نظریه تیر مرکب غیرخطی برای مهندسان (پیشرفت در فضانوردی و هوافضا)

From an authoritative expert whose work on modern helicopter rotor blade analysis has spanned over three decades, comes the first consistent and rigorous presentation of beam theory. Beginning with an overview of the theory developed over the last 60 years, Dr. Hodges addresses the kinematics of beam deformation, provides a simple way to characterize strain in an initially curved and twisted beam, and offers cross-sectional analysis for beams with arbitrary cross sections and composed of arbitrary materials. He goes on to present a way to accurately recover all components of cross-sectional strain and stress before providing a natural one-dimensional (1D) theory of beams. Sample results for both cross-sectional and 1D analysis are presented as is a parallel treatment for thin-walled beams. - Data and information appearing in this book are for informational purposes only. AIAA and the author are not responsible for any injury or damage resulting from use or reliance, nor do AIAA and the author warrant that use or reliance will be free from privately owned rights. Front Matter 1 Preface 3 Table of Contents 5 1. Introduction 7 1.1 Developments in Beam Theory before 1985 9 1.2 Developments in Beam Theory after 1985 11 1.2.1 Analytical Cross-Sectional Modeling 13 1.2.2 General Beam Cross-Sectional Modeling 15 1.2.3 The Trapeze Effect 21 1.3 How Should Beams Be Classified? 23 1.4 Goals of This Book 25 2. Kinematical Preliminaries 28 2.1 Points, Frames, and Rigid Bodies 28 2.2 Vectors and Dyadics 29 2.3 Finite Rotation 30 2.4 Angular Velocity and Differentiation of Vectors 31 2.5 Virtual Rotation and Variation of Vectors 33 2.6 Velocity Primitives 35 2.7 Tilde Notation 35 2.8 Implications of Euler's Theorem 36 3. Kinematics of Beams 39 3.1 Beam Geometry and Global Rotation 40 3.1.1 Beam Configuration and Base Vectors 40 3.1.2 Generalized Strain Measures 43 3.1.3 Velocity Field 46 3.2 Strain and Local Rotation 47 3.2.1 Simplification for Small Strain and Local Rotation 50 3.2.2 Applying the Method 51 3.3 Example: Beam with Specified Warping 51 3.4 Beam Kinematics for the General Case 56 4. Cross-Sectional Analysis for Beams 62 4.1 Variational Asymptotic Method 62 4.1.1 Mathematical Foundation 63 4.1.2 Illustrative Example 66 4.2 General Cross-Sectional Dimensional Reduction 73 4.2.1 Three-Dimensional Strain Energy and Physical Interpretation of Stress 73 4.2.2 Classical Theory for Anisotropic Beams 74 4.2.3 Asymptotically Correct Refined Theory 77 4.2.4 Transformation to Generalized Timoshenko Theory 78 4.2.5 Important Special Case for Generalized Timoshenko Model 86 4.2.6 Applications of the Generalized Timoshenko Model 87 4.2.7 The Trapeze Effect 91 4.2.8 Generalized Vlasov Theory 99 4.3 Epilogue 102 5. One-Dimensional Theory of Beams 105 5.1 Generalized Timoshenko Refined Theory of Beams 105 5.1.1 Intrinsic Equations from Hamilton's Extended Principle 106 5.1.2 Mixed Variational Formulation 114 5.1.3 Examples 117 5.2 Classical Theory of Beams 122 5.3 Generalized Vlasov Refined Theory of Beams 127 5.4 Fully Intrinsic Generalized Timoshenko Theory 128 5.4.1 Equations of Motion 129 5.4.2 Constitutive Equations 130 5.4.3 Closing the Formulation 130 5.4.4 Example Showing Advantages of the Intrinsic Formulation 132 5.4.5 Conservation Laws for the Intrinsic Formulation 135 5.4.6 Applications of the Conservation Laws 137 5.5 Epilogue 142 6. Thin-Walled Beams 144 6.1 Analysis of I-Beams as an Assemblage of Strips 145 6.1.1 Approach 145 6.1.2 Torsion of Isotropic Strips 151 6.1.3 Isotropic I-Beams 155 6.1.4 Anisotropic I-Beams 158 6.1.5 Comparing Theories 166 6.2 More General Approach to Thin-Walled Beams 172 6.2.1 Setting Up the Problem 175 6.2.2 Phantom Step 177 6.2.3 Classical Approximation 178 6.2.4 Strips and Open Cross-Sections 180 6.2.5 Closed Cross-Sections 181 6.2.6 Second-Order Terms 189 6.2.7 Double-Cell Formulae 189 6.2.8 Multi-Celled Sections 192 6.3 Nonlinear Analysis of Initially Twisted Strips 193 6.3.1 Analytical Development 195 6.3.2 Applications 206 6.4 Epilogue 211 7. Validation and Sample Results 213 7.1 Analytical Validation 213 7.1.1 Three-Dimensional Formulation 213 7.1.2 Classical Model 216 7.1.3 Generalized Timoshenko Model 219 7.1.4 Example Cross Sections 224 7.2 Numerical Validation 228 7.2.1 Stiffness Model and Shear Correction Factors 229 7.2.2 Locating the Shear Center 232 7.2.3 Beam Analysis with the VABS Generalized Timoshenko Model 236 7.2.4 Recovering Three-Dimensional Results 240 7.3 Examples for Thin-Walled Beams 246 7.3.1 Strips 247 7.3.2 I-Beams 252 7.3.3 Closed-Section Beams 257 7.4 Epilogue 269 8. A Look Back and a Look Forward 270 8.1 Concluding Remarks 270 8.2 Recommendations for Future Research 271 Appendices 273 Appendix A: VABS Tutorial 273 A.1 VABS History 273 A.2 VABS Features 274 A.3 VABS Functionalities 274 A.4 VABS Conventions 275 A.5 VABS Inputs 277 A.6 VABS Outputs 280 A.7 Epilogue 280 References 281 Index 291 A 291 B 292 C 293 D 295 E 296 F 296 G 296 I 297 K 297 L 297 M 298 N 298 O 299 P 299 R 299 S 301 T 303 V 305 W 306 Z 307 This book provides a comprehensive overview of both the theoretical underpinnings and the practical application of aircraft modeling based on experimental data-also known as aircraft system identification. Much of the material presented comes from the authors' own extensive research and teaching activities at the NASA Langley Research Center and is based on real world applications of system identification to aircraft. The book uses actual flight-test and wind-tunnel data for examples.All aspects of the system identification problem-including their interdependency-are covered: model postulation, experiment design, instrumentation, data compatibility analysis, model structure determination, state and parameter estimation, and model validation.The methods described in the book have been successfully applied to projects such as flight envelope expansion for new or modified aircraft, verification and correction of wind-tunnel test results and analytic methods such as computational fluid dynamics (CFD), control system design and refinement, stability analysis, simulation development, flying qualities assessment, and accident investigation, among others. The book includes SIDPAC (System IDentification Programs for AirCraft), a software toolbox written in MATLAB[Registered]. SIDPAC is composed of many different tools that implement a wide variety of approaches explained fully in the book. These tools can be readily applied to solve system identification problems of interest to the reader.

from An Authoritative Expert Whose Work On Modern Helicopter Rotor Blade Analysis Has Spanned Over Three Decades, Comes The First Consistent And Rigorous Presentation Of Beam Theory. Beginning With An Overview Of The Theory Developed Over The Last 60 Years, Dr. Hodges Addresses The Kinematics Of Beam Deformation, Provides A Simple Way To Characterize Strain In An Initially Curved And Twisted Beam, And Offers Cross-sectional Analysis For Beams With Arbitrary Cross Sections And Composed Of Arbitrary Materials. He Goes On To Present A Way To Accurately Recover All Components Of Cross-sectional Strain And Stress Before Providing A Natural One-dimensional (1-d) Theory Of Beams. Sample Results For Both Cross-sectional And 1-d Analysis Are Presented As Is A Parallel Treatment For Thin-walled Beams.

Beginning with an overview of the theory developed over the years, the author addresses the kinematics of beam deformation. He provides a simple way to characterize strain in an initially curved and twisted beam, and offers cross-sectional analysis for beams with arbitrary cross sections and composed of arbitrary materials. Content: Front Matter • Preface • Table of Contents 1. Introduction 2. Kinematical Preliminaries 3. Kinematics of Beams 4. Cross-Sectional Analysis for Beams 5. One-Dimensional Theory of Beams 6. Thin-Walled Beams 7. Validation and Sample Results 8. A Look Back and a Look Forward Appendices • References Index