Introduction to Finite Elements in Engineering

International Edition

Häftad, Engelska, 2012

Av Tirupathi Chandrupatla, Ashok Belegundu

1 429 kr

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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 4th Edition has been updated and improved to include new material on additional topics.

Produktinformation

Utgivningsdatum2012-01-13
Mått180 x 230 x 24 mm
Vikt720 g
FormatHäftad
SpråkEngelska
Upplaga4
FörlagPearson Education Limited
ISBN9780273763680

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PREFACE XIIIABOUT THE AUTHOR XVI 1 FUNDAMENTAL CONCEPTS 1 1.1 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 21 2 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, 49 3 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, 111 4 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, 147 5 BEAMS AND FRAMES 1505.1 Introduction