Relevant bibliographies by topics / Numerical Limit Analysis

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Numerical Limit Analysis'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Numerical Limit Analysis"

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JIN, SHI, XIAOMEI LIAO, and XU YANG. "THE VLASOV–POISSON EQUATIONS AS THE SEMICLASSICAL LIMIT OF THE SCHRÖDINGER–POISSON EQUATIONS: A NUMERICAL STUDY." Journal of Hyperbolic Differential Equations 05, no. 03 (September 2008): 569–87. http://dx.doi.org/10.1142/s021989160800160x.

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In this paper, we numerically study the semiclassical limit of the Schrödinger–Poisson equations as a selection principle for the weak solution of the Vlasov–Poisson in one space dimension. Our numerical results show that this limit gives the weak solution that agrees with the zero diffusion limit of the Fokker–Planck equation. We also numerically justify the multivalued solution given by a moment system of the Vlasov–Poisson equations as the semiclassical limit of the Schrödinger–Poisson equations.
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Labbé, Stéphane, and Lionel Paumond. "Numerical comparisons of two long-wave limit models." ESAIM: Mathematical Modelling and Numerical Analysis 38, no. 3 (May 2004): 419–36. http://dx.doi.org/10.1051/m2an:2004020.

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Liu, Ying Hua, Bing Ye Xu, and Xian He Du. "A Numerical Approach for Lower Bound Limit Analysis." Key Engineering Materials 626 (August 2014): 474–81. http://dx.doi.org/10.4028/www.scientific.net/kem.626.474.

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In this paper, a numerical procedure for plastic limit analysis of 3-D elastic-perfectly plastic bodies under complex loads is presented. The method is based on the lower-bound limit theorem and von Mises yield criterion so that the lower-bound limit analysis can be conducted by solving a nonlinear mathematical programming problem. A SQP algorithm and a dimension reduction-based technique are used to solve the discretized finite element optimization formulation. A conception of active constraint set is introduced, so that the number of constraints can be reduced greatly. The basis vectors of reduced residual stress spaces are constructed by performing an equilibrium iteration procedure of elasto-plastic finite element analysis. The numerical procedure is applied to carry out the plastic limit analysis of pipelines with part-through slots under internal pressure, bending moment and axial force. The effects of different sizes of part-through slots on the limit loads of pipelines are studied.
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Beran, P. S., N. S. Khot, F. E. Eastep, R. D. Snyder, and J. V. Zweber. "Numerical Analysis of Store-Induced Limit-Cycle Oscillation." Journal of Aircraft 41, no. 6 (November 2004): 1315–26. http://dx.doi.org/10.2514/1.404.

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Clarke, Samuel D., Colin C. Smith, and Matthew Gilbert. "Modelling discrete soil reinforcement in numerical limit analysis." Canadian Geotechnical Journal 50, no. 7 (July 2013): 705–15. http://dx.doi.org/10.1139/cgj-2012-0387.

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Soil reinforcement is widely used in geotechnical engineering. While there are various means of accounting for the presence of soil reinforcement in limit analysis and limit equilibrium type calculations, these are often highly problem-specific. In this paper, a general means of incorporating soil reinforcement within numerical limit analysis calculations is presented. A key feature of this implementation is that the reinforcement is modelled “in parallel” with the soil model, which allows the soil to flow past the reinforcement as might occur in soil nailing. To illustrate this, the “discontinuity layout optimization” (DLO) numerical limit analysis procedure is used, and the efficacy of the approach is evaluated via application to reinforced slope problems involving rigid soil nails under plane strain conditions. The analyses are calibrated against a two-part wedge analysis method, as presented in British Standard BS 8006:1995 or AASHTO’s LRFD bridge design specifications. It is shown that the DLO-based procedure produces identical results only when the two-part wedge collapse mechanism is prescribed in advance (achieved by artificially strengthening the soil except along pre-defined failure planes). A more critical mechanism is otherwise predicted, with the soil strength at collapse required to be approximately 10% higher than predicted by the two-part wedge method (or alternatively, soil nail lengths required to be approximately 20% greater).
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Kuznetsov, Yu A., W. Govaerts, E. J. Doedel, and A. Dhooge. "Numerical Periodic Normalization for Codim 1 Bifurcations of Limit Cycles." SIAM Journal on Numerical Analysis 43, no. 4 (January 2005): 1407–35. http://dx.doi.org/10.1137/040611306.

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Jiang, Kai Yu, Jing Cao, and Yue Ma. "Slope Stability Analysis Based on Limit Equilibrium and Numerical Analysis." Applied Mechanics and Materials 256-259 (December 2012): 198–202. http://dx.doi.org/10.4028/www.scientific.net/amm.256-259.198.

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Based on the background of a foundation pit slope of the tertiary strong weathered basalt(TSWB), a quantitative analysis of the slope stability is proposed by combination of the limit equilibrium and the numerical analysis. The analysis also considers the effects of the natural state and soaking state Then, as an example, an ultra-deep foundation pit slope (UFPS) is analyzed under the background of TSWB. The Janbu method is used in the limit equilibrium because it can meet all the equilibrium conditions, including the force and moment equilibrium equation. The Lagrangian difference method which based on shear strength reduction is adopted in numerical analysis. Some meaningful conclusions can be obtained through comparing analysis the calculation results of Janbu method with finite difference method. These conclusions can be given a reference to similar projects.
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Cáceres, María-José, José-Antonio Carrillo, and Pierre Degond. "The Child–Langmuir limit for semiconductors: a numerical validation." ESAIM: Mathematical Modelling and Numerical Analysis 36, no. 6 (November 2002): 1161–76. http://dx.doi.org/10.1051/m2an:2003011.

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Antão, A. N., and M. Vicente da Silva. "Three-dimensional Limit Analysis with Lade-Duncan criterion." Géotechnique Letters 12, no. 2 (June 1, 2022): 1–21. http://dx.doi.org/10.1680/jgele.22.00015.

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The paper describes the three-dimensional numerical implementation of the Lade-Duncan criterion in a finite element limit analysis (FELA) code. Validation is done using examples with a known solution. To conclude the proposed numerical tool is applied to the calculation of the ultimate bearing capacity of square footing.
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Bambach, Markus, M. Todorova, and Gerhard Hirt. "Experimental and Numerical Analysis of Forming Limits in CNC Incremental Sheet Forming." Key Engineering Materials 344 (July 2007): 511–18. http://dx.doi.org/10.4028/www.scientific.net/kem.344.511.

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Asymmetric incremental sheet forming (AISF) is a relatively new manufacturing process for the production of low volumes of sheet metal parts. Forming is accomplished by the CNC controlled movements of a simple ball-headed tool that follows a 3D trajectory to gradually shape the sheet metal blank. Due to the local plastic deformation under the tool, there is almost no draw-in from the flange region to avoid thinning in the forming zone. As a consequence, sheet thinning limits the amount of bearable deformation, and thus the range of possible applications. Much attention has been given to the maximum strains that can be attained in AISF. Several authors have found that the forming limits are considerably higher than those obtained using a Nakazima test and that the forming limit curve is approximately a straight line (mostly having a slope of -1) in the stretching region of the FLD. Based on these findings they conclude that the “conventional” forming limit curves cannot be used for AISF and propose dedicated tests to record forming limit diagrams for AISF. Up to now, there is no standardised test and no evaluation procedure for the determination of FLCs for AISF. In the present paper, we start with an analysis of the range of strain states and strain paths that are covered by the various tests that can be found in the literature. This is accomplished by means of on-line deformation measurements using a stereovision system. From these measurements, necking and fracture limits are derived. It is found that the fracture limits can be described consistently by a straight line with negative slope. The necking limits seem to be highly dependent on the test shapes and forming parameters. It is concluded that standardisation in both testing conditions and the evaluation procedures is necessary, and that a forming limit curve does not seem to be an appropriate tool to predict the feasibility of a given part design.
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Dissertations / Theses on the topic "Numerical Limit Analysis"

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Visram, Abeed. "Asymptotic limit analysis for numerical models of atmospheric frontogenesis." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/23219.

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Accurate prediction of the future state of the atmosphere is important throughout society, ranging from the weather forecast in a few days time to modelling the effects of a changing climate over decades and generations. The equations which govern how the atmosphere evolves have long been known; these are the Navier-Stokes equations, the laws of thermodynamics and the equation of state. Unfortunately the nonlinearity of the equations prohibits analytic solutions, so simplified models of particular flow phenomena have historically been, and continue to be, used alongside numerical models of the full equations. In this thesis, the two-dimensional Eady model of shear-driven frontogenesis (the creation of atmospheric fronts) was used to investigate how errors made in a localised region can affect the global solution. Atmospheric fronts are the boundary of two different air masses, typically characterised by a sharp change in air temperature and wind direction. This occurs across a small length of O(10 km), whereas the extent of the front itself can be O(1000 km). Fronts are a prominent feature of mid-latitude weather systems and, despite their narrow width, are part of the large-scale, global solution. Any errors made locally in the treatment of fronts will therefore affect the global solution. This thesis uses the convergence of the Euler equations to the semigeostrophic equations, a simplified model which is representative of the large-scale flow, including fronts. The Euler equations were solved numerically using current operational techniques. It was shown that highly predictable solutions could be obtained, and the theoretical convergence rate maintained, even with the presence of near-discontinuous solutions given by intense fronts. Numerical solutions with successively increased resolution showed that the potential vorticity, which is a fundamental quantity in determining the large-scale, balanced flow, approached the semigeostrophic limit solution. Regions of negative potential vorticity, indicative of local areas of instability, were reduced at high resolution. In all cases, the width of the front reduced to the grid-scale. While qualitative features of the limit solution were reproduced, a stark contrast in amplitude was found. The results of this thesis were approximately half in amplitude of the limit solution. Some attempts were made at increasing the intensity of the front through spatial- and temporal-averaging. A scheme was proposed that conserves the potential vorticity within the Eady model.
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Degwitz, Fernando G. (Fernando Guillermo) 1980. "Numerical upper and lower bound limit analysis for braced excavations." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/30131.

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Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2004.
Includes bibliographical references (leaves62-63).
This thesis reviews limit theorems and their applications for stability problems in geotechnical engineering. Rigorous numerical solutions of limit analyses can be obtained through finite element discretization of the soil mass and formulation of the limit theorems within a linear programming framework. The current research uses a formulation proposed by Sloan et al. (1988) and extended in a recent Ph.D. thesis by Ukritchon (1998) to include soil-structure interactions. The thesis details the input and output required for numerical limit analysis and presents an example application for the stability of a broad excavation for the MUNI Metro Turnback project in San Francisco. This well documented case study involves a 13 M deep excavation within a deep deposit of May Mud that was supported by an SPTC wall with three levels of cross-lot bracing. The numerical limit analyses calculate factors of safety, FS = 1.03 - 1.36, against basal instability. The factor of safety used in the original design (FS = 1.2) is contained in this range. The results illustrate that numerical limit analysis offers a practical alternative to limit equilibrium methods in evaluating the stability of braced excavations.
by Fernando G. Degwitz.
M.Eng.
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ARAUJO, LUIZ GONZAGA DE. "NUMERICAL STUDIES OF THE STABILITY OF GEOTECHNICAL MATERIALS THROUGH LIMIT ANALYSIS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1997. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=2084@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
O presente trabalho apresenta um estudo de problemas de estabilidade, freqüentemente,encontrados, em Engenharia Geotécnica, através da técnica da Análise Limite associada ao Método dos Elementos Finitos (MEF).Inicialmente, faz-se uma revisão das formulações da Análise Limite, via MEF,encontradas, com maior freqüência, na literatura técnica especializada.Uma formulação mista que é descrita em detalhe na tese foi escolhida para implementação. Extensões das formulações da Análise Limite de meios contínuos são propostas para contemplar características de maciços rochosos fraturados. É proposto,também, um procedimento numérico para tratar de problemas de estabilidade de meios que exibem fluxo plástico não associado.As implementações realizadas foram validadas através de problemas cujas soluções podem ser obtidas por via analítica.Finalmente, um número considerável de problemas de interesse em Engenharia Geotécnica é estudado utilizando a implementação realizada. Os resultados destes estudos sugerem a viabilidade da utilização da técnica estudada na solução de problemas práticos de Engenharia Civil.
This work presents a study of stability problems often encountered in Geotechnical Engineering, through the use of Limit Analysis in conjunction with the Finite Element Method (FEM).Initially, a literature survey of the most often found formulations in Limit Analysis through the FEM is carried out.A mixed formulation of Limit Analysis was chosen for implementation and its details are fully described. Extensions of the formulation to deal with stability problems in fractured rock media are also proposed and described. A numerical procedure to take into account the effect of non associative plastic flow is proposed.The implementations carried out were validated through problems to which analytical solutions could be found.Finally, a considerable number of problems of interest to Geotechnical Engineering is studied with the implemented formulation. The results of these studies suggest that Limit Analysis can be considered as a viable tool in the solution of practical problems in Geotechnical Engineering.
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Prasad, Anamika 1979. "Development of user interface for numerical limit analysis of geotechnical stability problems." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/85751.

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Le, Canh. "Novel numerical procedures for limit analysis of structures : mesh-free methods and mathematical programming." Thesis, University of Sheffield, 2010. http://etheses.whiterose.ac.uk/856/.

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Current research in the field of limit analysis is focussing on the development of numerical tools which are sufficiently efficient and robust to be used in engineering practice. This places demands on the numerical discretisation strategy adopted as well as on the mathematical programming tools applied, which are the key ingredients of a typical computational limit analysis procedure. In this research, the Element-Free Galerkin (EFG) discretisation strategy is used to approximate the displacement and moment fields in plate and slab problems, and second-order cone programming (SOCP) is used to solve the resulting discretised formulations. A numerical procedure using the EFG method and second-order cone programming for the kinematic limit analysis problem was developed first. The moving least squares technique was used in combination with a stabilised conforming nodal integration scheme, both to keep the size of the optimisation problem small and to provide stable and accurate solutions. The formulation was expressed as a problem of minimizing a sum of Euclidean norms, which was then transformed into a form suitable for solution using SOCP. To improve the accuracy of solutions and to speed-up the computational process, an efficient h-adaptive EFG scheme was also developed. The naturally conforming property of meshfree approximations (with no nodal connectivity required) facilitates the implementation of h-adaptivity. The error in the computed displacement field was estimated accurately using the Taylor expansion technique. A stabilised conforming nodal integration scheme was also extended to error estimators, leading to an efficient and truly meshfree adaptive method. To obtain an indication of bounds on the solutions obtained, an equilibrium formulation was also developed. Pure moment fields were approximated using a moving least squares technique. The collocation method was used to enforce the strong form of the equilibrium equations and a stabilised conforming nodal integration scheme was introduced to eliminate numerical instability problems. The von Mises and Nielsen yield criteria were then enforced by introducing second-order cone constraints.
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Alves, Vian Marina. "Funicular solutions for masonry vaults: a review of recent and past numerical methods." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021.

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The great engineers, architects and master builders of 17th and 19th centuries constructed the most amazing vaults in the entire world. Considering that the advanced technologies were massively developed only in the 20th century, the traditional approach for constructing masonry vaults were based in the geometry. As Heyman said, the correct shape of a masonry structure ensures its safety. Nowadays, it can be consider that their practice was a success because many of these vaults still stand after all these years. This thesis describes the considerable existing approaches about funicular solution for masonry vaults with the principal features of each method and their extensions. All methods derives compression-only structural lower-bound solutions, which guarantees the safety of the vaulted structures with at least one admissible equilibrium state given its geometry and boundary conditions. The review comprehends the old methods, Graphic Statics and Limit Analysis that are a strong base to the recent ones, also presented in this paper, Thrust Network Method, Force Density Method, Thrust Network Analysis and Thrust Surface Method. In 2007, the Thrust Network Analysis was introduced by Block and Ochsendorf, since then some extensions of their work were brought up to the scientific community and they are summarized in this thesis due to the importance for upcoming improved methods. Lastly, it is presented an application of the software RhinoVAULT 2 for funicular form-finding using the Thrust Network Analysis approach. The project designed is the "Tettoia Nervi", placed in Bologna, Italy.
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ROJAS, JHONATAN EDWAR GARCIA. "NUMERICAL LIMIT ANALYSIS USING SEMIDEFINITE AND SECOND ORDER CONIC PROGRAMMING WITH APPLICATION IN STABILITY OF SHALLOW TUNNELS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2018. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36904@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
Nesse trabalho é avaliada a solução numérica do colapso na frente de escavação em túneis rasos, através da teoria de análise limite numérico, usando o teorema do limite inferior, a partir da condição de equilíbrio para as condições plásticas, além de considerar o comportamento do material rígido perfeitamente plástico. O teorema de limite inferior implica em maximizar o fator multiplicador na carga atuante, por isso a análise limite se torna um problema de otimização, nele tem que se usar a programação matemática para ser resolvido. É avaliada a solução numérica tridimensional da análise limite através do método dos elementos finitos, usando malha de elementos hexaédricos de oito nós, a análise dos elementos finitos é feita com o próprio código gerado na linguagem de programação do MATLAB 2017.As metodologias de programação matemática empregadas são: programação cônica de segunda ordem e programação semidefinida. Antes deve-se adaptar os critérios de ruptura de Drucker Prager à programação cônica de segunda ordem e Mohr-Coulomb tridimensional à programação semidefinida. Para a otimização se usa o algoritmo comercial MOSEK Aps 7.1 baseado no método do ponto interior em grande escala, na linguagem do MATLAB 2017. Além disso, obteve-se o mecanismo de colapso através da propriedade da dualidade do problema de otimização, dualidade que é cumprida pelos teoremas de limite superior e inferior.
In this work the numerical solution of the collapse in the front of excavation in shallow tunnels is evaluated through the theory of numerical limit analysis, using the lower limit theorem, from the equilibrium condition for the plastic conditions, considering the behavior of the perfectly plastic rigid material. The lower limit theorem implies maximizing the multiplier factor in the acting load, so that the limit analysis becomes an optimization problem. The three-dimensional numerical solution of the limit analysis using the finite element method is evaluated using a mesh of eight-node hexahedral elements. The finite element analysis is done using the code generated in the MATLAB 2017 programming language. The mathematical programming methodologies used are: second order conic programming and semidefinite programming. The Drucker-Prager three-dimensional criteria should be adapted to the conic programming of the second order and Mohr-Coulomb three-dimensional to the semidefinite programming. For the optimization, the MOSEK Aps 7.1 commercial algorithm based on the large-scale interior point method is used in the MATLAB 2017 language. In addition, the collapse mechanism was obtained through the duality property of the optimization problem, duality that is fulfilled by the upper and lower limit theorems.
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Antocheviz, Rafael Bugs. "Metodologia para determinação do procedimento a ser utilizado em uma análise de estabilidade de taludes : ruptura circular." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2018. http://hdl.handle.net/10183/184854.

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Análises de estabilidade de taludes, em mineração, são uma das atividades mais importantes do processo de obtenção de um bem mineral. Assegurar a estabilidade das escavações e a segurança do empreendimento são vitais para o processo de extração e, para tanto, a escolha da forma de análise (2D, quasi-tridimensional ou 3D) ou do método (equilíbrio limite ou análise numérica) mais propício para esse tipo de estudo é de suma importância. Muitas vezes o engenheiro responsável acaba baseando sua escolha na familiaridade com determinada metodologia ou na praticidade de determinado programa, em detrimento a fatores técnicos e de relevância para o estudo. Dessa forma, visando preencher tal lacuna existente atualmente e facilitar a escolha da melhor metodologia a ser utilizada, o presente estudo reúne os principais métodos conhecidos, suas vantagens e desvantagens e, assim, propõem uma metodologia para que essa escolha seja baseada em parâmetros técnicos relevantes. A metodologia proposta é, de certa forma, restritiva na escolha dos procedimentos que serão considerados, uma vez que, buscou-se utilizar métodos que tenham sua aplicabilidade comprovada, que possuam vantagens consideráveis sobre outros métodos e que sejam rigorosos, ou seja, satisfaçam todas as condições de equilíbrio (forças e momentos). Para corroborar com a metodologia proposta, quatro situações práticas diferentes foram apresentadas, demonstrando a aplicabilidade da metodologia.
Analysis of slope stability in mining is one of the most important activities of the process of obtaining a mineral resources. Ensuring the excavation stability and the safety of the project are vital to the extraction process. The choice of the form of analysis (2D, quasi-threedimensional or 3D) or of the method (limit equilibrium or numerical analysis) more suitable for this type of study is of paramount importance since, the responsible engineer often end up basing the analysis on familiarity with a particular methodology or on the availability of a particular program, to the detriment of technical factors and relevance to the study. Thus, in order to fill this existing gap and facilitate the selection of the best methodology to be used, the present study brings together the main known methods, their advantages and disadvantages and, therefore, presents a methodology for such a choice to be based on relevant technical parameters. The proposed methodology is somewhat restrictive in the choice of procedures that will be considered, since it has been tried to use methods that have proven applicability, that have considerable advantages over other methods and that are rigorous, satisfying all equilibrium conditions (forces and moments). In order to corroborate the proposed methodology, four different practical situations were presented, demonstrating the applicability of the methodology.
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Franca, Paulo Ricardo Behrens da. "Analysis of slope stability using limit equilibrium and numerical methods with case examples from the Águas Claras Mine, Brazil." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq20637.pdf.

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Janssen, Arend. "Order book models, signatures and numerical approximations of rough differential equations." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:264e96b3-f449-401b-8768-337acab59cab.

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We construct a mathematical model of an order driven market where traders can submit limit orders and market orders to buy and sell securities. We adapt the notion of no free lunch of Harrison and Kreps and Jouini and Kallal to our setting and we prove a no-arbitrage theorem for the model of the order driven market. Furthermore, we compute signatures of order books of different financial markets. Signatures, i.e. the full sequence of definite iterated integrals of a path, are one of the fundamental elements of the theory of rough paths. The theory of rough paths provides a framework to describe the evolution of dynamical systems that are driven by rough signals, including rough paths based on Brownian motion and fractional Brownian motion (see the work of Lyons). We show how we can obtain the solution of a polynomial differential equation and its (truncated) signature from the signature of the driving signal and the initial value. We also present and analyse an ODE method for the numerical solution of rough differential equations. We derive error estimates and we prove that it achieves the same rate of convergence as the corresponding higher order Euler schemes studied by Davie and Friz and Victoir. At the same time, it enhances stability. The method has been implemented for the case of polynomial vector fields as part of the CoRoPa software package which is available at http://coropa.sourceforge.net. We describe both the algorithm and the implementation and we show by giving examples how it can be used to compute the pathwise solution of stochastic rough differential equations driven by Brownian rough paths and fractional Brownian rough paths.
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Books on the topic "Numerical Limit Analysis"

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Alexandrov, Sergey. Upper bound limit load solutions for welded joints with cracks. Heidelberg: Springer, 2012.

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Bensoussan, Alain. Asymptotic analysis for periodic structures. Providence, R.I: American Mathematical Society, 2011.

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Yeom, D. J. Limit and shakedown analyses if axisymmetric structures by numerical methods. Manchester: UMIST, 1996.

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Cockshott, W. Paul. Computation and its limits. Oxford [England]: Oxford University Press, 2012.

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M, Mackenzie L., and Michaelson Greg 1953-, eds. Computation and its limits. Oxford [England]: Oxford University Press, 2012.

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Infinite Matrices and their Finite Sections: An Introduction to the Limit Operator Method (Frontiers in Mathematics). Birkhäuser Basel, 2006.

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Alexandrov, Sergey. Upper Bound Limit Load Solutions for Welded Joints with Cracks. Springer, 2012.

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Infinite Matrices and their Finite Sections: An Introduction to the Limit Operator Method (Frontiers in Mathematics). Birkhäuser, 2006.

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Optimization of Objective Functions: Analytics. Numerical Methods. Design of Experiments. Moscow, Russia: Fizmatlit Publisher, 2009.

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Mathematical Statistics: Theory and Applications. Berlin, Germany: De Gruyter, 2020.

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Book chapters on the topic "Numerical Limit Analysis"

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Brigadnov, Igor A. "Limit Analysis Method in Electrostatics." In Numerical Mathematics and Advanced Applications, 176–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-18775-9_15.

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Bender, C. "Continuum limit of lattice approximation schemes." In Group Theory and Numerical Analysis, 33–48. Providence, Rhode Island: American Mathematical Society, 2005. http://dx.doi.org/10.1090/crmp/039/03.

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Spiliopoulos, Konstantinos V., and Theodoros N. Patsios. "Numerical Analysis of Nonholonomic Elastoplastic Frames by Mathematical Programming." In Limit State of Materials and Structures, 129–44. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-5425-6_7.

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Pisano, Aurora Angela, Paolo Fuschi, and Dario De Domenico. "Limit Analysis on RC-Structures by a Multi-yield-criteria Numerical Approach." In Direct Methods for Limit and Shakedown Analysis of Structures, 199–219. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12928-0_11.

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Morelle, P., and G. Fonder. "Shakedown and Limit Analysis of Shells — A Variational and Numerical Approach." In Lecture Notes in Engineering, 381–405. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-83015-0_35.

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Costa, Pedro Alves, Patrícia Lopes, and António Silva Cardoso. "Lower Bound Shakedown Limit Analysis of Slab Railway Tracks: Numerical Approach." In Lecture Notes in Civil Engineering, 479–92. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-2349-6_30.

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Konnur, S. S., A. M. Hulagabali, C. H. Solanki, and G. R. Dodagoudar. "Numerical Analysis of MSE Wall Using Finite Element and Limit Equilibrium Methods." In Lecture Notes in Civil Engineering, 199–205. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-0562-7_22.

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Senthil, P., and Hari Dev. "Numerical Analysis of Gravity Dam-Foundation and Comparison with Limit Equilibrium Method." In Lecture Notes in Civil Engineering, 235–44. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-1886-7_20.

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He, Xuan’ang, Dalin Zhang, and Xiang Wang. "Visualized Numerical Analysis of Fustar Reactor Based on Modelica Language." In Springer Proceedings in Physics, 276–87. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-1023-6_26.

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AbstractFuSTAR is a new small fluoride-salt-cooled high-temperature reactor designed for the energy needs of remote western regions. The TRISO fuel and helical cruciform fuel elements used in FuSTAR and the integrated core design enables inherent safety. Modelica is a process description language based on object equations. It has key features such as non-causal expression and model reuse, which achieve repeatable visual modeling by connecting components. By modeling and simulating FuSTAR using the Modelica, studies were carried out under steady-state as well as multiple transients to understand the primary loop system response of FuSTAR under accident scenarios. The results show that the parameters of the primary loop system cannot exceed the safety limit with the insertion of step reactivity and after changing the size of the temperature coefficient of reactivity, the model can give a reasonable response.
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Rashidifar, Rasoul, F. Frank Chen, Hamed Bouzary, and Mohammad Shahin. "A Mathematical Model for Cloud-Based Scheduling Using Heavy Traffic Limit Theorem in Queuing Process." In Lecture Notes in Mechanical Engineering, 197–206. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-18326-3_20.

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AbstractCloud manufacturing (CMfg) is a service-oriented manufacturing paradigm that distributes resources in an on-demand business model. In the cloud manufacturing environment, scheduling is considered as an effective tool for satisfying customer requirements which has attracted attention from researchers. In this case, quality of service (QoS) in the scheduling plays a vital role in assessing the impacts of the distributed resources in operation on the performance of scheduling functions. In this paper, a queuing system is employed to model the scheduling problem with multiple servers and then scheduling in cloud manufacturing is classified based on various QoS requirements. Moreover, a set of heavy traffic limit theorems is introduced as a new approach to solving this scheduling problem in which different heavy traffic limits are provided for each of QoS-based scheduling classes. Finally, the number of operational resources in the scheduling is determined by considering the results obtained in the numerical analysis of the heavy traffic limit with different queue disciplines. The results show that different numbers of active machines in various QoS requirements classes play a vital role in that the required QoS metrics such as the expected waiting time and the expected completion time which are critical performance indicators of the cloud’s service are intimately related.
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Conference papers on the topic "Numerical Limit Analysis"

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Tiţa, Nicolae, Anca Armăşelu, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "On Some Limit Scales of Approximation Ideals." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636784.

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Pingaro, Natalia, Gabriele Milani, and Simone Tiberti. "Automatic CAD kinematic limit analysis approach for the limit analysis of masonry towers." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0026420.

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Chang, Keh‐Chin, Jian‐Hung Lin, and Yi‐Mei Liu. "Applicability Limit of Binary Collision Model in Dense Particle Flow." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991046.

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Gürdal, M., M. B. Huban, and U. Yamancı. "On generalized statistical limit points in random 2-normed spaces." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756300.

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Demi̇ralp, Metin, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Series Expansion of a Function's Expectation Matrix at the Zero Interval Length Limit." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790096.

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Boscarino, S., Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Implicit-Explicit Runge-Kutta Schemes for Hyperbolic Systems in the Diffusion Limit." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637861.

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Gürvit, Ercan, N. A. Baykara, Metin Demiralp, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Taylor Formula with Remainder Term Evaluated under a Weight Factor at Fluctuationlessness Limit." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637826.

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Kala, Zdeněk, and Giedrė Sandovič. "Fuzzy stochastic analysis of serviceability and ultimate limit states of two-span pedestrian steel bridge." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756597.

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Kutaiba, Shaban, and Vladimir Vasilyev. "On solutions of certain limit boundary value problems." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0026562.

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Oleynik, Anna, John Wyller, Igor Wertgeim, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "The Weakly Nonlocal Limit of a One-Population Wilson-Cowan Model." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241465.

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Reports on the topic "Numerical Limit Analysis"

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Walshire, Lucas, Joseph Dunbar, and Benjamin Breland. Stability analysis of Old River Low Sill Structure. Engineer Research and Development Center (U.S.), September 2022. http://dx.doi.org/10.21079/11681/45349.

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An updated stability analysis was performed on the Old River Low Sill Structure due to a change in the operating conditions from historic river sedimentation. Sedimentation of the Mississippi River channel since the 1973 spring flood has caused higher river stages at lower discharges. Numerical methods used included nonlinear analysis of pile group stability, seepage analyses, and limit equilibrium methods. The structure’s foundation was compromised during the 1973 flood, and emergency repairs were conducted to prevent scouring and undermining of the foundation by the flood scour. Rehabilitation included the reconstruction of a failed wing wall on the left abutment, rock and riprap fill in the forebay channel, and emergency grouting to fill the scour hole beneath the structure. An operating restriction was emplaced to limit the differential head across the structure due to flood damage. Taking these conditions into account, results from an updated analysis showed that full headwater uplift caused increased tension in the piles, while the increased body load caused increased compressive loads in the piles. Review of piezometric monitoring and the seepage analyses showed that full headwater uplift is unlikely, indicating the foundation grouting adequately sealed the scour hole beneath the structure. Analysis results exhibited lower magnitude compression and tension loads in the piles with design load cases compared to previous analyses. Recommendations from these analyses indicate that increased monitoring and additional investigation may support increasing the differential head limitation.
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Ebeling, Robert, Barry White, John Hite, James Tallent, Locke Williams, Brad McCoy, Aaron Hill, Cameron Dell, Jake Bruhl, and Kevin McMullen. Load and resistance factors from reliability analysis Probability of Unsatisfactory Performance (PUP) of flood mitigation, batter pile-founded T-Walls given a target reliability index (𝛽). Engineer Research and Development Center (U.S.), July 2023. http://dx.doi.org/10.21079/11681/47245.

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This technical report documents the research and development (R&D) study in support of the development of a combined Load and Resistance Factor Design (LRFD) methodology that accommodates both geotechnical and structural design limit states for design of the US Army Corps of Engineers (USACE) batter pile-founded, reinforced concrete flood walls. Development of the required reliability and corresponding LRFD procedures has been progressing slowly in the geotechnical topic area as compared to those for structural limit state considerations, and therefore this has been the focus of this first-phase R&D effort. This R&D effort extends reliability procedures developed for other non-USACE structural systems, primarily bridges and buildings, for use in the design of batter pile-founded USACE flood walls. Because the foundation system includes batter piles under flood loading, the design procedure involves frame analysis with significant soil structure interaction. Three example batter pile-founded T-Wall flood structures on three different rivers have been examined considering 10 geotechnical and structural limit states. Numerical procedures have been extended to develop precise multiple limit state Reliability calculations and for complete LRFD analysis of the example batter pile-founded, T-Wall reinforced concrete, flood walls.
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Patel, Reena, David Thompson, Guillermo Riveros, Wayne Hodo, John Peters, and Felipe Acosta. Dimensional analysis of structural response in complex biological structures. Engineer Research and Development Center (U.S.), July 2021. http://dx.doi.org/10.21079/11681/41082.

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The solution to many engineering problems is obtained through the combination of analytical, computational and experimental methods. In many cases, cost or size constraints limit testing of full-scale articles. Similitude allows observations made in the laboratory to be used to extrapolate the behavior to full-scale system by establishing relationships between the results obtained in a scaled experiment and those anticipated for the full-scale prototype. This paper describes the application of the Buckingham Pi theorem to develop a set of non-dimensional parameters that are appropriate for describing the problem of a distributed load applied to the rostrum of the paddlefish. This problem is of interest because previous research has demonstrated that the rostrum is a very efficient structural system. The ultimate goal is to estimate the response of a complex, bio-inspired structure based on the rostrum to blast load. The derived similitude laws are verified through a series of numerical experiments having a maximum error of 3.39%.
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Francis, Andrew, Chas Jandu, and Mike Taylor. PR-408-124500-R01 Mechanical Damage Instantaneous Failure Model Numerical Simulation of Physical Tests. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), March 2013. http://dx.doi.org/10.55274/r0010819.

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The overall objective was to develop two models for determining the effect of mechanical damage on the structural integrity of buried pipelines. The models that are to be developed are the instantaneous failure model (MD4-3) and the delayed failure model (MD4-4). The subject of this report is part of the work that has been undertaken in support of the development of the instantaneous failure model which is being undertaken within the remit of MD4-3. The overall objective of MD4-3 to produce a closed form expression that will be used as: (i) A Limit State Function in structural reliability and risk assessment methodologies and associated software. (ii) A means of determining the safety margin associated with known existing damage to establish whether immediate repair is required (iii) An initial condition for the delayed failure model (MD4-4) which is being developed separately. The objective of this report is to present the outcomes of detailed numerical simulation of physical tests that have been performed as part of MD4-1. The development is progressing based on a combination of physical testing and numerical simulation and analysis. The objective of this report is to present the outcomes of detailed numerical simulation of physical tests that have been performed as part of MD4-1.
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Yoosef-Ghodsi, Ozkan, and Bandstra. PR-244-114501-R01 Review of Compressive Strain Capacity Assessment Methods Final Report. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), October 2013. http://dx.doi.org/10.55274/r0010402.

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Buried pipelines subjected to non-continuous ground movement such as frost heave, thaw settlement, slope instability and seismic movement experience high compressive strains that can cause local buckling (or wrinkling), in which the pipe wall buckles like a thin cylindrical shell in axial compression. In a strain-based design and assessment framework, excessive local buckling deformation that may cause loss of serviceability, or even pressure containment in some cases, is managed by limiting the strain demand below the strain limit. The determination of compressive strain limit is typically performed by full-scale structural testing or nonlinear finite element analysis that takes into account material and geometric non-linearity associated with the inelastic buckling of cylindrical shells. Before performing testing and numerical analysis (or when such options do not exist), empirical equations are used to estimate the strain limit. In this report a number of representative equations were evaluated by comparing strain limit predictions to full-scale test results. Work prior to this study has identified the importance of key variables that have the greatest impact on the local buckling behaviour. Examples of these variables include the diameter-to-thickness (D/t) ratio, internal pressure and shape of the stress strain curve. The evaluation focused on how existing equations address these key variables, and the performance with respect to key variables and in different ranges.
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Ebeling, Robert, and Barry White. Load and resistance factors for earth retaining, reinforced concrete hydraulic structures based on a reliability index (β) derived from the Probability of Unsatisfactory Performance (PUP) : phase 2 study. Engineer Research and Development Center (U.S.), March 2021. http://dx.doi.org/10.21079/11681/39881.

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This technical report documents the second of a two-phase research and development (R&D) study in support of the development of a combined Load and Resistance Factor Design (LRFD) methodology that accommodates geotechnical as well as structural design limit states for design of the U.S. Army Corps of Engineers (USACE) reinforced concrete, hydraulic navigation structures. To this end, this R&D effort extends reliability procedures that have been developed for other non-USACE structural systems to encompass USACE hydraulic structures. Many of these reinforced concrete, hydraulic structures are founded on and/or retain earth or are buttressed by an earthen feature. Consequently, the design of many of these hydraulic structures involves significant soil structure interaction. Development of the required reliability and corresponding LRFD procedures has been lagging in the geotechnical topic area as compared to those for structural limit state considerations and have therefore been the focus of this second-phase R&D effort. Design of an example T-Wall hydraulic structure involves consideration of five geotechnical and structural limit states. New numerical procedures have been developed for precise multiple limit state reliability calculations and for complete LRFD analysis of this example T-Wall reinforced concrete, hydraulic structure.
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Liu and Nixon. L52305 Probabilistic Analysis of Pipeline Uplift Resistance. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), June 2010. http://dx.doi.org/10.55274/r0000002.

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To investigate the feasibility of probabilistic analyses of the peak uplift resistance in frozen soils by varying parameters that are known to be important for the development of the uplift resistance under the upward movement of a pipe. A buried pipeline will be subjected to a variety of forces, both internal and external, including the interaction of the pipe with the surrounding soil. The soil-pipe interaction in permafrost regions have to account for the behavior of frozen and unfrozen soil, and transitions between the two as the pipeline traverses in a discontinuous permafrost zone. The variations in the properties and behavior of frozen soils are expected to be substantial in three dimensions of the Right-of-Way (ROW) and with time (seasonal fluctuations and changes with the history of pipeline operation). Given the uncertainties with frozen soil properties and the changes in behavior with time and location, a large variation in soil-pipe interaction characteristics can exist. The uplift resistance of a pipeline is one of these soil-pipe interactions that can be impacted by a variation in soil condition and state. A need was identified to outline the use of a probabilistic analysis of pipe uplift resistance in an attempt to capture the magnitude of these variations and uncertainties of frozen soil and the impact on the soil-pipe interaction. The probabilistic analysis allows the designer of a pipeline to consider a range of uplift resistance to a certain confidence level that would represent the likely values that a pipe may be subjected to. The work presented in this report is more focused on the methodology of the probabilistic approach, rather than the analysis itself for a specific design case, even though an example is provided for illustration purposes. A series of numerical simulations using Fast Lagrangian Analysis of Continua (FLAC) were completed varying one parameter with each run to develop a library of peak uplift resistances for a variety of different temperatures, soil properties and pipe parameters. The FLAC model was previously developed for PRC, a summary of this report is provided here to outline important parameters that were used to complete this analysis. The simulations were used to develop a correlation of peak uplift resistance as a function of soil tensile strain limit, modulus of deformation, and creep of frozen soils. Each of these parameters is dependent of the pipeline conditions such as temperature, displacement rate, and effective frozen cover depth. It is noted that the scope of the work was to develop a probabilistic method of estimating peak uplift resistance in frozen soils. Even though some sensitivity analysis were carried out, as outlined later in this report, to assess the impacts of the variable, detailed uncertainty analysis or risk assessment were not performed.
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SEISMIC PERFORMANCE OF SINGLE-LAYER SPHERICAL RETICULATED SHELLS CONSIDERING JOINT STIFFNESS AND BEARING CAPACITY. The Hong Kong Institute of Steel Construction, June 2022. http://dx.doi.org/10.18057/ijasc.2022.18.2.9.

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Fabricated joints are gradually applied in architectural structures because of their advantages of good economy, high installation quality and efficiency. However, the mechanical properties of this kind of joint are semi-rigid differing from traditional rigid and hinged joints. Therefore, the performance of the structures with such joints is not clear, which greatly limits the wide application of fabricated joints. This paper presents the investigation on the seismic performance of the semi-rigid single-layer reticulated shell structure (SRSS) under earthquake load by numerical simulation and theoretical analysis. A finite element model (FEM) of the semi-rigid reticulated shell was established. The influence of joint stiffness on the seismic performance of semi-rigid SRSS was obtained by taking both initial defects and material damage accumulation into account. The two design parameters, limit stiffness ratio and limit yield moment of the joints, were proposed for the semi-rigid reticulated shells. The influence of the roof span, roof weight and member section on the two design parameters was obtained and the calculation formula was established. The seismic force coefficient for the semi-rigid SRSS was obtained, which can provide support for the seismic design of semi-rigid SRSS.
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STUDY ON MECHANICAL PROPERTIES OF SIMPLIFIED STEEL FRAME MODEL WITH EXTERNAL WALL PANELS. The Hong Kong Institute of Steel Construction, August 2022. http://dx.doi.org/10.18057/icass2020.p.334.

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A simplified analysis model of the overall steel frame with external wall panels is established by finite element numerical method, and the influence of external wall panels on the internal force and seismic performance of the steel frame is studied. Pushover analysis and cyclic loading analysis are carried out on the simplified model. The results show that the external wall panel can improve the initial stiffness and ultimate bearing capacity of the steel frame, and after considering the external wall panel, the shear demand of the column increases accordingly. Moreover, compared with the pure steel frame, the ability of the steel frame structure with the external wall panel to maintain the strength and rigidity and the energy consumption capacity are significantly improved, and the cumulative energy consumption can increase by about 16.6%. The contribution of the external wall panels to the horizontal force of the steel frame structure can reach up to about 22% when the node sliding reaches the limit, and then gradually decreases to 3.5-5.4% with the increase of the loading displacement, which still has a non-negligible impact on improving the lateral resistance of the structure.
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