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E-raamat: Cosserat Plate Theory [Taylor & Francis e-raamat]

(University of Puerto Rico at Aguadilla), (University of Puerto Rico at Mayagüez)
  • Formaat: 160 pages, 35 Tables, black and white; 29 Line drawings, black and white; 11 Halftones, black and white; 40 Illustrations, black and white
  • Ilmumisaeg: 15-Sep-2022
  • Kirjastus: CRC Press
  • ISBN-13: 9781003190264
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  • Taylor & Francis e-raamat
  • Hind: 77,54 €*
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  • Tavahind: 110,77 €
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Cosserat Plate TheorySuurem pilt
  • Formaat: 160 pages, 35 Tables, black and white; 29 Line drawings, black and white; 11 Halftones, black and white; 40 Illustrations, black and white
  • Ilmumisaeg: 15-Sep-2022
  • Kirjastus: CRC Press
  • ISBN-13: 9781003190264
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003190264
"The book presents the foundation and validation of the Cosserat Plate Theory, numerical computations, and the unique properties of the Cosserat plates"--

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.



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. It incorporates comparison with three-dimensional Cosserat elastodynamics.

Preface xi
Acknowledgments xiii
Introduction xv
Notations xxi
Chapter 1 Cosserat Elasticity
1(24)
1.1 Scope Of The
Chapter
1(1)
1.2 Cosserat Elasticity
1(1)
1.3 Linear Theory Of Cosserat Elasticity
2(11)
1.3.1 Cosserat Space
3(1)
1.3.2 Cosserat Body Deformation
3(3)
1.3.3 Infinitesimal Cosserat Deformation And Motion
6(1)
1.3.4 Conservation Of Mass And Microinertia
7(1)
1.3.5 Conservation Of Linear And Angular Momentum
8(2)
1.3.6 Law Of Conservation Of Energy
10(1)
1.3.7 Cosserat Elastic Energy
11(2)
1.4 Variational Principle For Cosserat Elastostatics
13(2)
1.5 Principle Of Minimum Potential Energy
15(4)
1.6 Variational Principle For Cosserat Elastodynamics
19(6)
Chapter 2 Analysis Of Cosserat Sample Bodies
25(22)
2.1 Scope Of The
Chapter
25(1)
2.2 Cosserat Sample Bodies
25(2)
2.3 Statics Of Cosserat Sample Bodies
27(7)
2.4 Dynamics Of Cosserat Sample Bodies
34(5)
2.5 Plate Geometry Restriction For Cosserat Bodies
39(8)
Chapter 3 Cosserat Plate Statics
47(22)
3.1 Scope Of The
Chapter
47(1)
3.2 Plate Assumptions
47(7)
3.2.1 Boundary Conditions
47(2)
3.2.2 Stress Approximations
49(2)
3.2.3 Couple Stress Approximations
51(1)
3.2.4 Kinematic Approximations
52(2)
3.3 Cosserat Plate Static Equilibrium Equations
54(2)
3.4 Stress Energy Of The Cosserat Plate
56(2)
3.5 Strain-Displacement And Torsion-Microrotation Relations
58(2)
3.6 Constitutive Formulas For Cosserat Plate
60(2)
3.7 Variational Formulation Of Cosserat Plate Bending
62(1)
3.8 Optimal Value Of The Splitting Parameter
62(2)
3.9 Statics Field Equations
64(5)
Chapter 4 Cosserat Plate Dynamics
69(16)
4.1 Scope Of The
Chapter
69(1)
4.2 Plate Assumptions
69(11)
4.2.1 Boundary And Initial Conditions
70(1)
4.2.2 Stresses And Kinematic Approximations
71(9)
4.3 Dynamic Field Equations
80(5)
Chapter 5 Validation Of The Cosserat Plate Theory
85(12)
5.1 Scope Of The
Chapter
85(1)
5.2 Cosserat Sample Plate
85(2)
5.3 Validation Of The Cosserat Plate Statics
87(7)
5.4 Validation Of The Cosserat Plate Dynamics
94(3)
Chapter 6 Finite Element Method For Cosserat Plates
97(16)
6.1 Scope Of The
Chapter
97(1)
6.2 Clamped Cosserat Plate Bending Problem
97(1)
6.3 Finite Element Algorithm For Cosserat Elastic Plates
98(2)
6.4 Solutions Space For The Clamped Cosserat Plate
100(1)
6.5 Weak Formulation Of The Cosserat Plate Bending Problem
101(3)
6.6 Construction Of The Finite Element Spaces
104(3)
6.7 Calculation Of The Stiffness Matrix And The Load Vector
107(1)
6.8 Numerical Results
108(5)
Chapter 7 Validation Of The Finite Element Computation
113(12)
7.1 Scope Of The
Chapter
113(1)
7.2 Sample Cosserat Plate
113(2)
7.3 Validation Of The Fem For Dirichlet Boundary Conditions
115(3)
7.4 Validation Of The Fem For Mixed Dirichlet-Neumann Boundary Conditions
118(2)
7.5 Validation Of The Fem For Simply Supported Cosserat Plate
120(5)
Chapter 8 Unique Properties Of Cosserat Plates
125(14)
8.1 Scope Of The
Chapter
125(1)
8.2 Cosserat Sample Plate
125(1)
8.3 Cosserat Plate Statics
126(5)
8.3.1 Plate Stiffness
126(3)
8.3.2 Stress Concentration
129(2)
8.4 Cosserat Plate Dynamics
131(8)
8.4.1 Plate Resonances
131(4)
8.4.2 Dynamic Anisotropy
135(4)
Appendix A 139(6)
Appendix B 145(6)
Appendix C 151(2)
Bibliography 153(6)
Index 159
Roman Kvasov is a professor of Mathematics at the University of Puerto Rico at Aguadilla, USA. He is an expert in Scientific Computing and the Finite Element Method and an active researcher in the area of Cosserat Plates and Mathematical Modeling. His research has been published in such prestigious journals as Applied Mathematics, Thin-Walled Structures, Modelling and Simulation in Engineering and the chapter in the book "Dynamical Systems Theory".

Dr. Lev Steinberg is a professor of Mathematics at the University of Puerto Rico at Mayagüez. His academic, scientific, and industrial background includes advising of graduate students, research in Mathematical Modelling, experience at Sandia National Laboratories and US Naval Warfare Centers. Most of his work is related to the Continuum Mechanics, Solids with Complex Microstructures, and Inverse Problems. He is the author and co-author of dozens of patents and research publications in Applied Differential Equation and Applied Mechanics.
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