the context of the estimation of the parameters of SDEs, however, a closed-form expression for the likelihood function is rarely available and hence exact maximum-likelihood (EML) estimation is
usually infeasible. The key research problem examined in this thesis is the development
of generic, accurate and computationally feasible estimation procedures based on the ML principle, that can be implemented in the absence of a closed-form expression for the likelihood function. The overall recommendation to come out of the thesis is that an estimation procedure based on the finite-element solution of a reformulation of the Fokker-Planck equation in terms of the transitional cumulative distribution function(CDF) provides the best balance across all of the desired characteristics. The recommended approach involves the use of an interpolation technique proposed in this thesis which greatly reduces the required computational effort.
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Jeisman, Joseph Ian. "Estimation of the parameters of stochastic differential equations." Queensland University of Technology, 2006. http://eprints.qut.edu.au/16205/.
Full textAbstract:
Stochastic di®erential equations (SDEs) are central to much of modern finance theory and have been widely used to model the behaviour of key variables such as the instantaneous short-term interest rate, asset prices, asset returns and their volatility. The explanatory and/or predictive power of these models depends crucially on the particularisation of the model SDE(s) to real data through the choice of values for their parameters. In econometrics, optimal parameter estimates are generally considered to be those that maximise the likelihood of the sample. In the context of the estimation of the parameters of SDEs, however, a closed-form expression for the likelihood function is rarely available and hence exact maximum-likelihood (EML) estimation is usually infeasible. The key research problem examined in this thesis is the development of generic, accurate and computationally feasible estimation procedures based on the ML principle, that can be implemented in the absence of a closed-form expression for the likelihood function. The overall recommendation to come out of the thesis is that an estimation procedure based on the finite-element solution of a reformulation of the Fokker-Planck equation in terms of the transitional cumulative distribution function(CDF) provides the best balance across all of the desired characteristics. The recommended approach involves the use of an interpolation technique proposed in this thesis which greatly reduces the required computational effort.
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Fitzgerald, Anthony P. "A general variational principle for random and fields in elastic solid mechanics." Thesis, Georgia Institute of Technology, 1987. http://hdl.handle.net/1853/21462.
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Banz, Lothar [Verfasser]. "hp-finite element and boundary element methods for elliptic, elliptic stochastic, parabolic and hyperbolic obstacle and contact problems / Lothar Banz." Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2012. http://d-nb.info/1022752340/34.
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Baingo, Darek. "A Framework for Stochastic Finite Element Analysis of Reinforced Concrete Beams Affected by Reinforcement Corrosion." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/23063.
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Corrosion of reinforcing bars is the major cause of deterioration of reinforced concrete (RC) structures in North America, Europe, the Middle East, and many coastal regions around the world. This deterioration leads to a loss of serviceability and functionality and ultimately affects the structural safety. The objective of this research is to formulate and implement a general stochastic finite element analysis (SFEA) framework for the time-dependent reliability analysis of RC beams with corroding flexural reinforcement. The framework is based on the integration of nonlinear finite element and reliability analyses through an iterative response surface methodology (RSM). Corrosion-induced damage is modelled through the combined effects of gradual loss of the cross-sectional area of the steel reinforcement and the reduction bond between steel and concrete for increasing levels of corrosion. Uncertainties in corrosion rate, material properties, and imposed actions are modelled as random variables. Effective implementation of the framework is achieved by the coupling of commercial finite element and reliability software. Application of the software is demonstrated through a case study of a simply-supported RC girder with tension reinforcement subjected to the effects of uniform (general) corrosion, in which two limit states are considered: (i) a deflection serviceability limit state and (ii) flexural strength ultimate limit state. The results of the case study show that general corrosion leads to a very significant decrease in the reliability of the RC beam both in terms of flexural strength and maximum deflections. The loss of strength and serviceability was shown to be predominantly caused by the loss of bond strength, whereas the gradual reduction of the cross-sectional area of tension reinforcement was found to be insignificant. The load-deflection response is also significantly affected by the deterioration of bond strength (flexural strength and stiffness). The probability of failure at the end of service life, due to the effects of uniform corrosion-induced degradation, is observed to be approximately an order of magnitude higher than in the absence of corrosion. Furthermore, the results suggest that flexural resistance of corroded RC beams is controlled by the anchorage (bond) of the bars and not by the yielding of fully bonded tensile reinforcement at failure. This is significant since the end regions can be severely corroded due to chloride, moisture, and oxygen access at connections and expansion joints. The research strongly suggests that bond damage must be considered in the assessment of the time-dependent reliability of RC beams subjected to general corrosion.
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Scinocca, Francisco. "Uncertainty quantification of aircraft modal analysis using perturbation technique in the stochastic finite element method." Instituto Tecnológico de Aeronáutica, 2012. http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2062.
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Structural members, such as, stiffeners are applied to aeronautical structures in order to promote the necessary global or local dynamic stiffness. The manufacture and assembly process of these parts and machines capability can introduce variability in the parts and thereby incorporating uncertainties in the structural performance. Tolerances known as GD&T (Geometrical dimensioning and Tolerance), must be specified for several dimensions during the engineering design, in order to enable the manufacture of the structure. In the same way, some material properties have variability, when different suppliers are involved. Thus, the uncertainties must be incorporated into the structural analysis in order to obtain a more reliable design. Therefore, the present thesis applies the SFEM to incorporate these uncertainties in a typical structural member and panel applied in the aeronautical industry. The approach used was Perturbation Technique using Taylor series expansions to incorporate the uncertainties in the structural members typically used in aircraft. Natural frequencies, frequency response functions and modal analysis are studied in order to understand the consequences of these uncertainties in a beam with hat and "Z" section normally applied as an aircraft panel stiffener. The stiffeners were modeled considering the Timoshenko Theory in Matlab software. Sensitivity analyses were applied for the correct interpretations and trends of the top contributors. Also an aircraft panel was performed using Nastran and Matlab software together to incorporate these uncertainties on the modal analysis. Final conclusions and issues of implementation and applicability are performed using MCS as a validation model for the stiffeners and the total range variation for the aircraft panel.
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Jeong, Gi Young. "Tensile Properties of Loblolly Pine Strands Using Digital Image Correlation and Stochastic Finite Element Method." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/29563.
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Previous modeling of wood materials has included many assumptions of unknown mechanical properties associated with the hierarchical structure of wood. The experimental validation of previous models did not account for the variation of mechanical properties present in wood materials. Little research has explored the uncertainties of mechanical properties in earlywood and latewood samples as well as wood strands. The goal of this study was to evaluate the effect of the intra-ring properties and grain angles on the modulus of elasticity (MOE) and ultimate tensile strength (UTS) of different orientation wood strands and to analyze the sensitivity of the MOE and UTS of wood strands with respect to these variables.
Tension testing incorporating digital image correlation (DIC) was employed to measure the MOE and UTS of earlywood and latewood bands sampled from growth ring numbers 1-10 and growth ring numbers 11-20. A similar technique adjusted for strand size testing was also applied to measure the MOE and UTS of different orientation wood strands from the two growth ring numbers. The stochastic finite element method (SFEM) was used with the results from the earlywood and latewood testing as inputs to model the mechanical property variation of loblolly pine wood strands. A sensitivity analysis of the input parameters in the SFEM model was performed to identify the most important parameters related to mechanical response.
Modulus of elasticity (MOE), Poisson ratio, and ultimate tensile strength (UTS) from earlywood and latewood generally increased as the growth ring number increased except for the UTS of latewood, which showed a slight decrease. MOE and UTS from radial, tangential, and angled grain orientation strands increased as the growth ring numbers increased while MOE and UTS from cross-grain strands decreased as the growth ring number increased. Shear modulus of wood strands increased as the growth ring number increased while shear strength decreased as the growth ring number increased. Poisson ratio from radial and angled grain strands decreased as the growth ring number increased while Poisson ratio from tangential and cross grain orientation strands increased as the growth ring number increased.
The difference of average MOE from different grain strands between experimental results and SFEM results ranged from 0.96% to 22.31%. The cumulative probability distribution curves from experimental tests and SFEM results agreed well except for the radial grain models from growth ring numbers 11-20. From sensitivity analysis, earlywood MOE was the most important contributing factor to the predicted MOE from different grain orientation strand models. From the sensitivity analysis, earlywood and latewood participated differently in the computation of MOE of different grain orientation strand models. The predicted MOE was highly associated with the strain distribution caused by different orientation strands and interaction of earlywood and latewood properties. In general, earlywood MOE had a greater effect on the predicted MOE of wood strands than other SFEM input parameters.
The difference in UTS between experimental and SFEM results ranged from 0.09% to 11.09%. Sensitivity analysis showed that grain orientation and growth ring number influenced the UTS of strands. UTS of strands from growth ring numbers 1-10 showed strength indexes (Xt, Yt, and S) to be the dominant factors while UTS of strands from growth ring numbers 11-20 showed both strength indexes and stress components (Ï 1, Ï 2, and Ï 12) to be the dominant factors. Grain orientations of strands were a strong indicator of mechanical properties of wood strands.Ph. D.
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Dechamps, Xavier. "Numerical simulation of incompressible magnetohydrodynamic duct and channel flows by a hybrid spectral, finite element solver." Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209203.
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In this dissertation, we are concerned with the numerical simulation for flows of electrically conducting fluids exposed to an external magnetic field (also known as magnetohydrodynamics or in short MHD). The aim of the present dissertation is twofold. First, the in-house CFD hydrodynamic solver SFELES is extended to MHD problems. Second, MHD turbulence is studied in the simple configuration of a MHD pipe flow within an external transverse magnetic field. Chapter 2 of this dissertation aims at reminding the physical equations that govern incompressible MHD problems. Two equivalent formulations are put forward in the particular case of quasi-static MHD. Chapter 3 is devoted to the detailed development of the hybrid spectral - stabilized finite element methods for quasi-static MHD problems. The extension of SFELES is made for both Cartesian and axisymmetric systems of coordinates. The short chapter 4 follows to provide the performances of SFELES executed by several processes in a parallel environment. The addition of a parallel direct solver is studied in regards with the memory and time requirements. The extension of SFELES is then validated in chapter 5 with test cases of increasing complexity. For this purpose, laminar flows with an existing analytical-asymptotic solution are considered. The subject of chapter 6 is the MHD turbulent pipe flow within an external transverse and uniform magnetic field. The results are partially compared with the corresponding hydrodynamic flow and with a few data available in the literature. / Le thème de cette thèse de doctorat est la simulation numérique d'écoulements de fluides conducteurs d'électricité qui sont exposés à un champ magnétique extérieur (également connu sous le nom de magnétohydrodynamique ou encore MHD). L'objectif de ce travail est double. Premièrement, le code CFD maison SFELES est étendu aux problèmes MHD. Deuxièmement, la turbulence MHD est étudiée dans la configuration de l'écoulement en conduite cylindrique à l'intérieur d'un champ magnétique transverse. Le chapitre 2 de cette thèse a pour but de rappeler les équations qui gouvernent les problèmes de MHD incompressible. Deux formulations équivalente sont mises en évidence dans le cas particulier de la MHD quasi-statique. Le chapitre 3 est dévoué au développement détaillé des méthodes spectrale - éléments finis pour la MHD quasi-statique. L'extension de SFELES est réalisée dans les systèmes de coordonnées cartésiennes et axisymétriques. Le court chapitre 4 suit pour fournir les performances de SFELES exécuté sur plusieurs processeurs dans un environnement parallèle. L'ajout d'un solveur parallèle direct est étudié en ce qui concerne les demandes en temps et mémoire. L'extension de SFELES est alors validée dans le chapitre 5 avec des cas d'étude de complexité croissante. Dans ce but, des écoulements laminaires avec solution théorique-asymptotique sont envisagés. Le sujet du chapitre 6 est l'écoulement MHD turbulent en conduite cylindrique à l'intérieur d'un champ magnétique transverse et uniforme. Les résultats sont partiellement comparés avec l'écoulement hydrodynamique correspondant et avec des données disponibles dans la littérature.Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished
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Zeng, Wei. "Advanced Development of Smoothed Finite Element Method (S-FEM) and Its Applications." University of Cincinnati / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439309306.
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Birgersson, Fredrik. "Prediction of random vibration using spectral methods." Doctoral thesis, KTH, Aeronautical and Vehicle Engineering, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3694.
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Much of the vibration in fast moving vehicles is caused bydistributed random excitation, such as turbulent flow and roadroughness. Piping systems transporting fast flowing fluid isanother example, where distributed random excitation will causeunwanted vibration. In order to reduce these vibrations andalso the noise they cause, it is important to have accurate andcomputationally efficient prediction methods available.
The aim of this thesis is to present such a method. Thefirst step towards this end was to extend an existing spectralfinite element method (SFEM) to handle excitation of planetravelling pressure waves. Once the elementary response tothese waves is known, the response to arbitrary homogeneousrandom excitation can be found.
One example of random excitation is turbulent boundary layer(TBL) excitation. From measurements a new modified Chase modelwas developed that allowed for a satisfactory prediction ofboth the measured wall pressure field and the vibrationresponse of a turbulence excited plate. In order to model morecomplicated structures, a new spectral super element method(SSEM) was formulated. It is based on a waveguide formulation,handles all kinds of boundaries and its elements are easily putinto an assembly with conventional finite elements.
Finally, the work to model fluid-structure interaction withanother wave based method is presented. Similar to the previousmethods it seems to be computationally more efficient thanconventional finite elements.
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Khokhar, Zahid R. "Finite-element analysis of delamination in CFRP laminates : effect of material randomness." Thesis, Loughborough University, 2010. https://dspace.lboro.ac.uk/2134/6125.
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Laminated carbon fibre-reinforced polymer (CFRP) composites are already well established in structural applications where high specific strength and stiffness are required. Damage in these laminates is usually localised and may involve numerous mechanisms, such as matrix cracking, laminate delamination, fibre debonding or fibre breakage. Microstructures in CFRPs are non-uniform and irregular, resulting in an element of randomness in the localised damage. This may in turn affect the global properties and failure parameters of components made of CFRPs. This raises the question of whether the inherent stochasticity of localised damage is of significance for application of such materials. This PhD project is aimed at developing numerical models to analyze the effect of material randomness on delamination damage in CFRP materials by the implementation of the cohesive-zone model (CZM) within the framework of the finite-element (FE) method. Both the unidirectional and cross-ply laminates subjected to quasi-static loading conditions were studied. The initiation and propagation in delamination of unidirectional CFRP laminates were analyzed. The CZM was used to simulate the progress of that failure mechanism in a pre-cracked double-cantilever beam (DCB) specimen loaded under mode-I employing initially, a two-dimensional FE model. Model validation was then carried out comparing the numerical results with experimental data. The inherent microstructural stochasticity of CFRP laminates was accounted for in the simulations, and various statistical realizations for a half-scatter of 50% of fracture energy were performed, based on the approximation of that parameter with the Weibull s two-parameter probability density function. More detailed analyses were undertaken employing three-dimensional DCB models, and a number of statistical realizations based on variation of fracture energy were presented. In contrast to the results of two-dimensional analyses, simulations with 3D models demonstrated a lower load-bearing capacity for most of the random models as compared to the deterministic model with uniform material properties. The damaged area and the crack lengths in laminates were analyzed, and the results showed higher values of those parameters for random realizations compared to the uniform case for the same levels of applied displacement. The effect of material randomness on delamination in CFRP cross-ply laminates was also investigated. Initially, two-dimensional finite-element analyses were carried out to study the effect of microstructural randomness in a cross-ply laminate under bending with the direct introduction of matrix cracks with varying spacings and delamination zones. A considerable variation in the stiffness for cases with different crack spacings suggested that the assumption of averaged distributions of defects can lead to unreliable predictions of structural response. Three-dimensional uniform, deterministic cross-ply laminate models subjected to a tensile load were analyzed to study the delamination initiation and propagation from the tips of a pre-existing matrix crack. The material s stochasticity was then introduced, and a number of random statistical realizations were analyzed. It was observed that by neglecting the inherent material randomness of CFRP laminates, the initiation conditions for delamination as well as the character of its propagation cannot be properly detected and studied. For instance, the delamination crack length value for all the simulated random statistical realizations predicted its higher magnitudes compared to the uniform (deterministic) case for the same value of applied strain. Furthermore, the location of delamination initiation was shown to be different for different random statistical realizations. Another aspect, emphasizing the importance of microstructural randomness, was the scatter in the magnitudes of global strain at the instance of initiation and subsequent propagation of delamination. In summary, the material randomness in CFRPs can induce randomness in localised damage and it can affect the global properties of laminates and critical failure parameters. These effects can be investigated computationally through the use of stochastic cohesive-zone elements.
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Locatelli, Marco. "Order reduction strategies for stochastic Galerkin matrix equations." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/15881/.
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Lo scopo di questa tesi è l'implementazione di un algoritmo in grado di risolvere in maniera efficiente sistemi lineari provenienti da un'approssimazione agli elementi finiti di Galerkin stocastica di equazioni alle derivate parziali con dati aleatori.
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Lan, Shuang Wen. "Stochastic finite element analysis of structures with elementary stiffness matrix decomposition method and exponential polynomial moment method." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2148241.
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Haque, Md Zakiul. "A combined experimental and stochastic finite element analysis methodology for the probabilistic fracture behavior of composite laminates." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape4/PQDD_0017/MQ47836.pdf.
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Traverso, Luca. "Mixed finite element and stochastic Galerkin methods for groundwater flow modelling : efficiency analysis and real-life application." Thesis, Cardiff University, 2010. http://orca.cf.ac.uk/55531/.
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The thesis concludes with the development of a numerical model for a real case study in the United Kingdom, which is one of the first examples of formal characterization of model uncertainty for an actual site.
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Karavelić, Emir. "Stochastic Galerkin finite element method in application to identification problems for failure models parameters in heterogeneous materials." Thesis, Compiègne, 2019. http://www.theses.fr/2019COMP2501.
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Cette thèse traite de rupture localisée de structures construites en matériau composite hétérogène, comme le béton, à deux échelles différentes. Ces deux échelles sont connectées par le biais de la mise à l'échelle stochastique, où toute information obtenue à l'échelle méso est utilisée comme connaissance préalable à l'échelle macro. À l'échelle méso, le modèle de réseau est utilisé pour représenter la structure multiphasique du béton, à savoir le ciment et les granulats. L'élément de poutre représenté par une poutre Timoshenko 3D intégrée avec de fortes discontinuités assure un maillage complet indépendance de la propagation des fissures. La géométrie de la taille des agrégats est prise en accord avec la courbe EMPA et Fuller tandis que la distribution de Poisson est utilisée pour la distribution spatiale. Les propriétés des matériaux de chaque phase sont obtenues avec une distribution gaussienne qui prend en compte la zone de transition d'interface (ITZ) par l'affaiblissement du béton. À l'échelle macro, un modèle de plasticité multisurface est choisi qui prend en compte à la fois la contribution d'un écrouissage sous contrainte avec une règle d'écoulement non associative ainsi que des composants d'un modèle d'adoucissement de déformation pour un ensemble complet de différents modes de défaillance 3D. Le modèle de plasticité est représenté par le critère de rendement Drucker-Prager, avec une fonction potentielle plastique similaire régissant le comportement de durcissement tandis que le comportement de ramollissement des contraintes est représenté par le critère de St. Venant. La procédure d'identification du modèle macro-échelle est réalisée de manière séquentielle. En raison du fait que tous les ingrédients du modèle à l'échelle macro ont une interprétation physique, nous avons fait l'étalonnage des paramètres du matériau en fonction de l'étape particulière. Cette approche est utilisée pour la réduction du modèle du modèle méso-échelle au modèle macro-échelle où toutes les échelles sont considérées comme incertaines et un calcul de probabilité est effectué. Lorsque nous modélisons un matériau homogène, chaque paramètre inconnu du modèle réduit est modélisé comme une variable aléatoire tandis que pour un matériau hétérogène, ces paramètres de matériau sont décrits comme des champs aléatoires. Afin de faire des discrétisations appropriées, nous choisissons le raffinement du maillage de méthode p sur le domaine de probabilité et la méthode h sur le domaine spatial. Les sorties du modèle avancé sont construites en utilisant la méthode de Galerkin stochastique fournissant des sorties plus rapidement le modèle avancé complet. La procédure probabiliste d'identification est réalisée avec deux méthodes différentes basées sur le théorème de Bayes qui permet d'incorporer de nouvelles bservations générées dans un programme de chargement particulier. La première méthode Markov Chain Monte Carlo (MCMC) est identifiée comme mettant à jour la mesure, tandis que la deuxième méthode Polynomial Chaos Kalman Filter (PceKF) met à jour la fonction mesurable. Les aspects de mise en œuvre des modèles présentés sont donnés en détail ainsi que leur validation à travers les exemples numériques par rapport aux résultats expérimentaux ou par rapport aux références disponibles dans la littératureThis thesis deals with the localized failure for structures built of heterogeneous composite material, such as concrete, at two different scale. These two scale are latter connected through the stochastic upscaling, where any information obtained at meso-scale are used as prior knowledge at macro-scale. At meso scale, lattice model is used to represent the multi-phase structure of concrete, namely cement and aggregates. The beam element represented by 3D Timoshenko beam embedded with strong discontinuities ensures complete mesh independency of crack propagation. Geometry of aggregate size is taken in agreement with EMPA and Fuller curve while Poisson distribution is used for spatial distribution. Material properties of each phase is obtained with Gaussian distribution which takes into account the Interface Transition Zone (ITZ) through the weakening of concrete. At macro scale multisurface plasticity model is chosen that takes into account both the contribution of a strain hardening with non-associative flow rule as well as a strain softening model components for full set of different 3D failure modes. The plasticity model is represented with Drucker-Prager yield criterion, with similar plastic potential function governing hardening behavior while strain softening behavior is represented with St. Venant criterion. The identification procedure for macro-scale model is perfomed in sequential way. Due to the fact that all ingredients of macro-scale model have physical interpretation we made calibration of material parameters relevant to particular stage. This approach is latter used for model reduction from meso-scale model to macro-scale model where all scales are considered as uncertain and probability computation is performed. When we are modeling homogeneous material each unknown parameter of reduced model is modeled as a random variable while for heterogeneous material, these material parameters are described as random fields. In order to make appropriate discretizations we choose p-method mesh refinement over probability domain and h-method over spatial domain. The forward model outputs are constructed by using Stochastic Galerkin method providing outputs more quickly the the full forward model. The probabilistic procedure of identification is performed with two different methods based on Bayes’s theorem that allows incorporating new observation generated in a particular loading program. The first method Markov Chain Monte Carlo (MCMC) is identified as updating the measure, whereas the second method Polynomial Chaos Kalman Filter (PceKF) is updating the measurable function. The implementation aspects of presented models are given in full detail as well as their validation throughthe numerical examples against the experimental results or against the benchmarks available from literature