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Cosserat Plate Theory

Af: Lev Steinberg, Roman Kvasov Engelsk Hardback

Cosserat Plate Theory

Af: Lev Steinberg, Roman Kvasov Engelsk Hardback
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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.

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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.

Produktdetaljer
Sprog: Engelsk
Sider: 160
ISBN-13: 9781032040233
Indbinding: Hardback
Udgave:
ISBN-10: 1032040238
Kategori: Anvendt matematik
Udg. Dato: 15 sep 2022
Længde: 17mm
Bredde: 222mm
Højde: 144mm
Forlag: Taylor & Francis Ltd
Oplagsdato: 15 sep 2022
Forfatter(e): Lev Steinberg, Roman Kvasov
Forfatter(e) Lev Steinberg, Roman Kvasov


Kategori Anvendt matematik


ISBN-13 9781032040233


Sprog Engelsk


Indbinding Hardback


Sider 160


Udgave


Længde 17mm


Bredde 222mm


Højde 144mm


Udg. Dato 15 sep 2022


Oplagsdato 15 sep 2022


Forlag Taylor & Francis Ltd

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