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The Rayleigh-Ritz Method for Structural Analysis

ISBN: 978-1-84821-638-9
230 pages
December 2014, Wiley-ISTE
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Description

A presentation of the theory behind the Rayleigh-Ritz (R-R) method, as well as a discussion of the choice of admissible functions and the use of penalty methods, including recent developments such as using negative inertia and  bi-penalty terms.  While presenting the mathematical basis of the R-R method, the authors also give simple explanations and analogies to make it easier to understand. Examples include calculation of natural frequencies and critical loads of structures and structural components, such as beams, plates, shells and solids. MATLAB codes for some common problems are also supplied.

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Table of Contents

PREFACE xi

INTRODUCTION AND HISTORICAL NOTES xiii

CHAPTER 1. PRINCIPLE OF CONSERVATION OF ENERGY AND RAYLEIGH’S PRINCIPLE 1

CHAPTER 2. RAYLEIGH’S PRINCIPLE AND ITS IMPLICATIONS 11

CHAPTER 3. THE RAYLEIGH–RITZ METHOD AND SIMPLE APPLICATIONS 21

CHAPTER 4. LAGRANGIAN MULTIPLIER METHOD 33

CHAPTER 5. COURANT’S PENALTY METHOD INCLUDING NEGATIVE STIFFNESS AND MASS TERMS 39

CHAPTER 6. SOME USEFUL MATHEMATICAL DERIVATIONS AND APPLICATIONS 55

CHAPTER 7. THE THEOREM OF SEPARATION AND ASYMPTOTIC MODELING THEOREMS 67

CHAPTER 8. ADMISSIBLE FUNCTIONS 81

CHAPTER 9. NATURAL FREQUENCIES AND MODES OF BEAMS 89

CHAPTER 10. NATURAL FREQUENCIES AND MODES OF PLATES OF RECTANGULAR PLANFORM 113

CHAPTER 11. NATURAL FREQUENCIES AND MODES OF SHALLOW SHELLS OF RECTANGULAR PLANFORM 133

CHAPTER 12. NATURAL FREQUENCIES AND MODES OF THREE-DIMENSIONAL BODIES 149

CHAPTER 13. VIBRATION OF AXIALLY LOADED BEAMS AND GEOMETRIC STIFFNESS 161

CHAPTER 14. THE RRM IN FINITE ELEMENTS METHOD 181

BIBLIOGRAPHY 197

APPENDIX 203

INDEX 229

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