Asymptotic Methods in Mechanics of Solids

ISBN-13: 9783319386829 / Angielski / Miękka / 2016 / 325 str.

Svetlana M. Bauer; Sergei B. Filippov; Andrei L. Smirnov

Opis

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.

Recenzje

"The book might be considered as an advanced course with emphasize on applications. ... this book is a valuable contribution and a valuable complement of the existing literature in the field of asymptotic methods. The integration of the applications from Mechanics of solids should enlarge the circle of the potential readers." (Vladimir Rasvan, zbMATH 1330.34001, 2016)

Spis treści

Asymptotic Estimates.- Asymptotic Estimates for Integrals.- Regular Perturbation of ODE's.- Singularly Perturbed Linear ODE's.- Linear ODE's with Turning Points.- Asymptotic Integration of Nonlinear ODE's.- Bibliography.- Index.

Blurb

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.