Mathematical Models of Higher Orders: Shells in Temperature Fields

Description

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. Front Matter ....Pages i-xii Introduction (Vadim A. Krysko, Jan Awrejcewicz, Maxim V. Zhigalov, Valeriy F. Kirichenko, Anton V. Krysko)....Pages 1-19 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 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 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 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 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 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 Back Matter ....Pages 463-470