Numerical Methods in Computational Mechanics

Numerical Methods in Computational Mechanics
Author: Jamshid Ghaboussi,Xiping Steven Wu
Publsiher: CRC Press
Total Pages: 331
Release: 2016-11-25
Genre: Mathematics
ISBN: 9781315351643

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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.

Computational Engineering Introduction to Numerical Methods

Computational Engineering   Introduction to Numerical Methods
Author: Michael Schäfer
Publsiher: Springer Nature
Total Pages: 373
Release: 2021-07-19
Genre: Technology & Engineering
ISBN: 9783030760274

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Numerical simulation methods in all engineering disciplines gains more and more importance. The successful and efficient application of such tools requires certain basic knowledge about the underlying numerical techniques. The text gives a practice-oriented introduction in modern numerical methods as they typically are applied in mechanical, chemical, or civil engineering. Problems from heat transfer, structural mechanics, and fluid mechanics constitute a thematical focus of the text. For the basic understanding of the topic aspects of numerical mathematics, natural sciences, computer science, and the corresponding engineering area are simultaneously important. Usually, the necessary information is distributed in different textbooks from the individual disciplines. In the present text the subject matter is presented in a comprehensive multidisciplinary way, where aspects from the different fields are treated insofar as it is necessary for general understanding. Overarching aspects and important questions related to accuracy, efficiency, and cost effectiveness are discussed. The topics are presented in an introductory manner, such that besides basic mathematical standard knowledge in analysis and linear algebra no further prerequisites are necessary. The book is suitable either for self-study or as an accompanying textbook for corresponding lectures. It can be useful for students of engineering disciplines as well as for computational engineers in industrial practice.

Numerical Methods in Computational Mechanics

Numerical Methods in Computational Mechanics
Author: Jamshid Ghaboussi,Xiping Steven Wu
Publsiher: CRC Press
Total Pages: 313
Release: 2016-11-25
Genre: Mathematics
ISBN: 9781498746786

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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.

Computational Mechanics with Neural Networks

Computational Mechanics with Neural Networks
Author: Genki Yagawa,Atsuya Oishi
Publsiher: Springer Nature
Total Pages: 228
Release: 2021-02-26
Genre: Technology & Engineering
ISBN: 9783030661113

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This book shows how neural networks are applied to computational mechanics. Part I presents the fundamentals of neural networks and other machine learning method in computational mechanics. Part II highlights the applications of neural networks to a variety of problems of computational mechanics. The final chapter gives perspectives to the applications of the deep learning to computational mechanics.

Computational Mechanics of Discontinua

Computational Mechanics of Discontinua
Author: Antonio A. Munjiza,Earl E. Knight,Esteban Rougier
Publsiher: John Wiley & Sons
Total Pages: 304
Release: 2011-10-13
Genre: Technology & Engineering
ISBN: 9781119973010

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Mechanics of Discontinua is the first book to comprehensively tackle both the theory ofthis rapidly developing topic and the applications that span a broad field of scientific and engineering disciplines, from traditional engineering to physics of particulates, nano-technology and micro-flows. Authored by a leading researcher who has been at the cutting edge of discontinua simulation developments over the last 15 years, the book is organized into four parts: introductory knowledge, solvers, methods and applications. In the first chapter a short revision of Continuum Mechanics together with tensorial calculus is introduced. Also, a short introduction to the finite element method is given. The second part of the book introduces key aspects of the subject. These include a diverse field of applications, together with fundamental theoretical and algorithmic aspects common to all methods of Mechanics of Discontinua. The third part of the book proceeds with the most important computational and simulation methods including Discrete Element Methods, the Combined Finite-Discrete Element Method, Molecular Dynamics Methods, Fracture and Fragmentation solvers and Fluid Coupling. After these the reader is introduced to applications stretching from traditional engineering and industry (such as mining, oil industry, powders) to nanotechnology, medical and science.

Numerical Methods and Methods of Approximation in Science and Engineering

Numerical Methods and Methods of Approximation in Science and Engineering
Author: Karan S. Surana
Publsiher: CRC Press
Total Pages: 478
Release: 2018-10-31
Genre: Mathematics
ISBN: 9780429647864

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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

Computational Methods in Engineering

Computational Methods in Engineering
Author: S.P. Venkateshan,Prasanna Swaminathan
Publsiher: Elsevier
Total Pages: 692
Release: 2013-12-09
Genre: Computers
ISBN: 9780124167032

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Computational Methods in Engineering brings to light the numerous uses of numerical methods in engineering. It clearly explains the application of these methods mathematically and practically, emphasizing programming aspects when appropriate. By approaching the cross-disciplinary topic of numerical methods with a flexible approach, Computational Methods in Engineering encourages a well-rounded understanding of the subject. This book's teaching goes beyond the text—detailed exercises (with solutions), real examples of numerical methods in real engineering practices, flowcharts, and MATLAB codes all help you learn the methods directly in the medium that suits you best. Balanced discussion of mathematical principles and engineering applications Detailed step-by-step exercises and practical engineering examples to help engineering students and other readers fully grasp the concepts Concepts are explained through flowcharts and simple MATLAB codes to help you develop additional programming skills

Numerical Methods and Computational Mechanics

Numerical Methods and Computational Mechanics
Author: Anonim
Publsiher: Unknown
Total Pages: 228
Release: 2001
Genre: Engineering mathematics
ISBN: OCLC:248780374

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Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics

Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics
Author: Titus Petrila,Damian Trif
Publsiher: Springer Science & Business Media
Total Pages: 500
Release: 2006-06-14
Genre: Mathematics
ISBN: 9780387238388

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The present book – through the topics and the problems approach – aims at filling a gap, a real need in our literature concerning CFD (Computational Fluid Dynamics). Our presentation results from a large documentation and focuses on reviewing the present day most important numerical and computational methods in CFD. Many theoreticians and experts in the field have expressed their - terest in and need for such an enterprise. This was the motivation for carrying out our study and writing this book. It contains an important systematic collection of numerical working instruments in Fluid Dyn- ics. Our current approach to CFD started ten years ago when the Univ- sity of Paris XI suggested a collaboration in the field of spectral methods for fluid dynamics. Soon after – preeminently studying the numerical approaches to Navier–Stokes nonlinearities – we completed a number of research projects which we presented at the most important inter- tional conferences in the field, to gratifying appreciation. An important qualitative step in our work was provided by the dev- opment of a computational basis and by access to a number of expert softwares. This fact allowed us to generate effective working programs for most of the problems and examples presented in the book, an - pect which was not taken into account in most similar studies that have already appeared all over the world.

Computational Methods in Nonlinear Structural and Solid Mechanics

Computational Methods in Nonlinear Structural and Solid Mechanics
Author: Ahmed K. Noor,Harvey G. McComb
Publsiher: Elsevier
Total Pages: 470
Release: 2014-05-20
Genre: Technology & Engineering
ISBN: 9781483145648

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Computational Methods in Nonlinear Structural and Solid Mechanics covers the proceedings of the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics. The book covers the development of efficient discretization approaches; advanced numerical methods; improved programming techniques; and applications of these developments to nonlinear analysis of structures and solids. The chapters of the text are organized into 10 parts according to the issue they tackle. The first part deals with nonlinear mathematical theories and formulation aspects, while the second part covers computational strategies for nonlinear programs. Part 3 deals with time integration and numerical solution of nonlinear algebraic equations, while Part 4 discusses material characterization and nonlinear fracture mechanics, and Part 5 tackles nonlinear interaction problems. The sixth part discusses seismic response and nonlinear analysis of concrete structure, and the seventh part tackles nonlinear problems for nuclear reactors. Part 8 covers crash dynamics and impact problems, while Part 9 deals with nonlinear problems of fibrous composites and advanced nonlinear applications. The last part discusses computerized symbolic manipulation and nonlinear analysis software systems. The book will be of great interest to numerical analysts, computer scientists, structural engineers, and other professionals concerned with nonlinear structural and solid mechanics.

Handbook of Computational Fluid Mechanics

Handbook of Computational Fluid Mechanics
Author: Roger Peyret
Publsiher: Academic Press
Total Pages: 467
Release: 1996-01-01
Genre: Technology & Engineering
ISBN: 9780125530101

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This handbook covers computational fluid dynamics from fundamentals to applications. This text provides a well documented critical survey of numerical methods for fluid mechanics, and gives a state-of-the-art description of computational fluid mechanics, considering numerical analysis, computer technology, and visualization tools. The chapters in this book are invaluable tools for reaching a deeper understanding of the problems associated with the calculation of fluid motion in various situations: inviscid and viscous, incompressible and compressible, steady and unsteady, laminar and turbulent flows, as well as simple and complex geometries. Each chapter includes a related bibliography Covers fundamentals and applications Provides a deeper understanding of the problems associated with the calculation of fluid motion

Numerical and Analytical Methods with MATLAB

Numerical and Analytical Methods with MATLAB
Author: William Bober,Chi-Tay Tsai,Oren Masory
Publsiher: CRC Press
Total Pages: 472
Release: 2009-08-11
Genre: Technology & Engineering
ISBN: 9781420093575

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Numerical and Analytical Methods with MATLAB® presents extensive coverage of the MATLAB programming language for engineers. It demonstrates how the built-in functions of MATLAB can be used to solve systems of linear equations, ODEs, roots of transcendental equations, statistical problems, optimization problems, control systems problems, and stress analysis problems. These built-in functions are essentially black boxes to students. By combining MATLAB with basic numerical and analytical techniques, the mystery of what these black boxes might contain is somewhat alleviated. This classroom-tested text first reviews the essentials involved in writing computer programs as well as fundamental aspects of MATLAB. It next explains how matrices can solve problems of linear equations, how to obtain the roots of algebraic and transcendental equations, how to evaluate integrals, and how to solve various ODEs. After exploring the features of Simulink, the book discusses curve fitting, optimization problems, and PDE problems, such as the vibrating string, unsteady heat conduction, and sound waves. The focus then shifts to the solution of engineering problems via iteration procedures, differential equations via Laplace transforms, and stress analysis problems via the finite element method. The final chapter examines control systems theory, including the design of single-input single-output (SISO) systems. Two Courses in One Textbook The first six chapters are appropriate for a lower level course at the sophomore level. The remaining chapters are ideal for a course at the senior undergraduate or first-year graduate level. Most of the chapters contain projects that require students to write a computer program in MATLAB that produces tables, graphs, or both. Many sample MATLAB programs (scripts) in the text provide guidance on completing these projects.

Computational Methods in Solid Mechanics

Computational Methods in Solid Mechanics
Author: A. Curnier
Publsiher: Springer Science & Business Media
Total Pages: 404
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 9789401111126

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This volume presents an introduction to the three numerical methods most commonly used in the mechanical analysis of deformable solids, viz. the finite element method (FEM), the linear iteration method (LIM), and the finite difference method (FDM). The book has been written from the point of view of simplicity and unity; its originality lies in the comparable emphasis given to the spatial, temporal and nonlinear dimensions of problem solving. This leads to a neat global algorithm. Chapter 1 addresses the problem of a one-dimensional bar, with emphasis being given to the virtual work principle. Chapters 2--4 present the three numerical methods. Although the discussion relates to a one-dimensional model, the formalism used is extendable to two-dimensional situations. Chapter 5 is devoted to a detailed discussion of the compact combination of the three methods, and contains several sections concerning their computer implementation. Finally, Chapter 6 gives a generalization to two and three dimensions of both the mechanical and numerical aspects. For graduate students and researchers whose work involves the theory and application of computational solid mechanics.

Numerical Methods in Computational Mechanics

Numerical Methods in Computational Mechanics
Author: J. Ghaboussi,Xiping Wu
Publsiher: Taylor & Francis Group, LLC, CRC Press is
Total Pages: 135
Release: 2017
Genre: Engineering mathematics
ISBN: 1315332604

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Computational Contact Mechanics

Computational Contact Mechanics
Author: Peter Wriggers,Tod A. Laursen
Publsiher: Springer Science & Business Media
Total Pages: 248
Release: 2008-04-01
Genre: Science
ISBN: 9783211772980

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Topics of this book span the range from spatial and temporal discretization techniques for contact and impact problems with small and finite deformations over investigations on the reliability of micromechanical contact models over emerging techniques for rolling contact mechanics to homogenization methods and multi-scale approaches in contact problems.