Finite Element Multidisciplinary Analysis (Aiaa Education Series)

Annotation This book fills a gap within the finite element literature by addressing the challenges and developments in multidiscipli-nary analysis. Current developments include disciplines of structural mechanics, heat transfer, fluid mechanics, controls engineering and propulsion technology, and their interaction as encountered in many practical problems in aeronautical, aerospace, and mechanical engineering, among others. These topics are reflected in the 15 chapter titles of the book. Numerical problems are provided to illustrate the applicability of the techniques. Exercises may be solved either manually or by using suitable computer software. A version of the multidisciplinary analysis program STARS is available from the author. As a textbook, the book is useful at the senior undergraduate or graduate level. The practicing engineer will find it invaluable for solving full-scale practical problems. Read more... Abstract: Annotation This book fills a gap within the finite element literature by addressing the challenges and developments in multidiscipli-nary analysis. Current developments include disciplines of structural mechanics, heat transfer, fluid mechanics, controls engineering and propulsion technology, and their interaction as encountered in many practical problems in aeronautical, aerospace, and mechanical engineering, among others. These topics are reflected in the 15 chapter titles of the book. Numerical problems are provided to illustrate the applicability of the techniques. Exercises may be solved either manually or by using suitable computer software. A version of the multidisciplinary analysis program STARS is available from the author. As a textbook, the book is useful at the senior undergraduate or graduate level. The practicing engineer will find it invaluable for solving full-scale practical problems Cover 1 Title 2 Copyright 3 Foreword 8 Table of Contents 10 Preface to the Second Edition 14 Preface to the First Edition 16 Nomenclature 20 Chapter 1. Introduction 23 1.1 Introduction 23 1.2 Areas of Analysis 24 1.3 Methods of Analysis 27 1.4 Computer Software 31 1.5 Brief History of the Finite Element Method 32 1.6 Concluding Remarks 34 References 35 Chapter 2. Finite Element Discretization of Physical Systems 37 2.1 Introduction 37 2.2 Finite Element Solutions 38 2.3 Application of the Galerkin Method 40 2.4 Concluding Remarks 45 References 45 Chapter 3. Structural Mechanics—Basic Theory 47 3.1 Introduction 47 3.2 Modeling of Material Behavior 47 3.3 Finite Element Formulation Based on the Stationary Functional Method 56 3.4 Concluding Remarks 59 References 59 Chapter 4. Structural Mechanics—Finite Elements 61 4.1 Introduction 61 4.2 One-Dimensional Line Elements 61 4.3 Two-Dimensional Plane Elements 69 4.4 Three-Dimensional Solid Elements 85 4.5 Isoparametric Quadrilateral and Hexahedron Elements 94 4.6 Torsion of Prismatic Shafts 100 4.7 Plate Bending Elements 106 4.8 Shell Elements 110 4.9 Numerical Examples 121 4.10 Concluding Remarks 123 References 123 Chapter 5. Spinning Structures 127 5.1 Introduction 127 5.2 Derivation of Equation of Motion 127 5.3 Derivation of Nodal Centrifugal Forces 129 5.4 Derivation of Element Matrices 135 5.5 Numerical Examples 141 5.6 Concluding Remarks 143 References 145 Chapter 6. Dynamic Element Method 147 6.1 Introduction 147 6.2 Bar Element 149 6.3 Beam Element 151 6.4 Rectangular Prestressed Membrane Element 152 6.5 Plane Triangular Element 157 6.6 Shell Element 161 6.7 Numerical Examples 163 6.8 Concluding Remarks 166 References 167 Chapter 7. Generation of System Matrices 169 7.1 Introduction 169 7.2 Coordinate Systems and Transformations 169 7.3 Matrix Assembly 173 7.4 Imposition of Deflection Boundary Conditions 174 7.5 Matrix Bandwidth Minimization 176 7.6 Sparse Matrix Storage Schemes 179 7.7 Concluding Remarks 180 References 180 Chapter 8. Solution of System Equations 183 8.1 Introduction 183 8.2 Formulation and Solution of System Equation 183 8.3 Sparse Cholesky Factorization 190 8.4 Concluding Remarks 214 References 215 Chapter 9. Eigenvalue Problems 217 9.1 Introduction 217 9.2 Free Vibration Analysis of Undamped Nonspinning Structures 217 9.3 Free Vibration Analysis of Spinning Structures 228 9.4 Quadratic Matrix Eigenvalue Problem for Free Vibration Analysis 238 9.5 Structural Stability Problems 243 9.6 Vibration of Prestressed Structures 243 9.7 Vibration of Damped Structural Systems 244 9.8 Solution of Damped Free Vibration Problem 246 9.9 Concluding Remarks 250 References 250 Chapter 10. Dynamic Response of Elastic Structures 253 10.1 Introduction 253 10.2 Method of Modal Superposition 253 10.3 Direct Integration Methods 260 10.4 Frequency Response Method 263 10.5 Response to Random Excitation 265 10.6 Numerical Examples 267 References 271 Chapter 11. Nonlinear Analysis 273 11.1 Introduction 273 11.2 Geometric Nonlinearity 273 11.3 Material Nonlinearity 275 11.4 Numerical Examples 277 References 283 Chapter 12. Stress Computations and Optimization 285 12.1 Introduction 285 12.2 Line Elements 285 12.3 Triangular Shell Elements 286 12.4 Solid Elements 287 12.5 Optimization 289 12.6 Examples of Applications of Optimization 293 References 296 Chapter 13. Heat Transfer Analysis of Solids 299 13.1 Introduction 299 13.2 Heat Conduction 299 13.3 Solution of System Equations 303 13.4 Numerical Examples 307 13.5 Coupled Heat Transfer and Structural Analysis 311 References 314 Chapter 14. Computational Linear Aeroelasticity and Aeroservoelasticity 317 14.1 Introduction 317 14.2 Formulation of Numerical Procedure 318 14.3 Numerical Example 325 14.4 Concluding Remarks 327 References 332 Chapter 15. CFD-Based Aeroelasticity and Aeroservoelasticity 333 15.1 Introduction 333 15.2 Computational Fluid Dynamics 334 15.3 Time-Marched Aeroelastic and Aeroservoelastic Analysis 354 15.4 ARMA Model in Aeroelastic and Aeroservoelastic Analysis 359 15.5 Numerical Examples 369 15.6 Concluding Remarks 384 References 385 Appendix. Exercises 389 Index 423 A 423 B 423 C 424 D 426 E 429 F 430 G 432 H 432 I 433 J 434 K 434 L 434 M 434 N 436 O 436 P 436 Q 437 R 437 S 437 T 438 U 438 V 438 W 439 X 439 Y 439 Z 439 A variety of engineering problems encountered in practice exhibit behavior that is predicated by the interaction of complex physical phenomena, i.e., their response is determined not by a single phenomena but by multidisciplinary interaction.