Voyiadjis / Karamanlidis Advances in the Theory of Plates and Shells

1. Auflage 2013
ISBN: 978-1-4832-9096-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 24, 324 Seiten, Web PDF

Reihe: Studies in Applied Mechanics

Plates and shells play an important role in structural, mechanical, aerospace and manufacturing applications. The theory of plates and shells have advanced in the past two decades to handle more complicated problems that were previously beyond reach. In this book, the most recent advances in this area of research are documented. These include topics such as thick plate and shell analyses, finite rotations of shell structures, anisotropic thick plates, dynamic analysis, and laminated composite panels. The book is divided into two parts. In Part I, emphasis is placed on the theoretical aspects of the analysis of plates and shells, while Part II deals with modern applications. Numerous eminent researchers in the various areas of plate and shell analyses have contributed to this work which pays special attention to aspects of research such as theory, dynamic analysis, and composite plates and shells.

Autoren/Hrsg.

Voyiadjis, George Z.

Karamanlidis, D.

Inhaltsverzeichnis

1;Front Cover;1
2;Advances in the Theory of Plates and Shells;4
3;Copyright Page;5
4;Table of Contents;10
5;INTRODUCTION;6
5.1;REFERENCES;8
6;PART I: THEORETICAL ASPECTS OF THE ANALYSIS OF PLATES AND SHELLS;12
6.1;Chapter 1. Theory aid Finite-Element Formulation for Shell Structures Undergoing Finite Rotations;14
6.1.1;1. Introduction;14
6.1.2;2. Kinematic relations;15
6.1.3;3 . Two-dimensional force variables;21
6.1.4;4. Variational principles;22
6.1.5;5. Transformations;23
6.1.6;6. Incremental formulation;25
6.1.7;7. Development of element matrices in index formulation;27
6.1.8;8. Discretization of displacements and internal forces;28
6.1.9;9. Numerical results;32
6.1.10;10. Conclusions;34
6.1.11;References;36
6.2;Chapter 2. A Refined Theory of Anisotropic Thick Plates;38
6.2.1;1. INTRODUCTION;38
6.2.2;2. NOTATIONS AND COORDINATE SYSTEM;39
6.2.3;3. FUNDAMENTAL EQUATIONS OF ELASTIC BODY AND TWO-DIMENSIONAL EQUATIONS FOR DEFORMATION;40
6.2.4;4. BOUNDARY CONDITIONS AT THE SURFACES OF THE PLATE AND EQUATIONS OF DEFORMATION;43
6.2.5;5. EXAMPLES OF NUMERICAL CALCULATION;46
6.2.6;6. CONCLUSIONS;54
6.2.7;REFERENCES;55
6.3;Chapter 3. Generalized Theory for Bending of Thick Plates;56
6.3.1;1. INTRODUCTION;56
6.3.2;2. THEORETICAL FORMULATION;57
6.3.3;3. APPLICATION;67
6.3.4;4. CONCLUSIONS;71
6.3.5;ACKNOWLEDGEMENTS;71
6.3.6;REFERENCES;71
6.4;Chapter 4. Postbuckling of Long Thick Plates in Compression Including Higher Order Transverse Shearing Effects;74
6.4.1;ABSTRACT;74
6.4.2;INTRODUCTION;75
6.4.3;SYMBOLS;76
6.4.4;THEORY;77
6.4.5;RESULTS AND DISCUSSION;84
6.4.6;CONCLUDING REMARKS;86
6.4.7;APPENDIX;87
6.4.8;REFERENCES;89
6.5;Chapter 5. Bending of Thick Plates on an Elastic Foundation;98
6.5.1;1. INTRODUCTION;98
6.5.2;2. GOVERNING DIFFERENTIAL EQUATIONS;98
6.5.3;3. NAVIER-TYPE SOLUTION;103
6.5.4;4. LEVY-TYPE SOLUTION;106
6.5.5;5. SOLUTION IN POLAR COORDINATES;110
6.5.6;6. SOLUTION FOR THE AXISYMMETRIC CASE;113
6.5.7;7. THE INPLACE DISPLACEMENTS;114
6.5.8;8 . INFINITE PLATE RESTING ON AN ELASTIC FOUNDATION;115
6.5.9;9. CONCLUSION;127
6.5.10;REFERENCES;128
6.5.11;APPENDIX I;129
6.5.12;APPENDIX II;131
6.5.13;APPENDIX III;131
6.6;Chapter 6. Higher-Order Constitutive Equations for Thick Cylindrical Shells;134
6.6.1;1. INTRODUCTION;134
6.6.2;2. THEORETICAL FORMULATION OF THE REFINED THEORY OF THICK CYLINDRICAL SHELLS;137
6.6.3;3. EFFECTIVE STRESS RESULTMTS, STRESS COUPLESAND CORRESPONDING STRAIN COMPONENTS;150
6.6.4;4. COUPLED STRAIN ENERGY DENSITY AND THE ELEMENT STIFFNESS MATRIX;152
6.6.5;5. EVALUATING ELEMENT STRAIN FIELD BY THE QUASI-CONFORMING TECHNIQUE;154
6.6.6;6. NUMERICAL EXAMPLES;159
6.6.7;7. CONCLUSION;160
6.6.8;REFERENCES;162
6.7;Chapter 7. Boundary Layers and Saint-Venant's Principle for Slender and Thin Elastic Bodies;164
6.7.1;1. INTRODUCTION;164
6.7.2;2. BOUNDARY LAYER STATES IN END LOADED SLENDER BODIES;165
6.7.3;3. STRETCHING, BENDING AND TORSION OF SLENDER BODIES;167
6.7.4;4. ELEMENTARY BEAM STRETCHING AND BENDING;170
6.7.5;5. RECIPROCAL THEOREM AND BOUNDARY LAYER STATE;172
6.7.6;6. STRETCHING BY END DISPLACEMENTS;174
6.7.7;7. TORSION AND PURE BENDING BY END DISPLACEMENTS;176
6.7.8;8. BOUNDARY LAYER STATES IN EDGE LOADED FLAT PLATES;179
6.7.9;ACKNOWLEDGEMENT;183
6.7.10;REFERENCES;183
7;Part IIApplications of the Theory of Plates and Shells;186
7.1;Chapter 8. Dynamic Analysis of Plates and Shallow Shells by the D/BEM;188
7.1.1;1. INTRODUCTION;188
7.1.2;2. INTEGRAL FORMULATION OF PLATE DYNAMICS;190
7.1.3;3. MATRIX FORMULATION AND SOLUTION OF PLATE DYNAMIC PROBLEMS;192
7.1.4;4. INTEGRAL FORMULATION OF SHALLOW SHELL DYNAMICS;194
7.1.5;5. MATRIX FORMULATION AND SOLUTION OF SHALLOW SHELL DYNAMICS;196
7.1.6;6. EFFECT OF DAMPING ON THE RESPONSE;197
7.1.7;7. NUMERICAL EXAMPLES;198
7.1.8;8. CONCLUSIONS;201
7.1.9;REFERENCES;203
7.2;Chapter 9. Nonlinear Analysis of Imperfect Cylindrical Angle-Ply Panels;208
7.2.1;1. INTRODUCTION;208
7.2.2;2. NONLINEAR EQUATIONS OF MOTION;209
7.2.3;3. METHOD OF SOLUTION;211
7.2.4;4. NUMERICAL RESULTS AND DISCUSSION;214
7.2.5;5. CONCLUSIONS;220
7.2.6;ACKNOWLEDGEMENTS;220
7.2.7;REFERENCES;220
7.3;Chapter 10. Nonlinear Local-Global Static Analysis of Shells of Revolution;224
7.3.1;1. INTRODUCTION;224
7.3.2;2. ANALYTICAL MODEL;226
7.3.3;3. NONLINEARITIES;227
7.3.4;4. LOCAL-GLOBAL SYSTEM;230
7.3.5;5. SOLUTION TECHNIQUE;231
7.3.6;6. NUMERICAL EXAMPLES;231
7.3.7;REFERENCES;234
7.4;Chapter 11. Recent Studies on Buckling, Vibration and Static Response of Anisotropic Shear-Flexible Plates;238
7.4.1;1. INTRODDCTION;238
7.4.2;2. GOVERNING EQUATIONS;239
7.4.3;3. TRIAL FUNCTIONS;245
7.4.4;4. TEST STUDIES;246
7.4.5;5. CONCLUSIONS;248
7.4.6;6 . REFERENCES;248
7.5;Chapter 12. The Effects of Time-Dependent Excitation on the Oscillatory Motion of Viscously Damped Laminated Composite Flat Panels;260
7.5.1;1. INTRODUCTION;260
7.5.2;2. GOVERNING EQUATIONS;261
7.5.3;3. SOLUTION PROCEDURE;262
7.5.4;4. RESPONSE TO SONIC BOOM AND BLAST-TYPE LOADINGS;267
7.5.5;5. NUMERICAL ILLUSTRATIONS;268
7.5.6;6. CONCLUSIONS;273
7.5.7;REFERENCES;274
7.6;Chapter 13. Effect of Soil-Structure Interaction on the Vibrations of Stretched Circular Plates;280
7.6.1;1. INTRODUCTION;281
7.6.2;2. PROCEDURE OF ANALYSIS;282
7.6.3;3. HOLLCW AND SOLID CIRCULAR PLATES;288
7.6.4;4. FREE VIBRATION OF THE PLATES;292
7.6.5;5. FORCED VIBRATION OF THE PLATES;293
7.6.6;6. APPLICATION;296
7.6.7;7. CONCLUSION;299
7.6.8;8. REFERENCES;299
7.7;Chapter 14. The Internal Loading of a Fibre Reinforced Composite Plate;308
7.8;ABSTRACT;308
7.9;INTRODUCTION;308
7.10;FUNDAMENTAL EQUATIONS;309
7.11;INTERNAL LOADING OF THE SEMI-INFINITE PLATE;310
7.12;EXPERIMENTAL INVESTIGATIONS;316
7.13;CONCLUSIONS;319
7.14;REFERENCES;323