Introduction To Finite Elements In Engineering (international Edition)

By (author) Chandrupatla, Tirupathi R.; By (author) Belegundu, Ashok D.
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 4th Edition has been updated and improved to include new material on additional topics.
Table of contents
PREFACE XIII ABOUT THE AUTHOR XVI   1 FUNDAMENTAL CONCEPTS 1 1.1 Introduction 1 1.2 Historical Background 1 1.3 Outline of Presentation 2 1.4 Stresses and Equilibrium 2 1.5 Boundary Conditions 4 1.6 Strain—Displacement Relations 5 1.7 Stress—Strain Relations 6 Special Cases, 7 1.8 Temperature Effects 8 1.9 Potential Energy and Equilibrium: The Rayleigh—Ritz Method 9 Potential Energy ß , 9 Rayleigh—Ritz Method, 12 1.10 Galerkin’s Method 14 1.11 Saint Venant’s Principle 18 1.12 Von Mises Stress 19 1.13 Principle of Superposition 19 1.14 Computer Programs 20 1.15 Conclusion 20 Historical References 20 Problems 21   2 MATRIX ALGEBRA AND GAUSSIAN ELIMINATION 28 2.1 Matrix Algebra 28 Row and Column Vectors, 29 Addition and Subtraction, 29 Multiplication by a Scalar, 29 Matrix Multiplication, 29 Transposition, 30 Differentiation and Integration, 30 Square Matrix, 31 Diagonal Matrix, 31 Identity Matrix, 31 Symmetric Matrix, 32 Upper Triangular Matrix, 32 Determinant of a Matrix, 32 Matrix Inversion, 32 Eigenvalues and Eigenvectors, 33 Positive Definite Matrix, 35 Cholesky Decomposition, 35 2.2 Gaussian Elimination 35 General Algorithm for Gaussian Elimination, 37 Symmetric Matrix, 40 Symmetric Banded Matrices, 40 Solution with Multiple Right Sides, 40 Gaussian Elimination with Column Reduction, 42 Skyline Solution, 44 Frontal Solution, 45 2.3 Conjugate Gradient Method for Equation Solving 45 Conjugate Gradient Algorithm, 46 Input Data/Output 46 Problems 47 Program Listings, 49   3 ONE-DIMENSIONAL PROBLEMS 51 3.1 Introduction 51 3.2 Finite Element Modeling 52 Element Division, 52 Numbering Scheme, 53 3.3 Shape Functions and Local Coordinates 55 3.4 The Potential-Energy Approach 59 Element Stiffness Matrix, 60 Force Terms, 62 3.5 The Galerkin Approach 64 Element Stiffness, 64 Force Terms, 65 3.6 Assembly of the Global Stiffness Matrix and Load Vector 66 3.7 Properties of K 69 3.8 The Finite Element Equations: Treatment of Boundary Conditions 70 Types of Boundary Conditions, 70 Elimination Approach, 71 Penalty Approach, 76 Multipoint Constraints, 82 3.9 Quadratic Shape Functions 85 3.10 Temperature Effects 92 3.11 Problem Modeling and Boundary Conditions 96 Problem in Equilibrium, 96 Symmetry, 97 Two Elements with Same End Displacements, 97 Problem with a Closing Gap, 98 Input Data/Output, 98 Problems 99 Program Listing, 111   4 TRUSSES 117 4.1 Introduction 117 4.2 Plane Trusses 118 Local and Global Coordinate Systems, 118 Formulas for Calculating / and m, 119 Element Stiffness Matrix, 120 Stress Calculations, 121 Temperature Effects, 126 4.3 Three-Dimensional Trusses 129 4.4 Assembly of Global Stiffness Matrix for the Banded and Skyline Solutions 131 Assembly for Banded Solution, 131 Skyline Assembly , 132 4.5 Problem Modeling and Boundary Conditions 134 Inclined Support in Two Dimensions, 134 Inclined Support in Three Dimensions–Line Constraint, 134 Inclined Support in Three Dimensions–Plane Constraint, 135 Symmetry and Antisymmetry , 136 Input Data/Output, 138 Problems 139 Program Listing, 147