Published by Pearson (September 10, 2014) © 2015
Tirupathi Chandrupatla | Ashok BelegunduIntroduction 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.
The full text downloaded to your computer
With eBooks you can:
- search for key concepts, words and phrases
- make highlights and notes as you study
- share your notes with friends
eBooks are downloaded to your computer and accessible either offline through the Bookshelf (available as a free download), available online and also via the iPad and Android apps.
Upon purchase, you'll gain instant access to this eBook.
Time limit
The eBooks products do not have an expiry date. You will continue to access your digital ebook products whilst you have your Bookshelf installed.
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Historical References 20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
5 BEAMS AND FRAMES 150
5.1 Introduction