Asymptotical Mechanics of Thin-Walled Structures : A Handbook (Foundations of Engineering Mechanics) (2004. II, 535 p. w. 91 figs.)

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Asymptotical Mechanics of Thin-Walled Structures : A Handbook (Foundations of Engineering Mechanics) (2004. II, 535 p. w. 91 figs.)

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  • 製本 Hardcover:ハードカバー版/ページ数 535 p.
  • 商品コード 9783540408765

Full Description


In this book a detailed and systematic treatment of asymptotic methods in the theory of plates and shells is presented. The main features of the book are the basic principles of asymptotics and their applications, traditional approaches such as regular and singular perturbations, as well as new approaches such as the composite equations approach. The book introduces the reader to the field of asymptotic simplification of the problems of the theory of plates and shells and will be useful as a handbook of methods of asymptotic integration. Providing a state-of-the-art review of asymptotic applications, this book will be useful as an introduction to the field for novices as well as a reference book for specialists.

Table of Contents

Preface                                            15 (2)
Acknowledgments 17 (2)
Asymptotic Approximations 19 (28)
Asymptotic series 19 (2)
Fundamental concepts of asymptotics [129] 21 (2)
Transformations of asymptotical series 23 (2)
[129]
Nonuniform expansions [129] 25 (2)
Non-dimensionalization 27 (2)
Asymptotics of integrals [129] 29 (18)
Regular Perturbations of Parameters 47 (70)
Eigenvalue problems 47 (11)
Stability of oval cylindrical shell 58 (2)
uniformly loaded by external pressure
Stability of the cantilever beam 60 (2)
Adjoint operators method 62 (3)
Transformation of coordinates and 65 (6)
variables
Asymptotic and real error 71 (4)
Numerical verification of asymptotic 75 (2)
solution
Removal of nonuniformities 77 (4)
Nonlinear vibrations of a stringer shell 81 (3)
Non-quasilinear asymptotics of nonlinear 84 (4)
system
Artificial small parameters 88 (3)
Method of small δ 91 (3)
Method of large δ 94 (4)
Choice of zero approximation 98 (3)
Lyapunov--Schmidt procedure 101(2)
Nonlinear periodical vibrations of 103(14)
continuous structures
Singular Perturbation Problems 117(40)
The method of 117(5)
Gol'denveizer-Vishik-Lyusternik [313,
645, 672, 673, 674]
Multiscale method 122(3)
Newton polygon and asymptotic integration 125(6)
parameters
Stretched plate bending 131(2)
Simplification of the static equations of 133(3)
a cylindrical shell
Boundary layer: Papkovitch approach 136(2)
Edge boundary layer 138(2)
Incorporating of the singular part of 140(1)
solution
Plane theory of elasticity 140(4)
Asymptotic foundation model 144(5)
Vibrations of reinforced conical shells 149(8)
Boundary Value Problems of Isotropic 157(12)
Cylindrical Shells
Governing relations 157(2)
Operator method 159(1)
Simplified boundary value problems 160(9)
Boundary Value Problems -- Orthotropic 169(32)
Shells
Governing relations 169(4)
Statical problems 173(9)
Non-linear dynamical problems 182(7)
Stability problems 189(8)
Error estimation using Newton's method 197(4)
Composite Boundary Value Problems -- 201(22)
Isotropic Shells
Statical problems 202(4)
Equations of higher order approximations 206(2)
Error estimation 208(3)
Dynamical problems 211(6)
Non-linear dynamical problems 217(6)
Composite Boundary Value Problems -- 223(18)
Orthotropic Shells
Statical problems 223(11)
Dynamical problems 234(1)
Non-linear dynamical problems 235(4)
Stability problems 239(2)
Averaging 241(18)
Two-scales approach 241(3)
Visco-elastic problems and `freezing' 244(2)
method
The successive change of variables 246(3)
Application of the Lie groups 249(7)
Whitham method (non-linear WKB approach) 256(3)
Continualization 259(8)
Homogenization 267(66)
ODEs with rapidly oscillating coefficients 267(5)
Axisymmetric bending of corrugated circle 272(4)
plate
Deformation of reinforced membrane 276(4)
Ribbed strip -- two-scale and Fourier 280(4)
homogenization
Ribbed plate -- direct homogenization 284(8)
Perforated membrane 292(10)
Composite with periodic cubic inclusions 302(5)
Torsion of bar with periodic 307(6)
parallelepiped inclusions
Solution of cell problem: perturbation of 313(6)
boundary form
Linear vibartions of a beam with 319(14)
concentrated masses and discrete supports
Intermediate Asymptotics -- Dynamical Edge 333(30)
Effect Method
Linear preliminaries 333(3)
Nonlinear beam vibrations 336(4)
Nonlinear rectangular plate vibrations 340(5)
Nonlinear shallow shell vibrations 345(8)
Rayleigh-Ritz-Bolotin approach 353(4)
Parallelogram plate vibrations 357(3)
Sectorial plate nonlinear vibrations 360(3)
Localization 363(14)
Localization in linear chains 363(7)
Localization in nonlinear chain 370(2)
Localization of shell buckling 372(1)
Localization of vibration in plates and 373(4)
shells
Improvement of Perturbation Series 377(40)
Pade approximants (PA) 377(2)
The effect of autocorrection 379(2)
Extending of perturbation series 381(3)
Improvement iterational procedures 384(3)
convergence
Nonuniformities elimination 387(1)
Error estimation of asymptotic approaches 388(1)
Localized solutions and blow-up phenomenon 388(1)
Gibbs phenomena 389(3)
Boundary conditions perturbation method 392(9)
Bifurcation problem 401(1)
Borel summation and superasymptotics 402(2)
Domb--Sykes plot [340, 659] 404(2)
Extraction of singularities from 406(3)
perturbation series [340, 659]
Analytical continuation [407] 409(8)
Matching of Limiting Asymptotic Expansions 417(18)
Two-point Pade approximants 417(7)
Quasifractional approximants 424(5)
Post-buckling behaviour of shallow convex 429(6)
shell
Complex Variables in Nonlinear Dynamics 435(28)
Nonlinear oscillator with cubic 436(11)
anharmonicity
System of two weakly coupled nonlinear 447(6)
oscillators
Nonlinear dynamics of an infinite chain 453(7)
of coupled oscillators
Nonlinear dynamics of an infinite chain 460(3)
of coupled particles
Other Asymptotical Approaches 463(20)
Matched asymptotic procedure 463(2)
Hilbert transform 465(2)
Normal forms in non-linear problems 467(3)
WKB - approach 470(3)
The WKB method and turning points 473(5)
A distributional approach 478(5)
AFTERWORD 483(6)
Asymptotics and Computers 483(2)
Are Asymptotic Methods a Panacea? 485(4)
References 489(40)
Subject index 529