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Asymptotic Methods in Mechanics
Edited by: Rémi Vaillancourt and Andrei L. Smirnov
A co-publication of the AMS and Centre de Recherches Mathématiques.

CRM Proceedings & Lecture Notes
1993; 282 pp
Volume: 3
ISBN-10: 0-8218-6993-0
ISBN-13: 978-0-8218-6993-2
List Price: US$88
Member Price: US$70.40
Order Code: CRMP/3
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Asymptotic methods constitute an important area of both pure and applied mathematics and have applications to a vast array of problems. This collection of papers is devoted to asymptotic methods applied to mechanical problems, primarily thin structure problems. The first section presents a survey of asymptotic methods and a review of the literature, including the considerable body of Russian works in this area. This part may be used as a reference book or as a textbook for advanced undergraduate or graduate students in mathematics or engineering. The second part presents original papers containing new results. Among the key features of the book are its analysis of the general theory of asymptotic integration with applications to the theory of thin shells and plates, and new results about the local forms of vibrations and buckling of thin shells which have not yet made their way into other monographs on this subject.

Titles in this series are co-published with the Centre de Recherches Mathématiques.


Mathematics, physics, and engineering advanced undergraduates and graduate students in a course on asymptotic methods and solid mechanics. Scientists and engineers interested in the application of asymptotic methods to problems of mechanics and buckling and vibrations of thin structures.

Table of Contents

Part 1: A Survey
  • S. M. Bauer, S. B. Filippov, A. L. Smirnov, and P. E. Tovstik -- Asymptotic methods in mechanics with applications to thin shells and plates
Part 2. Thirteen Papers
  • M. Ya. Antimirov, A. A. Kolyshkin, and R. Vaillancourt -- Perturbation methods in eddy current testing
  • S. M. Bauer, S. B. Filippov, A. L. Maiboroda, A. L. Smirnov, and I. Yu. Teterin -- Buckling of thin cylindrical shells and shells of negative Gaussian curvature
  • S. M. Bauer and A. L. Smirnov -- Thermo-elastic deformations of mirrors
  • B. A. Ershov, Yu. A. Mochalova, and E. V. Polyakova -- A mathematical model for hydroelastic problems with a fluid memory. Part I
  • B. A. Ershov and I. I. Strelkovskaya -- A mathematical model for hydroelastic problems with a fluid memory. Part II
  • S. B. Filippov -- Low-frequency vibrations of cylindrical shells. Part I: Shells with a slanted edge
  • S. B. Filippov -- Low-frequency vibrations of cylindrical shells. Part II: Connected shells
  • A. L. Maiboroda -- Buckling of convex shells under nonaxisymmetric loading
  • G. V. Pavilainen -- Elasto-plastic deformations of ribbed plates
  • Yu. P. Shcheviev -- Elastic wave propagation through elastic shells
  • Yu. B. Shneerson -- Dynamic stability and forced vibrations of a horizontal rotor with a cracked shaft
  • P. E. Tovstik -- Edge effect under large axisymmetric deformations of shells of revolution
  • P. E. Tovstik -- Turning points and caustics in linear problems of thin shell free vibrations and buckling
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