## Asymptotic Methods in MechanicsR mi Vaillancourt, Andrei L. Smirnov 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. |

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### Contents

5 | |

Singular Perturbation of Linear Differential Equations | 23 |

CHAPTER 3 Degenerate Boundary Value Problems | 61 |

Asymptotic Solutions of Partial Differential Equations | 81 |

Asymptotic Solutions of Nonlinear Differential Equations | 103 |

Thirteen Papers | 141 |

### Common terms and phrases

airfoil analytical approximation asymptotic analysis asymptotic expansions asymptotic integration Asymptotic Methods asymptotic series asymptotic solution axisymmetric beam bending bifurcation boundary conditions boundary value problem buckling mode coefficients consider corresponding critical load CRM Proceedings cylindrical shell deflection deformations degeneracy determined displacement eddy current edge effect eigenfunctions eigenvalue English transl equilibrium formulae free vibrations frequencies functions Gaussian curvature index of variation Lecture Notes Leningrad University Leningrad University Press Math Mathematics Mathematics Subject Classification Mech Mechanics A. L. Smirnov Methods in Mechanics momentless Moscow Nauk SSSR Mekh Nauka negative Gaussian curvature neighbourhood neutral surface nonlinear obtained ordinary differential equations P. E. Tovstik perturbation Petersburg State University polynomials Prikl Proceedings and Lecture roots rotation Russian S. B. Filippov saddle point satisfy shell theory shell thickness shells of revolution small parameter stability thin elastic shells thin shells turning points Tverd Univ Vaillancourt variables velocity Vestnik Leningrad zero

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Page xvii - This work was supported in part by the Natural Sciences and Engineering Research Council of Canada...