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Mathematical Models of Higher Orders

Shells in Temperature Fields

  • Book
  • © 2019

Overview

Authors:
  1. Vadim A. Krysko

    1. Department of Mathematics and Modeling, Saratov State Technical University, Saratov, Russia

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  2. Jan Awrejcewicz

    1. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Lodz, Poland

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  3. Maxim V. Zhigalov

    1. Department of Mathematics and Modeling, Saratov State Technical University, Saratov, Russia

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  4. Valeriy F. Kirichenko

    1. Department of Mathematics and Modeling, Saratov State Technical University, Saratov, Russia

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  5. Anton V. Krysko

    1. Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, Saratov, Russia

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  • Exemplifies the vast range of mathematical models of nonlinear dynamics and statics of continuous mechanical structural members
  • Offers a new class of generalized problems of diffraction in theory of shells based on the fundamental variational equations of thermomechanics of shallow shells
  • Features new results regarding nonlinear dynamics of the studied objects, including regular and non-regular vibrations and their bifurcations

Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 42)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • Vadim A. Krysko, Jan Awrejcewicz, Maxim V. Zhigalov, Valeriy F. Kirichenko, Anton V. Krysko
    Pages 1-19

  3. Mathematical Modeling of Nonlinear Dynamics of Continuous Mechanical Structures with an Account of Internal and External Temperature Fields

    • Vadim A. Krysko, Jan Awrejcewicz, Maxim V. Zhigalov, Valeriy F. Kirichenko, Anton V. Krysko
    Pages 21-131

  4. Nonclassical Models and Stability of Multilayer Orthotropic Thermoplastic Shells within Timoshenko Modified Hypotheses

    • Vadim A. Krysko, Jan Awrejcewicz, Maxim V. Zhigalov, Valeriy F. Kirichenko, Anton V. Krysko
    Pages 133-247

  5. General Problems of Diffraction in the Theory of Design: Nonlinear Shells and Plates Locally Interacting with Temperature Fields

    • Vadim A. Krysko, Jan Awrejcewicz, Maxim V. Zhigalov, Valeriy F. Kirichenko, Anton V. Krysko
    Pages 249-305

  6. Stability of Flexible Shallow Shells Subject to Transversal Loads and Heat Flow

    • Vadim A. Krysko, Jan Awrejcewicz, Maxim V. Zhigalov, Valeriy F. Kirichenko, Anton V. Krysko
    Pages 307-330

  7. Mathematical Models of Multilayer Flexible Orthotropic Shells Under a Temperature Field

    • Vadim A. Krysko, Jan Awrejcewicz, Maxim V. Zhigalov, Valeriy F. Kirichenko, Anton V. Krysko
    Pages 331-421

  8. Chaotic Dynamics of Closed Cylindrical Shells Under Local Transversal Load and Temperature Field (First-Order Kirchhoff–Love Approximation Model)

    • Vadim A. Krysko, Jan Awrejcewicz, Maxim V. Zhigalov, Valeriy F. Kirichenko, Anton V. Krysko
    Pages 423-462

  9. Back Matter

    Pages 463-470
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Keywords

About this book

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 PDEs, and of finding their solutions based on the development of new and effective numerical techniques. The book is designed for a broad readership of graduate students in mechanical and civil engineering, applied mathematics, and physics, as well as to researchers and professionals interested in a rigorous and comprehensive study of modeling non-linear phenomena governed by PDEs.

Reviews

“The book is easy to read. The reviewer enjoyed reading the book. The book is a welcome reading for academics, researchers and professionals interested in a rigorous and comprehensive study of modeling nonlinear phenomena governed by PDEs. The book will also be useful to graduate and doctoral students in mechanical, civil and aeronautical engineering, and to applied mathematicians and physicists.” (Girish Kumar Ramaiah, zbMATH 1436.74001, 2020)

Authors and Affiliations

  • Department of Mathematics and Modeling, Saratov State Technical University, Saratov, Russia

    Vadim A. Krysko, Maxim V. Zhigalov, Valeriy F. Kirichenko

  • Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Lodz, Poland

    Jan Awrejcewicz

  • Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, Saratov, Russia

    Anton V. Krysko

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