This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. 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.

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Principle 18 1.12 Von Mises Stress 19 1.13 Principle of Superposition 19 1.14 Computer Programs 20 1.15 Conclusion 20 Historical References 20 Problems 21   2 MATRIX ALGEBRA AND GAUSSIAN ELIMINATION 28 2.1 Matrix Algebra 28 Row and Column Vectors, 29 Addition and Subtraction, 29 Multiplication by a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   5 BEAMS AND FRAMES 150 5.1 Introduction 150 Potential-Energy Approach, 151 Galerkin Approach, 152 5.2 Finite Element Formulation 153 Element Stiffness–Direct Approach, 157 5.3 Load Vector 158 5.4 Boundary Considerations 159 5.5 Shear Force and Bending Moment 160 5.6 Beams on Elastic Supports 162 5.7 Plane Frames 163 5.8 Three-Dimensional Frames 169 5.9 Problem Modeling and Boundary Conditions 173 5.10 Some Comments 174 Input Data/Output, 174 Problems 176 Program Listings, 183   6 TWO-DIMENSIONAL PROBLEMS USING CONSTANT STRAIN TRIANGLES 188 6.1 Introduction 188 6.2 Finite Element Modeling 189 6.3 Constant Strain Triangle (CST) 191 Isoparametric Representation, 192 Potential-Energy Approach, 198 Element Stiffness, 198 Force Terms, 199 Integration Formula on a Triangle, 206 Galerkin Approach, 206 Stress Calculations, 208 Temperature Effects, 210 6.4 Problem Modeling and Boundary Conditions 212 Some General Comments on Dividing into Elements, 215 6.5 Patch Test and Convergence 215 Patch Test, 215 6.6 Orthotropic Materials 216 Temperature Effects, 220 Input Data/Output, 222 Problems 225 Program Listing, 238   7 AXISYMMETRIC SOLIDS SUBJECTED TO AXISYMMETRIC LOADING 242 7.1 Introduction 242 7.2 Axisymmetric Formulation 243 7.3 Finite Element Modeling: Triangular Element 245 Potential-Energy Approach, 248 Body Force Term, 249 Rotating Flywheel, 249 Surface Traction, 250 Galerkin Approach, 252 Stress Calculations, 255 Temperature Effects, 256 7.4 Problem Modeling and Boundary Conditions 256 Cylinder Subjected to Internal Pressure, 256 Infinite Cylinder, 257 Press Fit on a Rigid Shaft, 257 Press Fit on an Elastic Shaft, 258 Belleville Spring, 259 Thermal Stress Problem, 260 Input Data/Output, 262 Problems 263 Program Listing, 271   8 TWO-DIMENSIONAL ISOPARAMETRIC ELEMENTS AND NUMERICAL INTEGRATION 273 8.1 Introduction 273 8.2 The Four-Node Quadrilateral 273 Shape Functions, 273 Element Stiffness Matrix, 276 Element Force Vectors, 279 8.3 Numerical Integration 279 Two-Dimensional Integrals, 283 Stiffness Integration, 283 Stress Calculations, 284 8.4 Higher Order Elements 286 Nine-Node Quadrilateral, 287 Eight-Node Quadrilateral, 289 Six-Node Triangle, 290 Integration on a Triangle–Symmetric Points, 291 Integration on a Triangle–Degenerate Quadrilateral, 292 8.5 Four-Node Quadrilateral for Axisymmetric Problems 294 8.6 Conjugate Gradient Implementation of the Quadrilateral Element 295 8.7 Concluding Remarks and Convergence 295 8.8 References for Convergence 297 Input Data/Output, 298 Problems 300 Program Listings, 308   9 THREE-DIMENSIONAL PROBLEMS IN STRESS ANALYSIS 312 9.1 Introduction 312 9.2 Finite Element Formulation 313 Element Stiffness, 316 Force Terms, 317 9.3 Stress Calculations 317 9.4 Mesh Preparation 318 9.5 Hexahedral Elements and Higher Order Elements 322 9.6 Problem Modeling 324 9.7 Frontal Method for Finite Element Matrices 326 Connectivity and Prefront Routine, 327 Element Assembly and Consideration of Specified dof, 328 Elimination of Completed dof, 328 Backsubstitution, 329 Consideration of Multipoint Constraints, 329 Input Data/Output, 330 Problems 332 Program Listings, 336   10 SCALAR FIELD PROBLEMS 345 10.1 Introduction 345 10.2 Steady State Heat Transfer 346 One-Dimensional Heat Conduction, 347 One-Dimensional Heat Transfer in Thin Fins, 355 Two-Dimensional Steady-State Heat Conduction, 359 Two-Dimensional Fins, 369 Preprocessing for Program Heat2D, 370 10.3 Torsion 370 Triangular Element, 372 Galerkin Approach, 373 10.4 Potential Flow, Seepage, Electric and Magnetic Fields, and Fluid Flow in Ducts 376 Potential Flow, 376 Seepage, 378 Electrical and Magnetic Field Problems, 379 Fluid Flow in Ducts, 381 Acoustics, 383 Boundary Conditions, 384 One-Dimensional Acoustics, 384 One-Dimensional Axial Vibrations, 386 Two-Dimensional Acoustics, 388 10.5 Conclusion 389 Input Data/Output, 389 Problems 391 Program Listings, 402   11 DYNAMIC CONSIDERATIONS 408 11.1 Introduction 408 11.2 Formulation 408 Solid Body with Distributed Mass, 409 11.3 Element Mass Matrices 411 11.4 Evaluation of Eigenvalues and Eigenvectors 416 Properties of Eigenvectors, 417 Eigenvalue—Eigenvector Evaluation, 417 Inverse Iteration Method , 420 Generalized Jacobi Method, 423 Tridiagonalization and Implicit Shift Approach, 427 Bringing Generalized Problem to Standard Form, 427 Tridiagonalization, 428 Implicit Symmetric QR Step with Wilkinson Shift for Diagonalization, 431 11.5 Interfacing with Previous Finite Element Programs and a Program for Determining Critical Speeds of Shafts 432 11.6 Guyan Reduction 433 11.7 Rigid Body Modes 436 11.8 Conclusion 438 Input Data/Output, 438 Problems 440 Program Listings, 446   12 PREPROCESSING AND POSTPROCESSING 453 12.1 Introduction 453 12.2 Mesh Generation 453 Region and Block Representation, 453 Block Corner Nodes, Sides, and Subdivisions, 454 12.3 Postprocessing 461 Deformed Configuration and Mode Shape, 461 Contour Plotting, 462 Nodal Values from Known Constant Element Values for a Triangle, 463 Least-Squares Fit for a Four-Noded Quadrilateral, 465 12.4 Conclusion 466 Input Data/Output, 467 Problems 468 Program Listings, 470   APPENDIX 483 BIBLIOGRAPHY 486 ANSWERS TO SELECTED PROBLEMS 490 INDEX 492