This book presents the foundation and validation of the Cosserat Plate Theory, numerical experiments of deformation and vibration, and the unique properties of the Cosserat plates. Our approach incorporates the high accuracy assumptions of the Cosserat plate deformation consistent with the Cosserat Elasticity equilibrium equations, constitutive formulas, strain-displacement and torsion-microrotation relations. The Cosserat Plate Theory is parametric, where the "splitting parameter" minimizes the Cosserat plate energy. The validation of the theory is based on the comparison with the three-dimensional Cosserat Elastostatics and Elastodynamics. The numerical results are obtained using the Finite Element Method (FEM) specifically developed to solve the parametric system of equations. The analysis of deformation of a variety of Cosserat plates shows the stress concentration reduction, higher stiffness of Cosserat plates, and the size-effect related to the microstructure. The analysis of vibration of Cosserat plates predicts size-related properties of the plate vibration, the existence of the additional so-called Cosserat plate resonances, and the dynamic anisotropy, related to the dependency of the resonances on the microelement's shapes and orientations.
- 170 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
Cosserat Plate Theory
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Table of contents
- Cover Page
- Half-Title Page
- Title Page
- Copyright Page
- Dedication Page
- Contents
- Preface
- Acknowledgments
- Introduction
- Notations
- Chapter 1 ◾ Cosserat Elasticity
- Chapter 2 ◾ Analysis of Cosserat Sample Bodies
- Chapter 3 ◾ Cosserat Plate Statics
- Chapter 4 ◾ Cosserat Plate Dynamics
- Chapter 5 ◾ Validation of the Cosserat Plate Theory
- Chapter 6 ◾ Finite Element Method for Cosserat Plates
- Chapter 7 ◾ Validation of the Finite Element Computation
- Chapter 8 ◾ Unique Properties of Cosserat Plates
- Appendix A
- Appendix B
- Appendix C
- Bibliography
- Index
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Yes, you can access Cosserat Plate Theory by Lev Steinberg,Roman Kvasov in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.