This book provides insight in the mathematics of Galerkin finite element method as applied to parabolic equations. The approach is based on first discretizing in the spatial variables by Galerkin's method, using piecewise polynomial trial functions, and then applying some single step or multistep time stepping method. The concern is stability and error analysis of approximate solutions in various norms, and under various regularity assumptions on the exact solution. The book gives an excellent insight in the present ideas and methods of analysis. The second edition has been influenced by recent progress in application of semigroup theory to stability and error analysis, particulatly in maximum-norm. Two new chapters have also been added, dealing with problems in polygonal, particularly noncovex, spatial domains, and with time discretization based on using Laplace transformation and quadrature.
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During the last years, scientific computing has become an important research branch located between applied mathematics and applied sciences and engineering. Highly efficient numerical methods are based on adaptive methods, higher order discretizations, fast linear and non-linear iterative solvers, multi-level algorithms, etc. Such methods are integrated in the adaptive finite element software ALBERTA. It is a toolbox for the fast and flexible implementation of efficient software for real life applications, based on modern algorithms. ALBERTA also serves as an environment for improving existent, or developing new numerical methods in an interplay with mathematical analysis and it allows the direct integration of such new or improved methods in existing simulation software. The book is accompanied by a full distribution of ALBERTA (Version 1.2) on a CD including an implementation of several model problems. System requirements for ALBERTA are a Unix/Linux environment with C and FORTRAN Compilers, OpenGL graphics and GNU make. These model implementations serve as a basis for students and researchers for the implementation of their own research projects within ALBERTA.
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CD is not included in this download!
Check home page for material from CD.
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Matrix Preconditioning Techniques and Applications
Author: Ke Chen | Size: 4.55 MB | Format:PDF | Quality:Original preprint | Publisher: Cambridge University Press | Year: July 25, 2005 | pages: 592 | ISBN: 0521838282, ISBN-13: 978-0521838283
Preconditioning techniques have emerged as an essential part of successful and efficient iterative solutions of matrices. Ke Chen's book offers a comprehensive introduction to these methods. A vast range of explicit and implicit sparse preconditioners are covered, including the conjugate gradient, multi-level and fast multi-pole methods, matrix and operator splitting, fast Fourier and wavelet transforms, incomplete LU and domain decomposition, Schur complements and approximate inverses. In addition, aspects of parallel realization using the MPI are discussed. Very much a users-guide, the book provides insight to the use of these techniques in areas such as acoustic wave scattering, image restoration and bifurcation problems in electrical power stations. Supporting MATLAB files are available from the Web to support and develop readers' understanding, and provide stimulus for further study. Pitched at graduate level, the book is intended to serve as a useful guide and reference for students, computational practitioners, engineers and researchers alike.
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In a large number of concrete structures and structural elements multiaxial compressive stress states occur. As is generally known, these stress states in general have an advantageous effect on the behaviour of the material, compared to the behaviour under uniaxial loading: the load bearing capacity increases and larger deformations are allowable. Unfortunately, this effect has not yet been implemented in the building codes, because there are too many unknowns to describe it in a useful quantitative manner. Therefore insight in the behaviour of concrete under this type of loading is important with respect to safety and deformational capacity of several kinds of concrete structures. At Eindhoven University of Technology (EUT) a research project was started in the early eighties to gain more insight in the failure behaviour of concrete in multiaxial compression. The research described in this thesis is to be regarded as a continuation of the work done earlier at EUT. It deals with several aspects of concrete behaviour in multiaxial compression that were not investigated before or from a different point of view, and intends to answer some remaining questions on the subject.
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Modeling Error of Strength of Short Reinforced Concrete Columns
Author: W. Zhou and H. P. Hong | Size: 1 MB | Format:PDF | Quality:Original preprint | Publisher: ACI | Year: 2000 | pages: 9
Abstract:
Probabilistic analyses of the modeling errors of several selected strength prediction models for short reinforced concrete (RC) columns are carried out. The selected strength models include the rectangular stress block model and the stress-strain relation-based theoretical model. A relatively large amount of test data on RC columns is collected from the literature, and the test results are com-pared with the predicted ones obtained from different strength mod-els. Both normal- and high-strength concrete columns are included in this study. The dependency of the modeling errors on concrete compressive strength and the load eccentricity is investigated. Probabilistic analyses of the modeling errors are carried out by using the pseudolikelihood estimation method. Sets of probabilistic models of the modeling errors by considering different analysis approaches are suggested for short RC columns.
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Behavior and Ductility of Reinforced Concrete Short Columns using Global Truss Model
Author: Marina L. Moretti and Theodosios P. Tassios | Size: 1 MB | Format:PDF | Quality:Original preprint | Publisher: ACI | Year: 2006 | pages: 9
Abstract:
The main results of an experimental program on eight full-scale reinforced concrete short columns are presented. The specimens were subjected to compression and cyclic reversed uniaxial shear displacements. The parameters investigated were the value of shear ratio, the ratios of longitudinal and transverse reinforcement, and the normalized axial force ratio. Two different layouts of main reinforcement were tested: conventional (longitudinal) and a combination of longitudinal and bidiagonal reinforcement. Columns with shear ratio equal to 1 were shown to behave in a particularly brittle manner. The presence of bidiagonal reinforcement improved to some extent the ductility of the specimens, but not to the level required by current aseismic design. The relative performance of the specimens tested is evaluated according to various ductility criteria. A model for designing short columns is also presented.
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Behavior and Ductility of Reinforced Concrete Short Columns using Global Truss Model in Concrete Beams
Author: Marina L. Moretti and Theodosios P. Tassios | Size: ?? MB | Format:PDF | Quality:Unspecified | Publisher: Structural Journal, Volume: 103, Issue: 3 | Year: May 1, 2006 | pages: 319-327
Abstract:
The main results of an experimental program on eight full-scale reinforced concrete short columns are presented. The specimens were subjected to compression and cyclic reversed uniaxial shear displacements. The parameters investigated were the value of shear ratio, the ratios of longitudinal and transverse reinforcement, and the normalized axial force ratio. Two different layouts of main reinforcement were tested: conventional (longitudinal) and a combination of longitudinal and bidiagonal reinforcement. Columns with shear ratio equal to 1 were shown to behave in a particularly brittle manner. The presence of bidiagonal reinforcement improved to some extent the ductility of the specimens, but not to the level required by current aseismic design. The relative performance of the specimens tested is evaluated according to various ductility criteria. A model for designing short columns is also presented.
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Modeling Error of Strength of Short Reinforced Concrete Columns
Author: W. Zhou and H. P. Hong | Size: ?? MB | Format:PDF | Quality:Unspecified | Publisher: Structural Journal, Volume: 97, Issue: 3 | Year: May 1, 2000 | pages: 427-435
Abstract:
Probabilistic analyses of the modeling errors of several selected strength prediction models for short reinforced concrete (RC) columns are carried out. The selected strength models include the rectangular stress block model and the stress-strain relation-based theoretical model. A relatively large amount of test data on RC columns is collected from the literature, and the test results are com-pared with the predicted ones obtained from different strength mod-els. Both normal- and high-strength concrete columns are included in this study. The dependency of the modeling errors on concrete compressive strength and the load eccentricity is investigated. Probabilistic analyses of the modeling errors are carried out by using the pseudolikelihood estimation method. Sets of probabilistic models of the modeling errors by considering different analysis approaches are suggested for short RC columns.
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Micromechanics of Failure in Granular Geomaterials
Author: François Nicot, Richard Wan | Size: 33.5 MB | Format:PDF | Quality:Scanner | Publisher: Wiley-ISTE | Year: 2009 | pages: 377 | ISBN: 978-1-84821-128-5
This book is a treatise that brings together some of the latest international research and advances in the failure of granular geomaterials within a micromechanical approach. It provides a view of the current scientific community on this topic, putting forward relevant methods and efficient tools for analysis. The chapters include either phenomenological contributions enriched with micromechanical ingredients, or purely micromechanical investigations. Various failure modes that are encountered in geomaterials and their implications in engineering applications are discussed throughout the chapters. The case of porous frictional materials with or without a fluid phase is considered together with the basic roles of the sliding and opening of contacts as a failure mechanism. The influence of grain crushing as a plausible mechanism under a variety of stress conditions and grain topologies is also addressed. Finally, fracture in continuous materials containing grain inclusions is dealt within the context of damage theory.
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Tubular Steel Structures Theory and Design-2nd edition
Author: M. S. Troitsky (Author) | Size: 24.5 MB | Format:PDF | Quality:Scanner | Publisher: The James F. Lincoln Arc Welding Foundation | Year: 1990 | pages: 409
In this second edition the contents have been thoroughly revised and every effort was made to correct errors and misprints detected in the first edition. Although much of the data of the first edition has been retained, the following changes and additions were made in the contents of the second edition.
In Chapter 7 "Bins and Bunkers" sections retained to the Ring Girders and Roofs for Circular Bins, were substituted by the new text for Circular Girders Supporting Bins and Roofs for Circular Bins. Also in Chapter 12 "Tubular Conveyor Galleries" new sections concerning the design of "Ring Girders at Supports, Method by Krupka" were added.
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