- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
Introduction to Finite Engineering is ideal for senior undergraduate and first-year graduate students and also as a learning resource to practicing engineers. This book provides an integrated approach to finite element methodologies. The development of finite element theory is combined with examples and exercises involving engineering applications. The steps used in the development of the theory are implemented in complete, self-contained computer programs. While the strategy and philosophy of the previous editions has been retained, the?Fourth Edition has been updated and improved to include new material on additional topics.
Contents
PREFACE XIIIABOUT THE AUTHOR XVI1 FUNDAMENTAL CONCEPTS 11.1 Introduction 11.2 Historical Background 11.3 Outline of Presentation 21.4 Stresses and Equilibrium 21.5 Boundary Conditions 41.6 Strain-Displacement Relations 51.7 Stress-Strain Relations 6Special Cases, 71.8 Temperature Effects 81.9 Potential Energy and Equilibrium: The Rayleigh-Ritz Method 9Potential Energy ss , 9Rayleigh-Ritz Method, 121.10 Galerkin's Method 141.11 Saint Venant's Principle 181.12 Von Mises Stress 191.13 Principle of Superposition 191.14 Computer Programs 201.15 Conclusion 20Historical References 20Problems 212 MATRIX ALGEBRA AND GAUSSIAN ELIMINATION 282.1 Matrix Algebra 28Row and Column Vectors, 29Addition and Subtraction, 29Multiplication by a Scalar, 29Matrix Multiplication, 29Transposition, 30Differentiation and Integration, 30Square Matrix, 31Diagonal Matrix, 31Identity Matrix, 31Symmetric Matrix, 32Upper Triangular Matrix, 32Determinant of a Matrix, 32Matrix Inversion, 32Eigenvalues and Eigenvectors, 33Positive Definite Matrix, 35Cholesky Decomposition, 352.2 Gaussian Elimination 35General Algorithm for Gaussian Elimination, 37Symmetric Matrix, 40Symmetric Banded Matrices, 40Solution with Multiple Right Sides, 40Gaussian Elimination with Column Reduction, 42Skyline Solution, 44Frontal Solution, 452.3 Conjugate Gradient Method for Equation Solving 45Conjugate Gradient Algorithm, 46Input Data/Output 46Problems 47Program Listings, 493 ONE-DIMENSIONAL PROBLEMS 513.1 Introduction 513.2 Finite Element Modeling 52Element Division, 52Numbering Scheme, 533.3 Shape Functions and Local Coordinates 553.4 The Potential-Energy Approach 59Element Stiffness Matrix, 60Force Terms, 623.5 The Galerkin Approach 64Element Stiffness, 64Force Terms, 653.6 Assembly of the Global Stiffness Matrix and Load Vector 663.7 Properties of K 693.8 The Finite Element Equations: Treatmentof Boundary Conditions 70Types of Boundary Conditions, 70Elimination Approach, 71Penalty Approach, 76Multipoint Constraints, 823.9 Quadratic Shape Functions 853.10 Temperature Effects 923.11 Problem Modeling and Boundary Conditions 96Problem in Equilibrium, 96Symmetry, 97Two Elements with Same End Displacements, 97Problem with a Closing Gap, 98Input Data/Output, 98Problems 99Program Listing, 1114 TRUSSES 1174.1 Introduction 1174.2 Plane Trusses 118Local and Global Coordinate Systems, 118Formulas for Calculating / and m, 119Element Stiffness Matrix, 120Stress Calculations, 121Temperature Effects, 1264.3 Three-Dimensional Trusses 1294.4 Assembly of Global Stiffness Matrix for the Banded and SkylineSolutions 131Assembly for Banded Solution, 131Skyline Assembly , 1324.5 Problem Modeling and Boundary Conditions 134Inclined Support in Two Dimensions, 134Inclined Support in Three Dimensions-Line Constraint, 134Inclined Support in Three Dimensions-Plane Constraint, 135Symmetry and Antisymmetry , 136Input Data/Output, 138Problems 139Program Listing, 1475 BEAMS AND FRAMES 1505.1 Introduction 150Potential-Energy Approach, 151Galerkin Approach, 1525.2 Finite Element Formulation 153Element Stiffness-Direct Approach, 1575.3 Load Vector 1585.4 Boundary Considerations 1595.5 Shear Force and Bending Moment 1605.6 Beams on Elastic Supports 1625.7 Plane Frames 1635.8 Three-Dimensional Frames 1695.9 Problem Modeling and Boundary Conditions 1735.10 Some Comments 174Input Data/Output, 174Problems 176Program Listings, 1836 TWO-DIMENSIONAL PROBLEMS USING CONSTANT STRAIN TRIANGLES 1886.1 Introduction 1886.2 Finite Element Modeling 1896.3 Constant Strain Triangle (CST) 191Isoparametric Representation, 192Potential-Energy Approach, 198Element Stiffness, 198Force Terms, 199Integration Formula on a Triangle, 206Galerkin Approach, 206Stress Calculations, 208Temperature Effects, 2106.4 Problem Modeling and Boundary Conditions 212Some General Comments on Dividing into Elements, 2156.5 Patch Test and Convergence 215Patch Test, 2156.6 Orthotropic Materials 216Temperature Effects, 220Input Data/Output, 222Problems 225Program Listing, 2387.1 Introduction 2427.2 Axisymmetric Formulation 2437.3 Finite Element Modeling: Triangular Element 245Potential-Energy Approach, 248Body Force Term, 249Rotating Flywheel, 249Surface Traction, 250Galerkin Approach, 252Stress Calculations, 255Temperature Effects, 2567.4 Problem Modeling and Boundary Conditions 256Cylinder Subjected to Internal Pressure, 256Infinite Cylinder, 257Press Fit on a Rigid Shaft, 257Press Fit on an Elastic Shaft, 258Belleville Spring, 259Thermal Stress Problem, 260Input Data/Output, 262Problems 263Program Listing, 2718 TWO-DIMENSIONAL ISOPARAMETRIC ELEMENTSAND NUMERICAL INTEGRATION 2738.1 Introduction 2738.2 The Four-Node Quadrilateral 273Shape Functions, 273Element Stiffness Matrix, 276Element Force Vectors, 2798.3 Numerical Integration 279Two-Dimensional Integrals, 283Stiffness Integration, 283Stress Calculations, 2848.4 Higher Order Elements 286Nine-Node Quadrilateral, 287Eight-Node Quadrilateral, 289Six-Node Triangle, 290Integration on a Triangle-Symmetric Points, 291Integration on a Triangle-Degenerate Quadrilateral, 2928.5 Four-Node Quadrilateral for Axisymmetric Problems 2948.6 Conjugate Gradient Implementation of the Quadrilateral Element 2958.7 Concluding Remarks and Convergence 2958.8 References for Convergence 297Input Data/Output, 298Problems 300Program Listings, 3089.1 Introduction 3129.2 Finite Element Formulation 313Element Stiffness, 316Force Terms, 3179.3 Stress Calculations 3179.4 Mesh Preparation 3189.5 Hexahedral Elements and Higher Order Elements 3229.6 Problem Modeling 3249.7 Frontal Method for Finite Element Matrices 326Connectivity and Prefront Routine, 327Element Assembly and Consideration of Specified dof, 328Elimination of Completed dof, 328Backsubstitution, 329Consideration of Multipoint Constraints, 329Input Data/Output, 330Problems 332Program Listings, 33610 SCALAR FIELD PROBLEMS 34510.1 Introduction 34510.2 Steady State Heat Transfer 346One-Dimensional Heat Conduction, 347One-Dimensional Heat Transfer in Thin Fins, 355Two-Dimensional Steady-State Heat Conduction, 359Two-Dimensional Fins, 369Preprocessing for Program Heat2D, 37010.3 Torsion 370Triangular Element, 372Galerkin Approach, 37310.4 Potential Flow, Seepage, Electric and Magnetic Fields,and Fluid Flow in Ducts 376Potential Flow, 376Seepage, 378Electrical and Magnetic Field Problems, 379Fluid Flow in Ducts, 381Acoustics, 383Boundary Conditions, 384One-Dimensional Acoustics, 384One-Dimensional Axial Vibrations, 386Two-Dimensional Acoustics, 38810.5 Conclusion 389Input Data/Output, 389Problems 391Program Listings, 40211 DYNAMIC CONSIDERATIONS 40811.1 Introduction 40811.2 Formulation 408Solid Body with Distributed Mass, 40911.3 Element Mass Matrices 41111.4 Evaluation of Eigenvalues and Eigenvectors 416Properties of Eigenvectors, 417Eigenvalue-Eigenvector Evaluation, 417Inverse Iteration Method , 420Generalized Jacobi Method, 423Tridiagonalization and Implicit Shift Approach, 427Bringing Generalized Problem to Standard Form, 427Tridiagonalization, 428Implicit Symmetric QR Step with Wilkinson Shiftfor Diagonalization, 43111.5 Interfacing with Previous Finite Element Programs and a Programfor Determining Critical Speeds of Shafts 43211.6 Guyan Reduction 43311.7 Rigid Body Modes 43611.8 Conclusion 438Input Data/Output, 438Problems 440Program Listings, 44612 PREPROCESSING AND POSTPROCESSING 45312.1 Introduction 45312.2 Mesh Generation 453Region and Block Representation, 453Block Corner Nodes, Sides, and Subdivisions, 45412.3 Postprocessing 461Deformed Configuration and Mode Shape, 461Contour Plotting, 462Nodal Values from Known Constant Element Valuesfor a Triangle, 463Least-Squares Fit for a Four-Noded Quadrilateral, 46512.4 Conclusion 466Input Data/Output, 467Problems 468Program Listings, 470APPENDIX 483BIBLIOGRAPHY 486INDEX 492
