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The Best Approximation Method In Computational Mechanics
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Author :Theodore V., II Hromadka Publisher :Springer Science & Business Media ISBN 13 :1447120205 Total Pages :259 pages Book Rating :4.4/5 (471 download)
Book Synopsis The Best Approximation Method in Computational Mechanics by : Theodore V., II Hromadka
Download or read book The Best Approximation Method in Computational Mechanics written by Theodore V., II Hromadka and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the overwhelming use of computers in engineering, science and physics, the approximate solution of complex mathematical systems of equations is almost commonplace. The Best Approximation Method unifies many of the numerical methods used in computational mechanics. Nevertheless, despite the vast quantities of synthetic data there is still some doubt concerning the validity and accuracy of these approximations. This publication assists the computer modeller in his search for the best approximation by presenting functional analysis concepts. Computer programs are provided which can be used by readers with FORTRAN capability. The classes of problems examined include engineering applications, applied mathematics, numerical analysis and computational mechanics. The Best Approximation Method in Computational Mechanics serves as an introduction to functional analysis and mathematical analysis of computer modelling algorithms. It makes computer modellers aware of already established principles and results assembled in functional analysis.
Book Synopsis The Best Approximation Method in Computational Mechanics by : Theodore V., II Hromadka
Download or read book The Best Approximation Method in Computational Mechanics written by Theodore V., II Hromadka and published by Springer. This book was released on 2011-12-12 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the overwhelming use of computers in engineering, science and physics, the approximate solution of complex mathematical systems of equations is almost commonplace. The Best Approximation Method unifies many of the numerical methods used in computational mechanics. Nevertheless, despite the vast quantities of synthetic data there is still some doubt concerning the validity and accuracy of these approximations. This publication assists the computer modeller in his search for the best approximation by presenting functional analysis concepts. Computer programs are provided which can be used by readers with FORTRAN capability. The classes of problems examined include engineering applications, applied mathematics, numerical analysis and computational mechanics. The Best Approximation Method in Computational Mechanics serves as an introduction to functional analysis and mathematical analysis of computer modelling algorithms. It makes computer modellers aware of already established principles and results assembled in functional analysis.
Book Synopsis Numerical Methods in Computational Mechanics by : Jamshid Ghaboussi
Download or read book Numerical Methods in Computational Mechanics written by Jamshid Ghaboussi and published by CRC Press. This book was released on 2016-11-25 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the numerical algorithms underpinning modern finite element based computational mechanics software. It covers all the major numerical methods that are used in computational mechanics. It reviews the basic concepts in linear algebra and advanced matrix theory, before covering solution of systems of equations, symmetric eigenvalue solution methods, and direct integration of discrete dynamic equations of motion, illustrated with numerical examples. This book suits a graduate course in mechanics based disciplines, and will help software developers in computational mechanics. Increased understanding of the underlying numerical methods will also help practicing engineers to use the computational mechanics software more effectively.
Author :Theodore V. II Hromadka Publisher :Springer Science & Business Media ISBN 13 :3642830382 Total Pages :185 pages Book Rating :4.6/5 (428 download)
Book Synopsis The Best Approximation Method An Introduction by : Theodore V. II Hromadka
Download or read book The Best Approximation Method An Introduction written by Theodore V. II Hromadka and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most commonly used numerical techniques in solving engineering and mathematical models are the Finite Element, Finite Difference, and Boundary Element Methods. As computer capabilities continue to impro':e in speed, memory size and access speed, and lower costs, the use of more accurate but computationally expensive numerical techniques will become attractive to the practicing engineer. This book presents an introduction to a new approximation method based on a generalized Fourier series expansion of a linear operator equation. Because many engineering problems such as the multi dimensional Laplace and Poisson equations, the diffusion equation, and many integral equations are linear operator equations, this new approximation technique will be of interest to practicing engineers. Because a generalized Fourier series is used to develop the approxi mator, a "best approximation" is achieved in the "least-squares" sense; hence the name, the Best Approximation Method. This book guides the reader through several mathematics topics which are pertinent to the development of the theory employed by the Best Approximation Method. Working spaces such as metric spaces and Banach spaces are explained in readable terms. Integration theory in the Lebesque sense is covered carefully. Because the generalized Fourier series utilizes Lebesque integration concepts, the integra tion theory is covered through the topic of converging sequences of functions with respect to measure, in the mean (Lp), almost uniformly IV and almost everywhere. Generalized Fourier theory and linear operator theory are treated in Chapters 3 and 4.
Book Synopsis Numerical Approximation Methods by : Harold Cohen
Download or read book Numerical Approximation Methods written by Harold Cohen and published by Springer Science & Business Media. This book was released on 2011-09-28 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques that are now formally collected as well as original methods developed by the author that do not appear in the literature. This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text. The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriate for students taking courses in numerical approximation techniques.
Book Synopsis Advances in the Complex Variable Boundary Element Method by : Theodore V. Hromadka
Download or read book Advances in the Complex Variable Boundary Element Method written by Theodore V. Hromadka and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: As well as describing the extremely useful applications of the CVBEM, the authors explain its mathematical background -- vital to understanding the subject as a whole. This is the most comprehensive book on the subject, bringing together ten years of work and can boast the latest news in CVBEM technology. It is thus of particular interest to those concerned with solving technical engineering problems -- while scientists, graduate students, computer programmers and those working in industry will all find the book helpful.
Book Synopsis Numerical Methods and Methods of Approximation in Science and Engineering by : Karan S. Surana
Download or read book Numerical Methods and Methods of Approximation in Science and Engineering written by Karan S. Surana and published by CRC Press. This book was released on 2018 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods and Methods of Approximation in Science and Engineering prepares students and other readers for advanced studies involving applied numerical and computational analysis. Focused on building a sound theoretical foundation, it uses a clear and simple approach backed by numerous worked examples to facilitate understanding of numerical methods and their application. Readers will learn to structure a sequence of operations into a program, using the programming language of their choice; this approach leads to a deeper understanding of the methods and their limitations. Features: Provides a strong theoretical foundation for learning and applying numerical methods Takes a generic approach to engineering analysis, rather than using a specific programming language Built around a consistent, understandable model for conducting engineering analysis Prepares students for advanced coursework, and use of tools such as FEA and CFD Presents numerous detailed examples and problems, and a Solutions Manual for instructors
Book Synopsis Approximate Solution Methods in Engineering Mechanics by : Arthur P. Boresi
Download or read book Approximate Solution Methods in Engineering Mechanics written by Arthur P. Boresi and published by John Wiley & Sons. This book was released on 2003 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The only complete collection of prevalent approximation methods Unlike any other resource, Approximate Solution Methods in Engineering Mechanics, Second Edition offers in-depth coverage of the most common approximate numerical methods used in the solution of physical problems, including those used in popular computer modeling packages. Descriptions of each approximation method are presented with the latest relevant research and developments, providing thorough, working knowledge of the methods and their principles. Approximation methods covered include: * Boundary element method (BEM) * Weighted residuals method * Finite difference method (FDM) * Finite element method (FEM) * Finite strip/layer/prism methods * Meshless method Approximate Solution Methods in Engineering Mechanics, Second Edition is a valuable reference guide for mechanical, aerospace, and civil engineers, as well as students in these disciplines.
Book Synopsis Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics by : Felix Fritzen
Download or read book Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics written by Felix Fritzen and published by MDPI. This book was released on 2019-09-18 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the construction of surrogate models or reduced order models. The articles contained in this compilation were presented at the EUROMECH Colloquium 597, « Reduced Order Modeling in Mechanics of Materials », held in Bad Herrenalb, Germany, from August 28th to August 31th 2018. In this book, Artificial Neural Networks are coupled to physics-based models. The tensor format of simulation data is exploited in surrogate models or for data pruning. Various reduced order models are proposed via machine learning strategies applied to simulation data. Since reduced order models have specific approximation errors, error estimators are also proposed in this book. The proposed numerical examples are very close to engineering problems. The reader would find this book to be a useful reference in identifying progress in machine learning and reduced order modeling for computational mechanics.
Book Synopsis The Finite Element Method for Boundary Value Problems by : Karan S. Surana
Download or read book The Finite Element Method for Boundary Value Problems written by Karan S. Surana and published by CRC Press. This book was released on 2016-11-17 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically rigorous, the FEM is presented as a method of approximation for differential operators that are mathematically classified as self-adjoint, non-self-adjoint, and non-linear, thus addressing totality of all BVPs in various areas of engineering, applied mathematics, and physical sciences. These classes of operators are utilized in various methods of approximation: Galerkin method, Petrov-Galerkin Method, weighted residual method, Galerkin method with weak form, least squares method based on residual functional, etc. to establish unconditionally stable finite element computational processes using calculus of variations. Readers are able to grasp the mathematical foundation of finite element method as well as its versatility of applications. h-, p-, and k-versions of finite element method, hierarchical approximations, convergence, error estimation, error computation, and adaptivity are additional significant aspects of this book.
Book Synopsis Applications of Computational Mechanics in Geotechnical Engineering by : R.F. Azevedo
Download or read book Applications of Computational Mechanics in Geotechnical Engineering written by R.F. Azevedo and published by CRC Press. This book was released on 2020-08-18 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of constitutive relations for geotechnical materials, with the help of numerical models, have increased notably the ability to predict and to interpret mechanical behaviour of geotechnical works. These proceedings cover the applications of computational mechanics in this area.
Book Synopsis Computational Mechanics by : J.T. Oden
Download or read book Computational Mechanics written by J.T. Oden and published by Springer. This book was released on 2006-11-14 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Mechanics by : Zhenhan Yao
Download or read book Computational Mechanics written by Zhenhan Yao and published by Springer Science & Business Media. This book was released on 2009-03-24 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Mechanics is the proceedings of the International Symposium on Computational Mechanics, ISCM 2007. This conference is the first of a series created by a group of prominent scholars from the Mainland of China, Hong Kong, Taiwan, and overseas Chinese, who are very active in the field. The book includes 22 full papers of plenary and semi-plenary lectures and approximately 150 one-page summaries.
Download or read book Mathematical Reviews written by and published by . This book was released on 2003 with total page 1310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Nonlinear Mechanics in Aerospace Engineering by : Satya N. Atluri
Download or read book Computational Nonlinear Mechanics in Aerospace Engineering written by Satya N. Atluri and published by AIAA. This book was released on 1992 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Extended Finite Element Method by : Zhuo Zhuang
Download or read book Extended Finite Element Method written by Zhuo Zhuang and published by Academic Press. This book was released on 2014-03-24 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extended Finite Element Method provides an introduction to the extended finite element method (XFEM), a novel computational method which has been proposed to solve complex crack propagation problems. The book helps readers understand the method and make effective use of the XFEM code and software plugins now available to model and simulate these complex problems. The book explores the governing equation behind XFEM, including level set method and enrichment shape function. The authors outline a new XFEM algorithm based on the continuum-based shell and consider numerous practical problems, including planar discontinuities, arbitrary crack propagation in shells and dynamic response in 3D composite materials. Authored by an expert team from one of China's leading academic and research institutions Offers complete coverage of XFEM, from fundamentals to applications, with numerous examples Provides the understanding needed to effectively use the latest XFEM code and software tools to model and simulate dynamic crack problems
Book Synopsis Mechanical Vibrations by : Michel Geradin
Download or read book Mechanical Vibrations written by Michel Geradin and published by John Wiley & Sons. This book was released on 2015-02-16 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanical Vibrations: Theory and Application to Structural Dynamics, Third Edition is a comprehensively updated new edition of the popular textbook. It presents the theory of vibrations in the context of structural analysis and covers applications in mechanical and aerospace engineering. Key features include: A systematic approach to dynamic reduction and substructuring, based on duality between mechanical and admittance concepts An introduction to experimental modal analysis and identification methods An improved, more physical presentation of wave propagation phenomena A comprehensive presentation of current practice for solving large eigenproblems, focusing on the efficient linear solution of large, sparse and possibly singular systems A deeply revised description of time integration schemes, providing framework for the rigorous accuracy/stability analysis of now widely used algorithms such as HHT and Generalized-α Solved exercises and end of chapter homework problems A companion website hosting supplementary material
