Asymptotic methods in mechanics of solids
Birkhäuser, 30 мая 2015 г. - Всего страниц: 325
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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2 Asymptotic Estimates for Integrals
3 Regular Perturbation of Ordinary Differential Equations
4 Singularly Perturbed Linear Ordinary Differential Equations
5 Singularly Perturbed Linear Ordinary Differential Equations with Turning Points
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Ai(n analytic assume asymptotic expansion asymptotic methods asymptotic series asymptotic solution beam boundary conditions boundary value problem buckling Cauchy problem characteristic equation Consider construct corresponding cosz curve cylindrical shell dashed line domain edge effect integrals eigenfunctions eigenvalue problem eigenvectors equal exact solution Example Exercise fastest descent Find the asymptotic free vibrations freely supported function F initial conditions linear lines of fastest main terms matrix membrane multiplicity neighborhood Newton polygon non-dimensional numerical solution obtain Ordinary Differential Equations periodic solution perturbed phase curves plotted roots of equation saddle points satisfy Sect seek a solution shell of revolution simple root small parameter solution of equation solution of system stationary point Substituting system of equations turning points unperturbed problem variable variation index vector vibrations frequencies zero zeroth approximation