Petr E Tovstik's Books

Asymptotic Methods In The Buckling Theory Of Elastic Shells

By: Andrei L Smirnov,Petr E Tovstik

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Asymptotic Methods In The Buckling Theory Of Elastic Shells

By: Andrei L Smirnov,Petr E Tovstik

This book contains solutions to the most typical problems of thin elastic shells buckling under conservative loads. The linear problems of bifurcation of shell equilibrium are considered using a two-dimensional theory of the Kirchhoff-Love type. The explicit approximate formulas obtained by means of the asymptotic method permit one to estimate the critical loads and find the buckling modes.The solutions to some of the buckling problems are obtained for the first time in the form of explicit formulas. Special attention is devoted to the study of the shells of negative Gaussian curvature, the buckling of which has some specific features. The buckling modes localized near the weakest lines or points on the neutral surface are constructed, including the buckling modes localized near the weakly supported shell edge. The relations between the buckling modes and bending of the neutral surface are analyzed. Some of the applied asymptotic methods are standard; the others are new and are used for the first time in this book to study thin shell buckling. The solutions obtained in the form of simple approximate formulas complement the numerical results, and permit one to clarify the physics of buckling.

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Page Count

359

Publisher

World Scientific

Published Date

ISBN 10

9814490296

ISBN 13

9789814490290

Localized Dynamics of Thin-Walled Shells

By: Gennadi I. Mikhasev,Petr E. Tovstik

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Localized Dynamics of Thin-Walled Shells

By: Gennadi I. Mikhasev,Petr E. Tovstik

Localized Dynamics of Thin-Walled Shells focuses on localized vibrations and waves in thin-walled structures with variable geometrical and physical characteristics. It emphasizes novel asymptotic methods for solving boundary-value problems for dynamic equations in the shell theory, in the form of functions which are highly localized near both fixed and moving lines/points on the shell surface. Features First-of-its-kind work, synthesizing knowledge of the localization of vibrations and waves in thin-walled shells with a mathematical tool to study them Suitable for researchers working on the dynamics of thin shells and also as supplementary reading for undergraduates studying asymptotic methods Offers detailed analysis of wave processes in shells with varying geometric and physical parameters

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Page Count

371

Publisher

CRC Press

Published Date

ISBN 10

1351630687

ISBN 13

9781351630689

Asymptotic methods in mechanics of solids

By: Svetlana M. Bauer,Sergei B. Filippov,Andrei L. Smirnov,Petr E. Tovstik,Rémi Vaillancourt

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Asymptotic methods in mechanics of solids

By: Svetlana M. Bauer,Sergei B. Filippov,Andrei L. Smirnov,Petr E. Tovstik,Rémi Vaillancourt

The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russian literature not well known for an English speaking reader makes this a indispensable textbook on the topic.

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