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