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Numerical Methods in Computational Mechanics

Author : Jamshid Ghaboussi

Publisher : CRC Press

Page : 332 pages

File Size : 43,95 MB

Release : 2016-11-25

Category : Mathematics

ISBN : 1498746780

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Book Description

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.



Numerical Methods in Structural Mechanics

Author : Zdenek Bittnar

Publisher : Thomas Telford

Page : 438 pages

File Size : 16,1 MB

Release : 1996-04-05

Category : Mathematics

ISBN : 9780727725554

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Book Description

A detailed presentation is offered of the fundamental equations in solid mechanics focusing on constitutive equations including quasibrittle materials. Details are provided on individual numerical algorithms, with a heavier emphasis placed on the understanding of basic principles.



Numerical Analysis with Applications in Mechanics and Engineering

Author : Petre Teodorescu

Publisher : John Wiley & Sons

Page : 458 pages

File Size : 34,64 MB

Release : 2013-05-07

Category : Computers

ISBN : 1118614623

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Book Description

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 in Contact Mechanics

Author : Vladislav A. Yastrebov

Publisher : John Wiley & Sons

Page : 303 pages

File Size : 30,80 MB

Release : 2013-02-13

Category : Mathematics

ISBN : 1118648056

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Book Description

Computational contact mechanics is a broad topic which brings together algorithmic, geometrical, optimization and numerical aspects for a robust, fast and accurate treatment of contact problems. This book covers all the basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes for both sequential and parallel computer architectures. The book is self-contained and intended for people working on the implementation and improvement of contact algorithms in a finite element software. Using a new tensor algebra, the authors introduce some original notions in contact kinematics and extend the classical formulation of contact elements. Some classical and new resolution methods for contact problems and associated ready-to-implement expressions are provided. Contents: 1. Introduction to Computational Contact. 2. Geometry in Contact Mechanics. 3. Contact Detection. 4. Formulation of Contact Problems. 5. Numerical Procedures. 6. Numerical Examples. About the Authors Vladislav A. Yastrebov is a postdoctoral-fellow in Computational Solid Mechanics at MINES ParisTech in France. His work in computational contact mechanics was recognized by the CSMA award and by the Prix Paul Caseau of the French Academy of Technology and Electricité de France.



Introduction to Numerical Methods

Author : Aniruddha Mitra

Publisher : Cognella Academic Publishing

Page : pages

File Size : 13,8 MB

Release : 2016-07-29

Category :

ISBN : 9781516500154

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Book Description

Written for sophomore-level students in mechanical engineering programs and designed to give them the math preparation they need to succeed in higher level mechanical engineering courses, Introduction to Numerical Methods incorporates theory and worked-out engineering-related problems that apply that theory, as well as relevant laboratory exercises. Ideally suited to one-semester, three-credit, problem solving session-based courses, the book covers errors in computation, rounding and chopping, solving equations with numerical techniques, matrixes and vectors, and complex numbers. The material also includes an introduction to optimization, linear programming problems, and instruction in probability and statistics. It should be noted that many of the exercises in the book suggest the use of a Ti-83 calculator, and that tips for using this calculator successfully are integrated into the text. Introduction to Numerical Methods is a well-organized, useful addition to undergraduate course work in engineering programs, especially in the mechanical discipline.



Computational Engineering - Introduction to Numerical Methods

Author : Michael Schäfer

Publisher : Springer Nature

Page : 374 pages

File Size : 50,82 MB

Release : 2021-07-19

Category : Technology & Engineering

ISBN : 3030760278

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Book Description

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 for Physics

Author : Alejando L. Garcia

Publisher : Createspace Independent Publishing Platform

Page : 0 pages

File Size : 28,99 MB

Release : 2015-06-06

Category : Differential equations, Partial

ISBN : 9781514136683

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Book Description

This book covers a broad spectrum of the most important, basic numerical and analytical techniques used in physics -including ordinary and partial differential equations, linear algebra, Fourier transforms, integration and probability. Now language-independent. Features attractive new 3-D graphics. Offers new and significantly revised exercises. Replaces FORTRAN listings with C++, with updated versions of the FORTRAN programs now available on-line. Devotes a third of the book to partial differential equations-e.g., Maxwell's equations, the diffusion equation, the wave equation, etc. This numerical analysis book is designed for the programmer with a physics background. Previously published by Prentice Hall / Addison-Wesley



Numerical Methods in Rock Mechanics

Author : G. N. Pande

Publisher : John Wiley & Sons

Page : 356 pages

File Size : 16,96 MB

Release : 1990

Category : Mathematics

ISBN :

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Book Description

There have been important changes in rock mechanics during the last decade. This book reflects these changes, particularly in the use of computational methods. It covers the properties and behaviour of rocks, and the ways in which these can be modelled numerically.



Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes

Author : Miguel Cerrolaza

Publisher : Academic Press

Page : 462 pages

File Size : 41,26 MB

Release : 2017-12-28

Category : Technology & Engineering

ISBN : 0128117192

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Book Description

Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes covers new and exciting modeling methods to help bioengineers tackle problems for which the Finite Element Method is not appropriate. The book covers a wide range of important subjects in the field of numerical methods applied to biomechanics, including bone biomechanics, tissue and cell mechanics, 3D printing, computer assisted surgery and fluid dynamics. Modeling strategies, technology and approaches are continuously evolving as the knowledge of biological processes increases. Both theory and applications are covered, making this an ideal book for researchers, students and R&D professionals. - Provides non-conventional analysis methods for modeling - Covers the Discrete Element Method (DEM), Particle Methods (PM), MessLess and MeshFree Methods (MLMF), Agent-Based Methods (ABM), Lattice-Boltzmann Methods (LBM) and Boundary Integral Methods (BIM) - Includes contributions from several world renowned experts in their fields - Compares pros and cons of each method to help you decide which method is most applicable to solving specific problems



Numerical Methods for Nonsmooth Dynamical Systems

Author : Vincent Acary

Publisher : Springer Science & Business Media

Page : 529 pages

File Size : 33,97 MB

Release : 2008-01-30

Category : Technology & Engineering

ISBN : 3540753923

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Book Description

This book concerns the numerical simulation of dynamical systems whose trajec- ries may not be differentiable everywhere. They are named nonsmooth dynamical systems. They make an important class of systems, rst because of the many app- cations in which nonsmooth models are useful, secondly because they give rise to new problems in various elds of science. Usually nonsmooth dynamical systems are represented as differential inclusions, complementarity systems, evolution va- ational inequalities, each of these classes itself being split into several subclasses. The book is divided into four parts, the rst three parts being sketched in Fig. 0. 1. The aim of the rst part is to present the main tools from mechanics and applied mathematics which are necessary to understand how nonsmooth dynamical systems may be numerically simulated in a reliable way. Many examples illustrate the th- retical results, and an emphasis is put on mechanical systems, as well as on electrical circuits (the so-called Filippov’s systems are also examined in some detail, due to their importance in control applications). The second and third parts are dedicated to a detailed presentation of the numerical schemes. A fourth part is devoted to the presentation of the software platform Siconos. This book is not a textbook on - merical analysis of nonsmooth systems, in the sense that despite the main results of numerical analysis (convergence, order of consistency, etc. ) being presented, their proofs are not provided.



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