Asymptotic methods in the theory of plates with mixed boundary conditions /

• Κύριος συγγραφέας: Andrianov, I. V. (Igorʹ Vasilʹevich), 1948-
• Άλλοι συγγραφείς: Awrejcewicz, J. (Jan), Danishevskiĭ, V. V. (Vladislav Valentinovich), Ivankov, Andrey
• Μορφή: Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Chichester, West Sussex, United Kingdom : John Wiley & Sons, Ltd., 2014.
• Θέματα: Plates (Engineering) > Mathematical models.; Asymptotic expansions.; Finite element method.; Plates (Engineering); TECHNOLOGY & ENGINEERING > Civil > General.; Electronic books.

This book covers the theoretical background of asymptotic approaches and their use in solving mechanical engineering-oriented problems of structural members, primarily plates (statics and dynamics) with mixed boundary conditions. Key features: Includes analytical solving of mixed boundary value prob...

Πίνακας περιεχομένων:

• Cover; Title Page; Copyright; Contents; Preface; List of Abbreviations; Chapter 1 Asymptotic Approaches; 1.1 Asymptotic Series and Approximations; 1.1.1 Asymptotic Series; 1.1.2 Asymptotic Symbols and Nomenclatures; 1.2 Some Nonstandard Perturbation Procedures; 1.2.1 Choice of Small Parameters; 1.2.2 Homotopy Perturbation Method; 1.2.3 Method of Small Delta; 1.2.4 Method of Large Delta; 1.2.5 Application of Distributions; 1.3 Summation of Asymptotic Series; 1.3.1 Analysis of Power Series; 1.3.2 Padé Approximants and Continued Fractions; 1.4 Some Applications of PA.
• 1.4.1 Accelerating Convergence of Iterative Processes1.4.2 Removing Singularities and Reducing the Gibbs-Wilbraham Effect; 1.4.3 Localized Solutions; 1.4.4 Hermite-Padé Approximations and Bifurcation Problem; 1.4.5 Estimates of Effective Characteristics of Composite Materials; 1.4.6 Continualization; 1.4.7 Rational Interpolation; 1.4.8 Some Other Applications; 1.5 Matching of Limiting Asymptotic Expansions; 1.5.1 Method of Asymptotically Equivalent Functions for Inversion of Laplace Transform; 1.5.2 Two-Point PA; 1.5.3 Other Methods of AEFs Construction; 1.5.4 Example: Schrödinger Equation.
• 1.5.5 Example: AEFs in the Theory of Composites1.6 Dynamical Edge Effect Method; 1.6.1 Linear Vibrations of a Rod; 1.6.2 Nonlinear Vibrations of a Rod; 1.6.3 Nonlinear Vibrations of a Rectangular Plate; 1.6.4 Matching of Asymptotic and Variational Approaches; 1.6.5 On the Normal Forms of Nonlinear Vibrations of Continuous Systems; 1.7 Continualization; 1.7.1 Discrete and Continuum Models in Mechanics; 1.7.2 Chain of Elastically Coupled Masses; 1.7.3 Classical Continuum Approximation; 1.7.4 ""Splashes''; 1.7.5 Envelope Continualization; 1.7.6 Improvement Continuum Approximations.
• 1.7.7 Forced Oscillations1.8 Averaging and Homogenization; 1.8.1 Averaging via Multiscale Method; 1.8.2 Frozing in Viscoelastic Problems; 1.8.3 The WKB Method; 1.8.4 Method of Kuzmak-Whitham (Nonlinear WKB Method); 1.8.5 Differential Equations with Quickly Changing Coefficients; 1.8.6 Differential Equation with Periodically Discontinuous Coefficients; 1.8.7 Periodically Perforated Domain; 1.8.8 Waves in Periodically Nonhomogenous Media; References; Chapter 2 Computational Methods for Plates and Beams with Mixed Boundary Conditions; 2.1 Introduction.
• 2.1.1 Computational Methods of Plates with Mixed Boundary Conditions2.1.2 Method of Boundary Conditions Perturbation; 2.2 Natural Vibrations of Beams and Plates; 2.2.1 Natural Vibrations of a Clamped Beam; 2.2.2 Natural Vibration of a Beam with Free Ends; 2.2.3 Natural Vibrations of a Clamped Rectangular Plate; 2.2.4 Natural Vibrations of the Orthotropic Plate with Free Edges Lying on an Elastic Foundation; 2.2.5 Natural Vibrations of the Plate with Mixed Boundary Conditions ""Clamping-Simple Support''; 2.2.6 Comparison of Theoretical and Experimental Results.