The Finite Element Method

Principles and Applications

Author: P. E. Lewis,J. P. Ward

Publisher: Addison-Wesley Longman

ISBN: 9780201544152

Category: Mathematics

Page: 421

View: 5961


Introduction to the Calculus of Variations and Control with Modern Applications

Author: John A. Burns

Publisher: CRC Press

ISBN: 1466571403

Category: Mathematics

Page: 562

View: 6433

Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions and discusses the importance of distinguishing between the necessary and sufficient conditions. In the first part of the text, the author develops the calculus of variations and provides complete proofs of the main results. He explains how the ideas behind the proofs are essential to the development of modern optimization and control theory. Focusing on optimal control problems, the second part shows how optimal control is a natural extension of the classical calculus of variations to more complex problems. By emphasizing the basic ideas and their mathematical development, this book gives you the foundation to use these mathematical tools to then tackle new problems. The text moves from simple to more complex problems, allowing you to see how the fundamental theory can be modified to address more difficult and advanced challenges. This approach helps you understand how to deal with future problems and applications in a realistic work environment.
Technology & Engineering

The Finite Element Method in Engineering

Author: Singiresu S. Rao

Publisher: Elsevier

ISBN: 9780080952048

Category: Technology & Engineering

Page: 726

View: 6299

The Finite Element Method in Engineering, Fifth Edition, provides a complete introduction to finite element methods with applications to solid mechanics, fluid mechanics, and heat transfer. Written by bestselling author S.S. Rao, this book provides students with a thorough grounding of the mathematical principles for setting up finite element solutions in civil, mechanical, and aerospace engineering applications. The new edition of this textbook includes examples using modern computer tools such as MatLab, Ansys, Nastran, and Abaqus. This book discusses a wide range of topics, including discretization of the domain; interpolation models; higher order and isoparametric elements; derivation of element matrices and vectors; assembly of element matrices and vectors and derivation of system equations; numerical solution of finite element equations; basic equations of fluid mechanics; inviscid and irrotational flows; solution of quasi-harmonic equations; and solutions of Helmhotz and Reynolds equations. New to this edition are examples and applications in Matlab, Ansys, and Abaqus; structured problem solving approach in all worked examples; and new discussions throughout, including the direct method of deriving finite element equations, use of strong and weak form formulations, complete treatment of dynamic analysis, and detailed analysis of heat transfer problems. All figures are revised and redrawn for clarity. This book will benefit professional engineers, practicing engineers learning finite element methods, and students in mechanical, structural, civil, and aerospace engineering. Examples and applications in Matlab, Ansys, and Abaqus Structured problem solving approach in all worked examples New discussions throughout, including the direct method of deriving finite element equations, use of strong and weak form formulations, complete treatment of dynamic analysis, and detailed analysis of heat transfer problems More examples and exercises All figures revised and redrawn for clarity

The Finite Element Method

An Introduction with Partial Differential Equations

Author: A. J. Davies

Publisher: Oxford University Press

ISBN: 0199609136

Category: Mathematics

Page: 297

View: 9968

An introduction to the application of the finite element method to the solution of boundary and initial-value problems posed in terms of partial differential equations. Contains worked examples throughout and each chapter has a set of exercises with detailed solutions.
Technology & Engineering

Mathematical Theory of Elasticity of Quasicrystals and Its Applications

Author: Tianyou Fan

Publisher: Springer Science & Business Media

ISBN: 3642146430

Category: Technology & Engineering

Page: 350

View: 7928

This inter-disciplinary work covering the continuum mechanics of novel materials, condensed matter physics and partial differential equations discusses the mathematical theory of elasticity of quasicrystals (a new condensed matter) and its applications by setting up new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions. The new theories developed here dramatically simplify the solving of complicated elasticity equation systems. Large numbers of complicated equations involving elasticity are reduced to a single or a few partial differential equations of higher order. Systematical and direct methods of mathematical physics and complex variable functions are developed to solve the equations under appropriate boundary value and initial value conditions, and many exact analytical solutions are constructed. The dynamic and non-linear analysis of deformation and fracture of quasicrystals in this volume presents an innovative approach. It gives a clear-cut, strict and systematic mathematical overview of the field. Comprehensive and detailed mathematical derivations guide readers through the work. By combining mathematical calculations and experimental data, theoretical analysis and practical applications, and analytical and numerical studies, readers will gain systematic, comprehensive and in-depth knowledge on continuum mechanics, condensed matter physics and applied mathematics.

Applications of Functional Analysis and Operator Theory

Author: V. Hutson,J. Pym,M. Cloud

Publisher: Elsevier

ISBN: 9780080527314

Category: Mathematics

Page: 432

View: 6365

Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces. Key Features - Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering. - Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results. - Introduces each new topic with a clear, concise explanation. - Includes numerous examples linking fundamental principles with applications. - Solidifies the reader’s understanding with numerous end-of-chapter problems. · Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering. · Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results. · Introduces each new topic with a clear, concise explanation. · Includes numerous examples linking fundamental principles with applications. · Solidifies the reader's understanding with numerous end-of-chapter problems.
Technology & Engineering

The Finite Element Method in Structural Mechanics

Principles and Practice of Design of Field-consistent Elements for Structural and Solid Mechanics

Author: Gangan Prathap

Publisher: Springer Science & Business Media

ISBN: 9401733198

Category: Technology & Engineering

Page: 414

View: 1946

This book is not intended to be a text-book, delineating the full scope of finite element methodology, nor is it a comprehensive handbook of modern finite element practice for the finite element engineer. There are enough books that serve to do these and more. It is however intended as a monograph or treatise on a very specific area - the design of robust and accurate elements for applications in struc tural mechanics. It attempts to describe the epistemological conflict between the principles in finite element technology that can be described as Art and those that have a scientific basis invested in it and which can be admitted as science as the subject evolved and came to be accepted. The principles of structural mechanics as a branch of physics are well founded and have a sound scientific basis. The mathematical description of it has also a long history and is rigorously based on the infinitesimal and variational calculus. Of much more recent origin has been the branch of knowledge dealing with the numerical modelling of the beha viour of structural material. The most powerful method available to do this today is the finite element method. It is eminently suited to carry out the entire cycle of design and analysis of a structural configuration on a digital computer.

Mechanics of Structures

Variational and Computational Methods

Author: Walter Wunderlich,Walter D. Pilkey

Publisher: CRC Press

ISBN: 1420041835

Category: Science

Page: 912

View: 4230

Resoundingly popular in its first edition, the second edition of Mechanics of Structures: Variational and Computational Methods promises to be even more so, with broader coverage, expanded discussions, and a streamlined presentation. The authors begin by describing the behavior of deformable solids through the differential equations for the strength of materials and the theory of elasticity. They next introduce variational principles, including mixed or generalized principles, and derive integral forms of the governing equations. Discussions then move to computational methods, including the finite element method, and these are developed to solve the differential and integral equations. New in the second edition: A one-dimensional introduction to the finite element method, complete with illustrations of numerical mesh refinement Expansion of the use of Galerkin's method. Discussion of recent developments in the theory of bending and torsion of thin-walled beams. An appendix summarizing the fundamental equations in differential and variational form Completely new treatment of stability, including detailed examples Discussion of the principal values of geometric properties and stresses Additional exercises As a textbook or as a reference, Mechanics of Structures builds a unified, variational foundation for structure mechanics, which in turn forms the basis for the computational solid mechanics so essential to modern engineering.
Technology & Engineering

Analysis of Aircraft Structures

An Introduction

Author: Bruce K. Donaldson

Publisher: Cambridge University Press

ISBN: 0521865832

Category: Technology & Engineering

Page: 932

View: 7685

As with the first edition, this textbook provides a clear introduction to the fundamental theory of structural analysis as applied to vehicular structures such as aircraft, spacecraft, automobiles and ships. The emphasis is on the application of fundamental concepts of structural analysis that are employed in everyday engineering practice. All approximations are accompanied by a full explanation of their validity. In this new edition, more topics, figures, examples and exercises have been added. There is also a greater emphasis on the finite element method of analysis. Clarity remains the hallmark of this text and it employs three strategies to achieve clarity of presentation: essential introductory topics are covered, all approximations are fully explained and many important concepts are repeated.

Methods of Applied Mathematics with a MATLAB Overview

Author: Jon H. Davis

Publisher: Springer Science & Business Media

ISBN: 9780817643317

Category: Mathematics

Page: 721

View: 6539

This text is broadly organized around the theme of applications of Fourier analysis. The treatment covers both classical applications in partial differential equations and boundary value problems and a number of topics associated with Laplace, Fourier and discrete transformation theories.
Technology & Engineering

Mechanics of Structural Elements

Theory and Applications

Author: Vladimir Slivker

Publisher: Springer Science & Business Media

ISBN: 3540447210

Category: Technology & Engineering

Page: 787

View: 9422

The book systematically presents variational principles and methods of analysis for applied elasticity and structural mechanics. The variational approach is used consistently for both, constructing numerical procedures and deriving basic governing equations of applied mechanics of solids; it is the derivation of equations where this approach is most powerful and best grounded by mathematics.
Technology & Engineering

Computational Analysis and Design of Bridge Structures

Author: Chung C. Fu,Shuqing Wang

Publisher: CRC Press

ISBN: 1466579854

Category: Technology & Engineering

Page: 631

View: 5289

Gain Confidence in Modeling Techniques Used for Complicated Bridge Structures Bridge structures vary considerably in form, size, complexity, and importance. The methods for their computational analysis and design range from approximate to refined analyses, and rapidly improving computer technology has made the more refined and complex methods of analyses more commonplace. The key methods of analysis and related modeling techniques are set out, mainly for highway bridges, but also with some information on railway bridges. Special topics such as strut-and-tie modeling, linear and nonlinear buckling analysis, redundancy analysis, integral bridges, dynamic/earthquake analysis, and bridge geometry are also covered. The material is largely code independent. The book is written for students, especially at MSc level, and for practicing professionals in bridge design offices and bridge design authorities worldwide. Effectively Analyze Structures Using Simple Mathematical Models Divided into three parts and comprised of 18 chapters, this text: Covers the methods of computational analysis and design suitable for bridge structures Provides information on the methods of analysis and related modeling techniques suitable for the design and evaluation of various types of bridges Presents material on a wide range of bridge structural types and is fairly code independent Computational Analysis and Design of Bridge Structures covers the general aspects of bridges, bridge behavior and the modeling of bridges, and special topics on bridges. This text explores the physical meanings behind modeling, and reveals how bridge structures can be analyzed using mathematical models.
Technology & Engineering

Finite Elements for Analysis and Design

Computational Mathematics and Applications Series

Author: J. E. Akin

Publisher: Elsevier

ISBN: 008050647X

Category: Technology & Engineering

Page: 560

View: 9425

The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material. Akin clearly explains the FEM, a numerical analysis tool for problem-solving throughout applied mathematics, engineering and scientific computing Basic theory has been added in the book, including worked examples to enable students to understand the concepts Contains coverage of computational topics, including worked examples to enable students to understand concepts Improved coverage of sensitivity analysis and computational fluid dynamics Uses example applications to increase students' understanding Includes a disk with the FORTRAN source for the programs cided in the text
Technology & Engineering

Finite Elements in Fracture Mechanics

Theory - Numerics - Applications

Author: Meinhard Kuna

Publisher: Springer Science & Business Media

ISBN: 9400766807

Category: Technology & Engineering

Page: 447

View: 6041

Fracture mechanics has established itself as an important discipline of growing interest to those working to assess the safety, reliability and service life of engineering structures and materials. In order to calculate the loading situation at cracks and defects, nowadays numerical techniques like finite element method (FEM) have become indispensable tools for a broad range of applications. The present monograph provides an introduction to the essential concepts of fracture mechanics, its main goal being to procure the special techniques for FEM analysis of crack problems, which have to date only been mastered by experts. All kinds of static, dynamic and fatigue fracture problems are treated in two- and three-dimensional elastic and plastic structural components. The usage of the various solution techniques is demonstrated by means of sample problems selected from practical engineering case studies. The primary target group includes graduate students, researchers in academia and engineers in practice.

Modern Computational Methods

Author: Herbert Koenig

Publisher: CRC Press

ISBN: 9781560324683

Category: Mathematics

Page: 416

View: 1686

This book is an introduction to computational mechanics, proceeding from basic computational tools to advanced computational procedures and applications. Emphasis is placed on the numerical techniques and how they form the bases for algorithms. Numerous worked examples in structural mechanics, heat transfer, fluid flow, and biomechanics are given with the numerical codes to illustrate how the methods are applied. A concluding section addresses advanced applications in such areas as finite volume methods and biomechanics.

Numerical Methods in Electromagnetism

Author: M. V. K. Chari,Sheppard Joel Salon

Publisher: Academic Press

ISBN: 9780126157604

Category: Mathematics

Page: 767

View: 7083

Electromagnetics is the foundation of our electric technology. It describes the fundamental principles upon which electricity is generated and used. This includes electric machines, high voltage transmission, telecommunication, radar, and recording and digital computing. This book will serve both as an introductory text for graduate students and as a reference book for professional engineers and researchers. This book leads the uninitiated into the realm of numerical methods for solving electromagnetic field problems by examples and illustrations. Detailed descriptions of advanced techniques are also included for the benefit of working engineers and research students. * Comprehensive descriptions of numerical methods * In-depth introduction to finite differences, finite elements, and integral equations * Illustrations and applications of linear and nonlinear solutions for multi-dimensional analysis * Numerical examples to facilitate understanding of the methods * Appendices for quick reference of mathematical and numerical methods employed

Principles of Differential Equations

Author: Nelson G. Markley

Publisher: John Wiley & Sons

ISBN: 1118031539

Category: Mathematics

Page: 352

View: 8887

An accessible, practical introduction to the principles ofdifferential equations The field of differential equations is a keystone of scientificknowledge today, with broad applications in mathematics,engineering, physics, and other scientific fields. Encompassingboth basic concepts and advanced results, Principles ofDifferential Equations is the definitive, hands-on introductionprofessionals and students need in order to gain a strong knowledgebase applicable to the many different subfields of differentialequations and dynamical systems. Nelson Markley includes essential background from analysis andlinear algebra, in a unified approach to ordinary differentialequations that underscores how key theoretical ingredientsinterconnect. Opening with basic existence and uniqueness results,Principles of Differential Equations systematically illuminates thetheory, progressing through linear systems to stable manifolds andbifurcation theory. Other vital topics covered include: Basic dynamical systems concepts Constant coefficients Stability The Poincaré return map Smooth vector fields As a comprehensive resource with complete proofs and more than200 exercises, Principles of Differential Equations is the idealself-study reference for professionals, and an effectiveintroduction and tutorial for students.

Variational, Incremental and Energy Methods in Solid Mechanics and Shell Theory

Author: J. Mason

Publisher: Elsevier

ISBN: 1483289648

Category: Mathematics

Page: 383

View: 3891

Studies in Applied Mechanics, 4: Variational, Incremental, and Energy Methods in Solid Mechanics and Shell Theory covers the subject of variational, incremental, and energy methods in Solid Mechanics and Shell Theory from a general standpoint, employing general coordinates and tensor notations. The publication first ponders on mathematical preliminaries, kinematics and stress in three-dimensional solid continua, and the first and second laws of thermodynamics. Discussions focus on the principles of virtual displacements and virtual forces, kinematics of rigid body motions, incremental stresses, kinematics of incremental deformation, description of motion, coordinates, reference and deformed states, tensor formulas for surfaces, and differentials and derivatives of operators. The text then elaborates on constitutive material laws, deformation and stress in shells, first law of thermodynamics applied to shells, and constitutive relations and material laws for shells. Concerns cover hyperelastic incremental material relations, material laws for thin elastic shells, incremental theory and stability, reduced and local forms of the first law of thermodynamics, and description of deformation and motion in shells. The book examines elastic stability, finite element models, variational and incremental principles, variational principles of elasticity and shell theory, and constitutive relations and material laws for shells. The publication is a valuable reference for researchers interested in the variational, incremental, and energy methods in solid mechanics and shell theory.