Advanced Continuum Theories And Finite Element Analyses

Advanced Continuum Theories And Finite Element Analyses PDF

Author: James D Lee

Publisher: World Scientific

Published: 2020-01-08

Total Pages: 523

ISBN-13: 9811201501

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This comprehensive volume presents a unified framework of continuum theories. It indicates that (i) microcontinuum theories (micromorphic and micropolar theories) are natural extension of classical continuum mechanics, and (ii) classical continuum mechanics is a special case of microcontinuum theories when the deformable material point is idealized as a single mathematical point. The kinematics and basic laws are rigorously derived. Based on axiomatic approach, constitutive theory is systematically derived for various kinds of materials, ranging from Stokesian fluid to thermo-visco-elastic-plastic solid. Material force and Thermomechanical-electromagnetic coupling are introduced and discussed. Moreover, general finite element methods for large-strain thermomechanical coupling physical phenomena are systematically formulated. Also, non-classical continuum theories (Nonlocal Theory, Mechanobiology, 4D printing, Poromechanics, and Non-Self-Similar Crack Propagation) are rigorously formulated with applications and demonstrated numerically.As an advanced monograph, this unique compendium can also be used as a textbook for several graduate courses, including continuum mechanics, finite element methods, and advanced engineering science theories. Extensive problems are provided to help students to better understand the topics covered.

Nonlinear Finite Elements for Continua and Structures

Nonlinear Finite Elements for Continua and Structures PDF

Author: Ted Belytschko

Publisher: John Wiley & Sons

Published: 2014-01-07

Total Pages: 834

ISBN-13: 1118632702

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Nonlinear Finite Elements for Continua and Structures p>Nonlinear Finite Elements for Continua and Structures This updated and expanded edition of the bestselling textbook provides a comprehensive introduction to the methods and theory of nonlinear finite element analysis. New material provides a concise introduction to some of the cutting-edge methods that have evolved in recent years in the field of nonlinear finite element modeling, and includes the eXtended Finite Element Method (XFEM), multiresolution continuum theory for multiscale microstructures, and dislocation- density-based crystalline plasticity. Nonlinear Finite Elements for Continua and Structures, Second Edition focuses on the formulation and solution of discrete equations for various classes of problems that are of principal interest in applications to solid and structural mechanics. Topics covered include the discretization by finite elements of continua in one dimension and in multi-dimensions; the formulation of constitutive equations for nonlinear materials and large deformations; procedures for the solution of the discrete equations, including considerations of both numerical and multiscale physical instabilities; and the treatment of structural and contact-impact problems. Key features: Presents a detailed and rigorous treatment of nonlinear solid mechanics and how it can be implemented in finite element analysis Covers many of the material laws used in today’s software and research Introduces advanced topics in nonlinear finite element modelling of continua Introduction of multiresolution continuum theory and XFEM Accompanied by a website hosting a solution manual and MATLAB® and FORTRAN code Nonlinear Finite Elements for Continua and Structures, Second Edition is a must-have textbook for graduate students in mechanical engineering, civil engineering, applied mathematics, engineering mechanics, and materials science, and is also an excellent source of information for researchers and practitioners.

Introduction to Finite Strain Theory for Continuum Elasto-Plasticity

Introduction to Finite Strain Theory for Continuum Elasto-Plasticity PDF

Author: Koichi Hashiguchi

Publisher: John Wiley & Sons

Published: 2012-10-09

Total Pages: 371

ISBN-13: 1118437721

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Comprehensive introduction to finite elastoplasticity, addressing various analytical and numerical analyses & including state-of-the-art theories Introduction to Finite Elastoplasticity presents introductory explanations that can be readily understood by readers with only a basic knowledge of elastoplasticity, showing physical backgrounds of concepts in detail and derivation processes of almost all equations. The authors address various analytical and numerical finite strain analyses, including new theories developed in recent years, and explain fundamentals including the push-forward and pull-back operations and the Lie derivatives of tensors. As a foundation to finite strain theory, the authors begin by addressing the advanced mathematical and physical properties of continuum mechanics. They progress to explain a finite elastoplastic constitutive model, discuss numerical issues on stress computation, implement the numerical algorithms for stress computation into large-deformation finite element analysis and illustrate several numerical examples of boundary-value problems. Programs for the stress computation of finite elastoplastic models explained in this book are included in an appendix, and the code can be downloaded from an accompanying website.

The Essentials of Finite Element Modeling and Adaptive Refinement

The Essentials of Finite Element Modeling and Adaptive Refinement PDF

Author: John O. Dow

Publisher: Momentum Press

Published: 2012-07-01

Total Pages: 271

ISBN-13: 1606503340

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Finite Element Analysis is a very popular, computer-based tool that uses a complex system of points called nodes to make a grid called a "mesh. " The mesh contains the material and structural properties that define how the structure will react to certain loading conditions, allowing virtual testing and analysis of stresses or changes applied to the material or component design. This groundbreaking text extends the usefulness of finite element analysis by helping both beginners and advanced users alike. It simplifies, improves, and extends both the finite element method while at the same time advancing adaptive refinement procedures. These improvements are made possible due to a change in notation that embeds knowledge of solid continuum mechanics into the equations used to formulate the stiffness matrices; this allows the modeling characteristics of individual elements to be identified by visual inspection. The ability to visually relate the equations involved in element formulation to the physical process they represent is like having an x-ray of the inner workings of the finite element method; it is similar is to the effect that Graphical User Interfaces or GUI's had on computing. As a result, students at any level of finite element study are provided with an understanding of the capabilities and limitations of this powerful analytic tool. The book presents * A more simplified approach to finite element analysis based on computational continuum mechanics * Physically interpretable notation that identifies a common basis for the finite element and the finite difference methods. * New point-wise error estimators that identify errors in terms of quantities of direct interest in solid mechanics

Finite Element Programs in Structural Engineering and Continuum Mechanics

Finite Element Programs in Structural Engineering and Continuum Mechanics PDF

Author: Carl T. F. Ross

Publisher: Elsevier

Published: 1996-01-01

Total Pages: 637

ISBN-13: 0857099833

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Bridging the gap between theoretical texts and the massive and expensive software packages, this handbook covers finite element programming in a wide range of problems in mechanical, civil, aeronautical and electrical engineering. Comprehensive, it ranges from the static analysis of two- and three-dimensional structures to stress analysis of thick slabs on elastic foundations, and from two- and three- dimensional vibration analysis problems to two-dimensional field problems including heat transfer and acoustic vibrations. The 24 printouts of powerful and valuable engineering computer programs, written in QUICK BASIC, are introduced by a preliminary chapter giving useful hints and formulae intended for structural design. The programs are capable of analysing problems in engineering design and manufacture, with text fully describing how to use the computer programs for their particular problems or tasks. The finite element method is used in all the programs, and the problems for analysis can be of quite complex design and shape and with complex boundary conditions. Covers finite element programming in a wide range of problems in mechanical, civil, aeronautical and electrical engineering Ranges from the static analysis of two- and three-dimensional structures to stress analysis of thick slabs on elastic foundations

Finite Elements of Nonlinear Continua

Finite Elements of Nonlinear Continua PDF

Author: J. T. Oden

Publisher: Courier Corporation

Published: 2013-04-15

Total Pages: 517

ISBN-13: 0486317900

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Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view. The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical solution of the equations governing the discrete model. Though the theory and methods are sufficiently general to be applied to any nonlinear problem, emphasis has been placed on problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity. Problems in rarefied gas dynamics and nonlinear partial differential equations are also examined. Other topics include topological properties of finite element models, applications to linear and nonlinear boundary value problems, and discrete models of nonlinear thermomechanical behavior of dissipative media. This comprehensive text is valuable not only to students of structural analysis and continuum mechanics but also to professionals researching the numerical analysis of continua

Nonlinear Finite Element Analysis of Solids and Structures

Nonlinear Finite Element Analysis of Solids and Structures PDF

Author: René de Borst

Publisher: John Wiley & Sons

Published: 2012-07-25

Total Pages: 481

ISBN-13: 1118376013

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Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist René de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature. Key features: Combines the two previous volumes into one heavily revised text with obsolete material removed, an improved layout and updated references and notations Extensive new material on more recent developments in computational mechanics Easily readable, engineering oriented, with no more details in the main text than necessary to understand the concepts. Pseudo-code throughout makes the link between theory and algorithms, and the actual implementation. Accompanied by a website (www.wiley.com/go/deborst) with a Python code, based on the pseudo-code within the book and suitable for solving small-size problems. Non-linear Finite Element Analysis of Solids and Structures, 2nd Edition is an essential reference for practising engineers and researchers that can also be used as a text for undergraduate and graduate students within computational mechanics.

Finite Element Analysis

Finite Element Analysis PDF

Author: David W. Nicholson

Publisher: CRC Press

Published: 2008-04-18

Total Pages: 480

ISBN-13: 9781420050950

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Explore a Unified Treatment of the Finite Element Method The finite element method has matured to the point that it can accurately and reliably be used, by a careful analyst, for an amazingly wide range of applications. With expanded coverage and an increase in fully solved examples, the second edition of Finite Element Analysis: Thermomechanics of Solids presents a unified treatment of the finite element method in theremomechanics, from the basics to advanced concepts. An Integrated Presentation of Critical Technology As in the first edition, the author presents and explicates topics in a way that demonstrates the highly unified structure of the finite element method. The presentation integrates continuum mechanics and relevant mathematics with persistent reliance on variational and incremental-variational foundations. The author exploits matrix-vector formalisms and Kronecker product algebra to provide transparent and consistent notation throughout the text. Nearly twice as long as the first edition, this second edition features: § Greater integration and balance between introductory and advanced material § Increased number of fully solved examples § Selected developments in numerical methods, detailing accelerating computations in eigenstructure extraction, time integration, and stiffness matrix triangularization § More extensive coverage of the arc length method for nonlinear problems § Expanded and enhanced treatment of rotating bodies and buckling Provides Sophisticated Understanding of Capabilities and Limitations This new edition of a popular text includes significant illustrative examples and applications, modeling strategies, and explores a range of computational issues. Written by a professor with years of practical engineering and instructional experience, the book provides a strong foundation for those requiring a sophisticated understanding of the method’s capabilities and limitations.

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