Introduction to Finite Elements in Engineering [With Access Code]

This work provides an integrated approach to finite element methodologies, combining sound theory, examples and exercises involving engineering applications and the implementation of theory in complete, self-contained computer programs. This edition introduces new material on many topics, including frontal method, conjugate gradient method, orthotropic materials, Guyan reduction, three dimensional frames, least squares fit for quadrilateral element, two dimensional fins and von Mises stress. It prepares BASIC programs to work efficiently in the QBASIC environment available on DOS 5.0 or higher, and provides FORTRAN and C versions of all programs in a separate directory for easy access. All programs have been revised to work with file input, and new programs introduced that deal with multipoint constraints involving two variables. The book also introduces temperature effect in 1D, 2D, and 3D deformation and stress analysis programs, as well as frontal method in the hexahedral element for 3D analysis in HEXAFNT. The DATAFEM program has been revised to simplify data entry, and colour contour lines are now available in the CONTOUR1 program as well as contour bands in CONTOUR2. Cover......Page 1 PREFACE......Page 14 ABOUT THE AUTHORS......Page 17 Contents......Page 6 1.2 Historical Background......Page 18 1.4 Stresses and Equilibrium......Page 19 1.5 Boundary Conditions......Page 21 1.6 Strain-Displacement Relations......Page 22 1.7 Stress-Strain Relations......Page 23 Special Cases......Page 24 1.8 Temperature Effects......Page 25 Potential Energy,∏......Page 26 Rayleigh-Ritz Method......Page 29 1.10 Galerkin's Method......Page 31 1.11 Saint Venant's Principle......Page 35 1.13 Principle of Superposition......Page 36 Historical References......Page 37 Problems......Page 38 2.1 Matrix Algebra......Page 45 Matrix Multiplication......Page 46 Differentiation and Integration......Page 47 Identity Matrix......Page 48 Matrix Inversion......Page 49 Eigenvalues and Eigenvectors......Page 50 2.2 Gaussian Elimination......Page 52 General Algorithm for Gaussian Elimination......Page 54 Symmetric Banded Matrices......Page 57 Gaussian Elimination with Column Reduction......Page 59 Skyline Solution......Page 61 2.3 Conjugate Gradient Method for Equation Solving......Page 62 Input Data/Output......Page 63 Problems......Page 64 Program Listings......Page 66 3.1 Introduction......Page 68 Element Division......Page 69 Numbering Scheme......Page 70 3.3 Shape Functions and Local Coordinates......Page 72 3.4 The Potential-Energy Approach......Page 76 Element Stiffness Matrix......Page 77 Force Terms......Page 79 Element Stiffness......Page 81 Force Terms......Page 82 3.6 Assembly of the Global Stiffness Matrix and Load Vector......Page 83 3.7 Properties of K......Page 86 Types of Boundary Conditions......Page 87 Elimination Approach......Page 88 Penalty Approach......Page 93 Multipoint Constraints......Page 99 3.9 Quadratic Shape Functions......Page 102 3.10 Temperature Effects......Page 109 Problem in Equilibrium......Page 113 Two Elements with Same End Displacements......Page 114 Input Data/Output......Page 115 Problems......Page 116 Program Listing......Page 128 4.1 Introduction......Page 134 Local and Global Coordinate Systems......Page 135 Formulas for Calculating l and m......Page 136 Element Stiffness Matrix......Page 137 Stress Calculations......Page 138 Temperature Effects......Page 143 4.3 Three-Dimensional Trusses......Page 146 Assembly for Banded Solution......Page 148 Skyline Assembly......Page 149 Inclined Support in Three Dimensions—Line Constraint......Page 151 Inclined Support in Three Dimensions—Plane Constraint......Page 152 Symmetry and Antisymmetry......Page 153 Input Data/Output......Page 155 Problems......Page 156 Program Listing......Page 164 5.1 Introduction......Page 167 Potential-Energy Approach......Page 168 Galerkin Approach......Page 169 5.2 Finite Element Formulation......Page 170 Element Stiffness—Direct Approach......Page 174 5.3 Load Vector......Page 175 5.4 Boundary Considerations......Page 176 5.5 Shear Force and Bending Moment......Page 177 5.6 Beams on Elastic Supports......Page 179 5.7 Plane Frames......Page 180 5.8 Three-Dimensional Frames......Page 186 5.9 Problem Modeling and Boundary Conditions......Page 190 Input Data/Output......Page 191 Problems......Page 193 Program Listings......Page 200 6.1 Introduction......Page 205 6.2 Finite Element Modeling......Page 206 6.3 Constant Strain Triangle (CST)......Page 208 Isoparametric Representation......Page 209 Element Stiffness......Page 215 Force Terms......Page 216 Galerkin Approach......Page 223 Stress Calculations......Page 225 Temperature Effects......Page 227 6.4 Problem Modeling and Boundary Conditions......Page 229 Patch Test......Page 232 6.6 Orthotropic Materials......Page 233 Temperature Effects......Page 237 Input Data/Output......Page 239 Problems......Page 242 Program Listing......Page 255 7.1 Introduction......Page 259 7.2 Axisymmetric Formulation......Page 260 7.3 Finite Element Modeling: Triangular Element......Page 262 Potential Energy Approach......Page 265 Rotating Flywheel......Page 266 Surface Traction......Page 267 Galerkin Approach......Page 269 Stress Calculations......Page 272 Cylinder Subjected to Internal Pressure......Page 273 Press Fit on a Rigid Shaft......Page 274 Press Fit on an Elastic Shaft......Page 275 Belleville Spring......Page 276 Thermal Stress Problem......Page 277 Input Data/Output......Page 279 Problems......Page 280 Program Listing......Page 288 Shape Functions......Page 290 Element Stiffness Matrix......Page 293 8.3 Numerical Integration......Page 296 Stiffness Integration......Page 300 Stress Calculations......Page 301 8.4 Higher Order Elements......Page 303 Nine-Node Quadrilateral......Page 304 Eight-Node Quadrilateral......Page 306 Six-Node Triangle......Page 307 Integration on a Triangle—Symmetric Points......Page 308 Integration on a Triangle—Degenerate Quadrilateral......Page 309 8.5 Four-Node Quadrilateral for Axisymmetric Problems......Page 311 8.7 Concluding Remarks and Convergence......Page 312 8.8 References for Convergence......Page 314 Input Data/Output......Page 315 Problems......Page 317 Program Listings......Page 325 9.1 Introduction......Page 329 9.2 Finite Element Formulation......Page 330 Element Stiffness......Page 333 9.3 Stress Calculations......Page 334 9.4 Mesh Preparation......Page 335 9.5 Hexahedral Elements and Higher Order Elements......Page 339 9.6 Problem Modeling......Page 341 9.7 Frontal Method for Finite Element Matrices......Page 343 Connectivity and Prefront Routine......Page 344 Elimination of Completed dof......Page 345 Consideration of Multipoint Constraints......Page 346 Input Data/Output......Page 347 Problems......Page 349 Program Listings......Page 353 10.1 Introduction......Page 362 10.2 Steady-State Heat Transfer......Page 363 One-Dimensional Heat Conduction......Page 364 One-Dimensional Heat Transfer in Thin Fins......Page 372 Two-Dimensional Steady-State Heat Conduction......Page 376 Two-Dimensional Fins......Page 386 10.3 Torsion......Page 387 Triangular Element......Page 389 Galerkin Approach[sup(2)]......Page 390 Potential Flow......Page 393 Seepage......Page 395 Electrical and Magnetic Field Problems......Page 396 Fluid Flow in Ducts......Page 398 Acoustics......Page 400 One-Dimensional Acoustics......Page 401 One-Dimensional Axial Vibrations......Page 403 Two-Dimensional Acoustics......Page 405 Input Data/Output......Page 406 Problems......Page 408 Program Listings......Page 419 11.2 Formulation......Page 425 Solid Body with Distributed Mass......Page 426 11.3 Element Mass Matrices......Page 428 11.4 Evaluation of Eigenvalues and Eigenvectors......Page 433 Eigenvalue-Eigenvector Evaluation......Page 434 Inverse Iteration Method......Page 437 Generalized Jacobi Method......Page 440 Bringing Generalized Problem to Standard Form......Page 444 Tridiagonalization......Page 445 Implicit Symmetric QR Step with Wilkinson Shift for Diagonalization[sup(2)]......Page 448 11.5 Interfacing with Previous Finite Element Programs and a Program for Determining Critical Speeds of Shafts......Page 449 11.6 Guyan Reduction......Page 450 11.7 Rigid Body Modes......Page 453 Input Data/Output......Page 455 Problems......Page 457 Program Listings......Page 463 Region and Block Representation......Page 470 Block Corner Nodes, Sides, and Subdivisions......Page 471 Deformed Configuration and Mode Shape......Page 478 Contour Plotting......Page 479 Nodal Values from Known Constant Element Values for a Triangle......Page 480 Least-Squares Fit for a Four-Noded Quadrilateral......Page 482 12.4 Conclusion......Page 483 Input Data/Output......Page 484 Problems......Page 485 Program Listings......Page 487 APPENDIX Proof of dA = det Jdξ dη......Page 500 BIBLIOGRAPHY......Page 503 ANSWERS TO SELECTED PROBLEMS......Page 507 C......Page 509 F......Page 510 L......Page 511 S......Page 512 W......Page 513 The first edition of this book appeared over 20 years ago and the second and third editions followed subsequently. Translations of the book appeared in Spanish, Korean, Greek, and Chinese languages. We received positive feedback from professors who taught from the book and from students and practicing engineers who used the book. We also benefited from the feedback received from the students in our courses for the past 30 years. We have incorporated several suggestions in this edition. The underlying philosophy of the book is to provide a clear presentation of theory, aspects of problem modeling and implementation into computer programs. The pedagogy of earlier editions has been retained and enhanced in this edition 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.

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. This title is ideal for senior undergraduate and first-year graduate students and also as a learning resource to practicing engineers. It provides an integrated approach to finite element methodologies. The development of finite element theory is combined with examples and exercises involving engineering applications This work provides an integrated approach to finite element methodologies. The development of finite element theory is combined with examples and exercises involving engineering applications