An Introduction to Linear and Nonlinear Finite Element Analysis : A Computational Approach / by Prem K. Kythe, Dongming Wei
| データ種別 | 電子ブック |
|---|---|
| 出版情報 | Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser , 2004 |
| 本文言語 | 英語 |
| 大きさ | XXIII, 445 p : online resource |
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| 内容注記 | Preface Notation 1 Introduction 1.1 Historical Sketch 1.2 Euler-Lagrange Equations 1.3 Weak Variational Form 1.4 Galerkin Method 1.5 1.6 2 One-Dimensional Shape Functions 2.1 Local and Global Linear Shape Functions 2.2 Local and Global Quadratic Shape Functions 2.3 Parametric Coordinates 2.4 Hermite Shape Functions 2.5 Exercises 3 One-Dimensional Second-Order Equation 3.1 Galerkin Finite Element Method 3.2 Two Dependent Variables 3.3 Exercises 4 One-Dimensional Fourth-Order Equation 4.1 Euler-Bernoulli Beam Equation 4.2 Exercises 5 Two-Dimensional Elements 5.1 Linear Three-Node Triangular Elements 5.2 Bilinear Four-Node Rectangular Elements 5.3 Global Shape Functions 5.4 Triangular Coordinates 5.5 Shape Functions on the Sides of a Triangle 5.6 Exercises 6 Two-Dimensional Problems 6.1 Single Dependent Variable Problems 6.2 Exercises 7 More Two-Dimensional Problems 7.1 Heat Transfer 7.2 Torsion 7.3 Seepage 7.4 Fluid Flows 7.5 Exercises 8 Axisymmetric Heat Transfer 8.1 Radial Symmetry 8.2 Linear Elements 8.3 Linear Elements for Heat Transfer in Fluids 8.4 Nonlinear Heat Transfer 8.5 Exercises 9 Transient Problems 9.1 Classical Methods 9.2 One-Dimensional Transient Problems 9.3 Time-Dependent Heat Conduction 9.4 Two-Dimensional Transient Problems 9.5 Exercises 10 Single Nonlinear One-Dimensional Problems 10.1 Newton’ method 10.2 Radiation Heat Transfer 10.3 Stress Analysis of Plastic Rods 10.4 Power-Law Pressure Driven Flow between Two Plates 10.5 Mixing-Length Equation for Turbulent Flow in Pipes 10.6 Rayleigh-Ritz and Nonlinear Gradient Methods 10.7 Exercises 11 Plane Elasticity 11.1 Stress-Strain Relations 11.2 Constant-Strain Triangular Element 11.3 Virtual Displacement Finite Element Model 11.4 Weak Form Finite Element Model 11.5 Stiffness Matrix and Load Vector 11.6 Exercises 12 Stokes Equations and Penalty Method 12.1 Equality-Constrained Programs and Lagrange Multipliers 12.2 Penalty Formulation for Linear Stokes Equation 12.3 Penalty Linear Triangular Stokes Element 12.4 Penalty Bilinear Rectangular Stokes Element 12.5 Penalty Linear Triangular Power-law Stokes Element 12.6 Solutions by Conjugate Gradient Methods 12.7 Exercises 13 Vibration Analysis 13.1 Hamiltonian Principle 13.2 Free Axial Vibrations of an Elastic Rod 13.3 Free Vibrations of a Euler Elastic Beam 13.4 Free In-Plane Vibrations of an Elastic Plate 13.5 Axial Vibrations of a Plastic Rod 13.6 Eigenvalue Problems 13.7 Exercises 14 Computer Codes 14.1 Mathematica Codes 14.2 Ansys Codes 14.3 Matlab Codes 14.4 Fortran Codes Integration Formulas A Special Cases B Temporal Approximations C Isoparametric Elements D Green’ Identities E Gaussian Quadrature F Gradient-Based Methods |
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| 一般注記 | Although finite element courses have become more popular in the undergraduate and graduate engineering, science, and applied mathematics curricula, there are very few introductory textbooks geared toward students accustomed to using computers for everyday assignments and research. 'An Introduction to Linear and Nonlinear Finite Element Analysis' fills this gap, offering a concise, integrated presentation of methods, applications, computational software tools, and hands-on programming projects. Suitable for junior/senior undergraduate and first-year graduate courses, the book is aimed at students from a variety of disciplines: engineering, physics, geophysics, and applied mathematics. Unlike existing texts designed with specific applications to a particular field of mechanical, civil, or chemical engineering, the emphasis here is on interdisciplinary applications. One- and two-dimensional linear and nonlinear initial/boundary value problems are solved using finite element, Newton's, and conjugate gradient methods. Mathematical theory is kept to a minimum, making the text accessible to students with varied backgrounds. Features: * Software tools using Mathematica, Matlab, Fortran, and commercial finite element codes, such as Ansys, integrated throughout the text * Numerous examples and exercises with diverse applications to linear and nonlinear heat transfer, fluid flows, mechanical vibrations, electromagnetics, and structures * Supporting material and selected solutions to problems available at the authors' websites: http://www.math.uno.edu/fac/pkythe.html and http://www.math.uno.edu/fac/dwei.html * Minimal prerequisites: a course in calculus of several variables, differential equations and linear algebra, as well as some knowledge of computers Primarily a classroom resource, the book may also be used as a self-study reference for researchers and practitioners who need a quick introduction to finite element methods. P> |
| 著者標目 | *Kythe, Prem K. author Wei, Dongming author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Partial differential equations LCSH:Applied mathematics LCSH:Engineering mathematics LCSH:Computer mathematics LCSH:Physics LCSH:Engineering FREE:Mathematics FREE:Applications of Mathematics FREE:Computational Mathematics and Numerical Analysis FREE:Partial Differential Equations FREE:Theoretical, Mathematical and Computational Physics FREE:Appl.Mathematics/Computational Methods of Engineering FREE:Engineering, general |
| 分 類 | DC23:519 |
| 巻冊次 | ISBN:9780817681609 
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| ISBN | 9780817681609 |
| URL | http://dx.doi.org/10.1007/978-0-8176-8160-9 |
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※2021年9月12日以降