Numerical Methods For Nonlinear Engineering Models

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Numerical Methods for Nonlinear Engineering Models

John R. Hauser
Numerical Methods for Nonlinear Engineering Models Book PDF

Author : John R. Hauser
Publisher : Springer Science & Business Media
Page : 1013 pages
File Size : 51,7 Mb
Release : 2009-03-24
Category : Technology & Engineering
ISBN : 9781402099205

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Numerical Methods for Nonlinear Engineering Models by John R. Hauser Pdf

There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.

Numerical Methods for Nonlinear Partial Differential Equations

Sören Bartels
Numerical Methods for Nonlinear Partial Differential Equations Book PDF

Author : Sören Bartels
Publisher : Springer
Page : 393 pages
File Size : 52,7 Mb
Release : 2015-01-19
Category : Mathematics
ISBN : 9783319137971

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Numerical Methods for Nonlinear Partial Differential Equations by Sören Bartels Pdf

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids

Laura De Lorenzis,Alexander Düster
Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids Book PDF

Author : Laura De Lorenzis,Alexander Düster
Publisher : Springer Nature
Page : 225 pages
File Size : 40,6 Mb
Release : 2020-02-08
Category : Science
ISBN : 9783030375188

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Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids by Laura De Lorenzis,Alexander Düster Pdf

The book examines innovative numerical methods for computational solid and fluid mechanics that can be used to model complex problems in engineering. It also presents innovative and promising simulation methods, including the fundamentals of these methods, as well as advanced topics and complex applications. Further, the book explores how numerical simulations can significantly reduce the number of time-consuming and expensive experiments required, and can support engineering decisions by providing data that would be very difficult, if not impossible, to obtain experimentally. It also includes chapters covering topics such as particle methods addressing particle-based materials and numerical methods that are based on discrete element formulations; fictitious domain methods; phase field models; computational fluid dynamics based on modern finite volume schemes; hybridizable discontinuous Galerkin methods; and non-intrusive coupling methods for structural models.

Numerical Analysis with Applications in Mechanics and Engineering

Petre Teodorescu,Nicolae-Doru Stanescu,Nicolae Pandrea
Numerical Analysis with Applications in Mechanics and Engineering Book PDF

Author : Petre Teodorescu,Nicolae-Doru Stanescu,Nicolae Pandrea
Publisher : John Wiley & Sons
Page : 458 pages
File Size : 42,5 Mb
Release : 2013-05-07
Category : Computers
ISBN : 9781118614624

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Numerical Analysis with Applications in Mechanics and Engineering by Petre Teodorescu,Nicolae-Doru Stanescu,Nicolae Pandrea Pdf

A much-needed guide on how to use numerical methods to solve practical engineering problems Bridging the gap between mathematics and engineering, Numerical Analysis with Applications in Mechanics and Engineering arms readers with powerful tools for solving real-world problems in mechanics, physics, and civil and mechanical engineering. Unlike most books on numerical analysis, this outstanding work links theory and application, explains the mathematics in simple engineering terms, and clearly demonstrates how to use numerical methods to obtain solutions and interpret results. Each chapter is devoted to a unique analytical methodology, including a detailed theoretical presentation and emphasis on practical computation. Ample numerical examples and applications round out the discussion, illustrating how to work out specific problems of mechanics, physics, or engineering. Readers will learn the core purpose of each technique, develop hands-on problem-solving skills, and get a complete picture of the studied phenomenon. Coverage includes: How to deal with errors in numerical analysis Approaches for solving problems in linear and nonlinear systems Methods of interpolation and approximation of functions Formulas and calculations for numerical differentiation and integration Integration of ordinary and partial differential equations Optimization methods and solutions for programming problems Numerical Analysis with Applications in Mechanics and Engineering is a one-of-a-kind guide for engineers using mathematical models and methods, as well as for physicists and mathematicians interested in engineering problems.

Numerical Methods for Nonlinear Variational Problems

Roland Glowinski
Numerical Methods for Nonlinear Variational Problems Book PDF

Author : Roland Glowinski
Publisher : Springer Science & Business Media
Page : 506 pages
File Size : 52,8 Mb
Release : 2013-06-29
Category : Science
ISBN : 9783662126134

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Numerical Methods for Nonlinear Variational Problems by Roland Glowinski Pdf

This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations such as transonic flows for compressible fluids and the Navier-Stokes equations for incompressible viscous fluids. Finite element approximations and non-linear relaxation, and nonlinear least square methods are all covered in detail, as are many applications. This volume is a classic in a long-awaited softcover re-edition.

Partial Differential Equations

Roland Glowinski,Pekka Neittaanmäki
Partial Differential Equations Book PDF

Author : Roland Glowinski,Pekka Neittaanmäki
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 40,8 Mb
Release : 2008-06-26
Category : Science
ISBN : 9781402087585

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Partial Differential Equations by Roland Glowinski,Pekka Neittaanmäki Pdf

For more than 250 years partial di?erential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at ?rst and then those originating from - man activity and technological development. Mechanics, physics and their engineering applications were the ?rst to bene?t from the impact of partial di?erential equations on modeling and design, but a little less than a century ago the Schr ̈ odinger equation was the key opening the door to the application of partial di?erential equations to quantum chemistry, for small atomic and molecular systems at ?rst, but then for systems of fast growing complexity. The place of partial di?erential equations in mathematics is a very particular one: initially, the partial di?erential equations modeling natural phenomena were derived by combining calculus with physical reasoning in order to - press conservation laws and principles in partial di?erential equation form, leading to the wave equation, the heat equation, the equations of elasticity, the Euler and Navier–Stokes equations for ?uids, the Maxwell equations of electro-magnetics, etc. It is in order to solve ‘constructively’ the heat equation that Fourier developed the series bearing his name in the early 19th century; Fourier series (and later integrals) have played (and still play) a fundamental roleinbothpureandappliedmathematics,includingmanyareasquiteremote from partial di?erential equations. On the other hand, several areas of mathematics such as di?erential ge- etry have bene?ted from their interactions with partial di?erential equations.

Nonlinear Systems and Optimization for the Chemical Engineer

Guido Buzzi-Ferraris,Flavio Manenti
Nonlinear Systems and Optimization for the Chemical Engineer Book PDF

Author : Guido Buzzi-Ferraris,Flavio Manenti
Publisher : John Wiley & Sons
Page : 522 pages
File Size : 48,9 Mb
Release : 2013-12-13
Category : Technology & Engineering
ISBN : 9783527667161

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Nonlinear Systems and Optimization for the Chemical Engineer by Guido Buzzi-Ferraris,Flavio Manenti Pdf

This third book in a suite of four practical guides is an engineer's companion to using numerical methods for the solution of complex mathematical problems. The required software is provided by way of the freeware mathematical library BzzMath that is developed and maintained by the authors. The present volume focuses on optimization and nonlinear systems solution. The book describes numerical methods, innovative techniques and strategies that are all implemented in a well-established, freeware library. Each of these handy guides enables the reader to use and implement standard numerical tools for their work, explaining the theory behind the various functions and problem solvers, and showcasing applications in diverse scientific and engineering fields. Numerous examples, sample codes, programs and applications are proposed and discussed. The book teaches engineers and scientists how to use the latest and most powerful numerical methods for their daily work.

Numerical Solutions of Realistic Nonlinear Phenomena

J. A. Tenreiro Machado,Necati Özdemir,Dumitru Baleanu
Numerical Solutions of Realistic Nonlinear Phenomena Book PDF

Author : J. A. Tenreiro Machado,Necati Özdemir,Dumitru Baleanu
Publisher : Springer
Page : 0 pages
File Size : 50,5 Mb
Release : 2021-02-20
Category : Mathematics
ISBN : 3030371433

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Numerical Solutions of Realistic Nonlinear Phenomena by J. A. Tenreiro Machado,Necati Özdemir,Dumitru Baleanu Pdf

This collection covers new aspects of numerical methods in applied mathematics, engineering, and health sciences. It provides recent theoretical developments and new techniques based on optimization theory, partial differential equations (PDEs), mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena. Specific topics covered in detail include new numerical methods for nonlinear partial differential equations, global optimization, unconstrained optimization, detection of HIV- Protease, modelling with new fractional operators, analysis of biological models, and stochastic modelling.

Analytical and Numerical Methods for Nonlinear Fluid Flow Problems in Porous Media

Wenchao Liu,Jun Yao,Weiyao Zhu
Analytical and Numerical Methods for Nonlinear Fluid Flow Problems in Porous Media Book PDF

Author : Wenchao Liu,Jun Yao,Weiyao Zhu
Publisher : Springer
Page : 0 pages
File Size : 47,8 Mb
Release : 2024-05-22
Category : Technology & Engineering
ISBN : 9819716349

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Analytical and Numerical Methods for Nonlinear Fluid Flow Problems in Porous Media by Wenchao Liu,Jun Yao,Weiyao Zhu Pdf

This book investigates in detail the mathematical methods and computation methods in efficient solution of some open nonlinear seepage flow problems involved in engineering problems. Developed engineering technologies and some relevant practical field applications are also provided. The introduced open nonlinear problems include nonlinear quadratic pressure gradient term problem, compressible gas seepage flow problem and low-velocity non-Darcy seepage flow problem. Studies on these nonlinear seepage flow problems have attracted engineers and scientists from various disciplines, such as geo-energy engineering, civil and environmental engineering, fluid mechanics, applied mathematics and computation. In particular, the book systematically establishes a fundamental theory for a strongly nonlinear problem of low-velocity non-Darcy seepage flow from a new perspective of moving boundary, while emphasizing the usage of mathematical linearization transformation methods and computational methods into the analytical and numerical solution of the strongly nonlinear partial differential equations. Sufficient knowledge of mathematics is always introduced ahead of model solution to assist readers. And the procedure of strict formula deduction in the model solution process is provided in detail. High-solution figures and tables from model solution are rich in the book. Therefore, it is very helpful for the readers to master the nonlinear model solution methods and engineering technologies. The book is intended for upper undergraduate students and graduate students who are interested in engineering technology, fluid mechanics and applied mathematics, researchers and engineers working on geo-energy science and engineering and field applications.

Numerical Methods for Evolutionary Differential Equations

Uri M. Ascher
Numerical Methods for Evolutionary Differential Equations Book PDF

Author : Uri M. Ascher
Publisher : SIAM
Page : 404 pages
File Size : 51,5 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780898718911

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Numerical Methods for Evolutionary Differential Equations by Uri M. Ascher Pdf

Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finance. This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well. Audience: suitable for researchers and graduate students from a variety of fields including computer science, applied mathematics, physics, earth and ocean sciences, and various engineering disciplines. Researchers who simulate processes that are modeled by evolutionary differential equations will find material on the principles underlying the appropriate method to use and the pitfalls that accompany each method.

Numerical Methods in Mechanics of Materials

Ken P. Chong,Arthur P. Boresi,Sunil Saigal,James D. Lee
Numerical Methods in Mechanics of Materials Book PDF

Author : Ken P. Chong,Arthur P. Boresi,Sunil Saigal,James D. Lee
Publisher : CRC Press
Page : 269 pages
File Size : 52,7 Mb
Release : 2017-11-27
Category : Technology & Engineering
ISBN : 9781351380980

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Numerical Methods in Mechanics of Materials by Ken P. Chong,Arthur P. Boresi,Sunil Saigal,James D. Lee Pdf

In the dynamic digital age, the widespread use of computers has transformed engineering and science. A realistic and successful solution of an engineering problem usually begins with an accurate physical model of the problem and a proper understanding of the assumptions employed. With computers and appropriate software we can model and analyze complex physical systems and problems. However, efficient and accurate use of numerical results obtained from computer programs requires considerable background and advanced working knowledge to avoid blunders and the blind acceptance of computer results. This book provides the background and knowledge necessary to avoid these pitfalls, especially the most commonly used numerical methods employed in the solution of physical problems. It offers an in-depth presentation of the numerical methods for scales from nano to macro in nine self-contained chapters with extensive problems and up-to-date references, covering: Trends and new developments in simulation and computation Weighted residuals methods Finite difference methods Finite element methods Finite strip/layer/prism methods Boundary element methods Meshless methods Molecular dynamics Multiphysics problems Multiscale methods

Numerical Methods in Biomedical Engineering

Stanley Dunn,Alkis Constantinides,Prabhas V. Moghe
Numerical Methods in Biomedical Engineering Book PDF

Author : Stanley Dunn,Alkis Constantinides,Prabhas V. Moghe
Publisher : Elsevier
Page : 632 pages
File Size : 44,9 Mb
Release : 2005-11-21
Category : Technology & Engineering
ISBN : 0080470807

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Numerical Methods in Biomedical Engineering by Stanley Dunn,Alkis Constantinides,Prabhas V. Moghe Pdf

Numerical Modeling in Biomedical Engineering brings together the integrative set of computational problem solving tools important to biomedical engineers. Through the use of comprehensive homework exercises, relevant examples and extensive case studies, this book integrates principles and techniques of numerical analysis. Covering biomechanical phenomena and physiologic, cell and molecular systems, this is an essential tool for students and all those studying biomedical transport, biomedical thermodynamics & kinetics and biomechanics. Supported by Whitaker Foundation Teaching Materials Program; ABET-oriented pedagogical layout Extensive hands-on homework exercises

Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics

Shen R. Wu,Lei Gu
Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics Book PDF

Author : Shen R. Wu,Lei Gu
Publisher : John Wiley & Sons
Page : 352 pages
File Size : 42,6 Mb
Release : 2012-07-30
Category : Mathematics
ISBN : 9781118382073

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Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics by Shen R. Wu,Lei Gu Pdf

A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in mastering the explicit finite element method and programming code without requiring extensive background knowledge of the general finite element. The authors present topics relating to the variational principle, numerical procedure, mechanical formulation, and fundamental achievements of the convergence theory. In addition, key topics and techniques are provided in four clearly organized sections: • Fundamentals explores a framework of the explicit finite element method for nonlinear transient dynamics and highlights achievements related to the convergence theory • Element Technology discusses four-node, three-node, eight-node, and two-node element theories • Material Models outlines models of plasticity and other nonlinear materials as well as the mechanics model of ductile damage • Contact and Constraint Conditions covers subjects related to three-dimensional surface contact, with examples solved analytically, as well as discussions on kinematic constraint conditions Throughout the book, vivid figures illustrate the ideas and key features of the explicit finite element method. Examples clearly present results, featuring both theoretical assessments and industrial applications. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is an ideal book for both engineers who require more theoretical discussions and for theoreticians searching for interesting and challenging research topics. The book also serves as an excellent resource for courses on applied mathematics, applied mechanics, and numerical methods at the graduate level.

Numerical Solution of Partial Differential Equations in Science and Engineering

Leon Lapidus,George F. Pinder
Numerical Solution of Partial Differential Equations in Science and Engineering Book PDF

Author : Leon Lapidus,George F. Pinder
Publisher : John Wiley & Sons
Page : 677 pages
File Size : 45,5 Mb
Release : 2011-02-14
Category : Mathematics
ISBN : 9781118031216

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Numerical Solution of Partial Differential Equations in Science and Engineering by Leon Lapidus,George F. Pinder Pdf

From the reviews of Numerical Solution of PartialDifferential Equations in Science and Engineering: "The book by Lapidus and Pinder is a very comprehensive, evenexhaustive, survey of the subject . . . [It] is unique in that itcovers equally finite difference and finite element methods." Burrelle's "The authors have selected an elementary (but not simplistic)mode of presentation. Many different computational schemes aredescribed in great detail . . . Numerous practical examples andapplications are described from beginning to the end, often withcalculated results given." Mathematics of Computing "This volume . . . devotes its considerable number of pages tolucid developments of the methods [for solving partial differentialequations] . . . the writing is very polished and I found it apleasure to read!" Mathematics of Computation Of related interest . . . NUMERICAL ANALYSIS FOR APPLIED SCIENCE Myron B. Allen andEli L. Isaacson. A modern, practical look at numerical analysis,this book guides readers through a broad selection of numericalmethods, implementation, and basic theoretical results, with anemphasis on methods used in scientific computation involvingdifferential equations. 1997 (0-471-55266-6) 512 pp. APPLIED MATHEMATICS Second Edition, J. David Logan.Presenting an easily accessible treatment of mathematical methodsfor scientists and engineers, this acclaimed work covers fluidmechanics and calculus of variations as well as more modernmethods-dimensional analysis and scaling, nonlinear wavepropagation, bifurcation, and singular perturbation. 1996(0-471-16513-1) 496 pp.

Introduction to Computation and Modeling for Differential Equations

Lennart Edsberg
Introduction to Computation and Modeling for Differential Equations Book PDF

Author : Lennart Edsberg
Publisher : John Wiley & Sons
Page : 288 pages
File Size : 40,8 Mb
Release : 2015-09-16
Category : Mathematics
ISBN : 9781119018469

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Introduction to Computation and Modeling for Differential Equations by Lennart Edsberg Pdf

Uses mathematical, numerical, and programming tools to solve differential equations for physical phenomena and engineering problems Introduction to Computation and Modeling for Differential Equations, Second Edition features the essential principles and applications of problem solving across disciplines such as engineering, physics, and chemistry. The Second Edition integrates the science of solving differential equations with mathematical, numerical, and programming tools, specifically with methods involving ordinary differential equations; numerical methods for initial value problems (IVPs); numerical methods for boundary value problems (BVPs); partial differential equations (PDEs); numerical methods for parabolic, elliptic, and hyperbolic PDEs; mathematical modeling with differential equations; numerical solutions; and finite difference and finite element methods. The author features a unique “Five-M” approach: Modeling, Mathematics, Methods, MATLAB®, and Multiphysics, which facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation and also demonstrates how a problem is solved numerically using the appropriate mathematical methods. With numerous real-world examples to aid in the visualization of the solutions, Introduction to Computation and Modeling for Differential Equations, Second Edition includes: New sections on topics including variational formulation, the finite element method, examples of discretization, ansatz methods such as Galerkin’s method for BVPs, parabolic and elliptic PDEs, and finite volume methods Numerous practical examples with applications in mechanics, fluid dynamics, solid mechanics, chemical engineering, heat conduction, electromagnetic field theory, and control theory, some of which are solved with computer programs MATLAB and COMSOL Multiphysics® Additional exercises that introduce new methods, projects, and problems to further illustrate possible applications A related website with select solutions to the exercises, as well as the MATLAB data sets for ordinary differential equations (ODEs) and PDEs Introduction to Computation and Modeling for Differential Equations, Second Edition is a useful textbook for upper-undergraduate and graduate-level courses in scientific computing, differential equations, ordinary differential equations, partial differential equations, and numerical methods. The book is also an excellent self-study guide for mathematics, science, computer science, physics, and engineering students, as well as an excellent reference for practitioners and consultants who use differential equations and numerical methods in everyday situations.