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Mathematical models of higher orders : shells in temperature fields

Author: V A Krysʹko; J Awrejcewicz; Maxim V Zhigalov; Valeriy F Kirichenko; Anton V Krysko
Publisher: Cham, Switzerland : Springer, 2019.
Series: Advances in mechanics and mathematics, v. 42.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book offers a valuable methodological approach to the state-of-the-art of the classical plate/shell mathematical models, exemplifying the vast range of mathematical models of nonlinear dynamics and statics of continuous mechanical structural members. The main objective highlights the need for further study of the classical problem of shell dynamics consisting of mathematical modeling, derivation of nonlinear  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
(OCoLC)1057762109
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: V A Krysʹko; J Awrejcewicz; Maxim V Zhigalov; Valeriy F Kirichenko; Anton V Krysko
ISBN: 9783030047146 3030047148 9783030047153 3030047156
OCLC Number: 1086377563
Description: 1 online resource (xii, 470 pages) : illustrations (some color)
Contents: Intro; Preface; Contents; 1 Introduction; References; 2 Mathematical Modeling of Nonlinear Dynamics of Continuous Mechanical Structures with an Account of Internal and External Temperature Fields; 2.1 Coupling of Temperature and Deformation: The First Approximation Models and Parabolic Heat Transfer Equation; 2.1.1 Fundamental Assumptions and Hypotheses; 2.1.2 Reduction of the 3D Problem to the 2D Problem; 2.1.3 Variational Formulation 2.1.4 Differential Equations Governing the Dynamics of Shallow Flexible Plates/Shells, Taking into Account the Coupling of Temperature and Deformation Field in the Mixed Form2.1.5 PDEs in Displacements in the Theory of Flexible Plates/Shells; 2.1.6 Existence of a Solution Within the Kirchhoff-Love Model in the Mixed Form and with Parabolic Heat Transfer Equations; 2.2 Mathematical Model of Continuous Mechanical Structures Based on the First-Order Approximation with a Hyperbolic Heat Transfer Equation; 2.2.1 Formulation of the Problem 2.2.2 Theorem of Existence of a Solution of the Problems (2.133)-(2.136)2.3 Numerical Investigation of Coupled Problems in the Theory of Shallow Shells with a Parabolic Heat Transfer Equation; 2.3.1 Criteria of Stability Loss; 2.3.2 Application of the Faedo-Galerkin Method; 2.3.3 Employing FDM of Second-Order Accuracy to Study Coupled Problems of Thermoelasticity of Shallow Shells in Mixed Form with a Parabolic Heat Transfer Equation; 2.4 Mathematical Models of Second-Order Approximation (Timoshenko Model) with a Parabolic Equation of Heat Transfer 2.5 Mathematical Models of a Three-Layer Structure Using First/Second Approximations for the External/Internal Layers and the Parabolic Heat Transfer EquationReferences; 3 Nonclassical Models and Stability of Multilayer Orthotropic Thermoplastic Shells within Timoshenko Modified Hypotheses; 3.1 ``Projection'' Condition of Motion for a Thermoelastic Rigid Body and Its Application in the Theory of Multilayer Orthotropic Shells; 3.2 Examples of Compatible, Asymptotically Compatible, and Incompatible Models (Theories) of Multilayer Orthotropic Thermoplastic Shallow Shells 3.2.1 Compatible, Continual, and Displacement Oriented Models3.2.2 Incompatible Models, Continual, in Displacements and Taking into Account the Contact Conditions; 3.2.3 Models Asymptotically Compatible, Continuous, Governed by Equations in Displacements and in Mixed Form; 3.2.4 Asymptotically Inconsistent, the Continuum Model in the ``Displacements'' or ``Mixed'' Form, Without Compression; 3.3 Qualitative Investigation of Asymptotically Compatible and Incompatible Models of Thermoelastic Shells
Series Title: Advances in mechanics and mathematics, v. 42.
Responsibility: Vadim A. Krysko, Jan Awrejcewicz, Maxim V. Zhigalov, Valeriy F. Kirichenko, Anton V. Krysko.

Abstract:

This book offers a valuable methodological approach to the state-of-the-art of the classical plate/shell mathematical models, exemplifying the vast range of mathematical models of nonlinear dynamics  Read more...

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