IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics

Thissymposiumwasorganisedtoprovidecross-linkingofresearchact- ities in the following areas of Applied Mathematics, Continuum Mechanics and Theoretical Physics: Perturbation problems for partial di?erential equations and their - plications in mechanics; Homogenisation theory in models of composite structures; Fracture. Mathematical models of cracks in solids; Wave propagation, scattering; Models of photonic and phononic band gap composite materials; Models of dislocations in lattice structures; Asymptotic and numerical models of imperfect interfaces. Thetopicscoveredinthisvolumerepresenttheresultsoftherecentwork in wave propagation and scattering, asymptotics for eigenvalue problems, analysis of localised defect modes , mathematical models of cracks and damage in solids, homogenisation approximations and models of comp- ites, modelsofplatesandshells, analysisofphysical?eldsnearnon-smooth boundaries, modelling of gas and ?uid ?ows, non-linear waves, models of combustion and advanced numerical methods. All the papers included in this volume have been carefully refereed. The Appendix, at the end of the volume, includes the complete programme of the meeting. The International Scienti?c Committee responsible for the Symposium comprised of the following: Prof. A.B. Movchan (UK) - Chairman, Prof. I.D. Abrahams (UK), Prof. A. Aslanyan (Russia), Prof. D. Bigoni (Italy), Prof. H. Gao (Germany/USA), Prof. K.Z. Markov (Bulgaria), Prof. R.C. McPhedran (Australia), Prof. J. Salencon (France), Prof. W. Wendland (Germany). On behalf of the Scienti?c Committee, I would like to acknowledge the ?nancial support for the Symposium from International Union of Theoretical and Applied Mechanics, 1 A.B. Movchan (ed.), IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, 1 2.

Contributes towards wider dissemination of the recent developments in asymptotic analysis, mathematical modelling in continuum mechanics and engineering applications

Klappentext

Homogenisation in Problems of Mechanics, 1-2.

Zusammenfassung
Proceedings of the IUTAM Symposium held in Liverpool, UK, 8-11 July 2002

Inhalt
Wave propagation and scattering.- Asymptotic Analysis of Higher Order Peripheral Modes in Acoustic Wave Scattering by an Elastic Cylinder or Sphere.- Embedding Formulas and Singularities in Acoustic Scattering.- Numerical Investigation of Photonic Crystal Fibers by Spectral and Multipole Methods.- Method of Hyperelliptic Surfaces for Vector Functional-Difference Equations.- Dynamics of Charge Rotators and Lattice Waves in a Plasma Environment.- Propagation of Elastic Waves along Interfaces in Layered Beams.- Low Frequency Band Gaps and Localised Modes for Arrays of Coated Inclusions.- Phononic Band Gap Structures as Optimal Designs.- A Parametric Investigation of the Acoustic Power in a Two-Dimensional Waveguide with Membrane Bounded Cavity.- Vibrations of a Circular Cylinder in Oblique Incidence Revisited.- Asymptotic Analysis of a Crack in a Layer of Finite Thickness.- Summation of Gaussian Beams in 3D Problems of Radiation and Scattering of Elastic Waves.- Asymptotics for eigenvalue problems.- Asymptotics for the First Six Eigenfrequencies of a 1D-3D Multi-Structure.- The Two-Term Interior Asymptotic Expansion in the Case of Low-frequency Longitudinal Vibrations of an Elongated Elastic Rectangle.- Transverse Propagating Waves in Perturbed Periodic Structures.- Anti-plane Harmonic Problems for a Class of Elastic Materials with Functional Inhomogeneity.- On Analysing the Performance of a Dissipative Silencer: A Mode-Matching Approach.- Green's functions and defect modes.- Localized Green's Functions for a Two-Dimensional Periodic Material.- Boundary Algebraic Equations for Lattice Problems.- Mathematical models of cracks.- Dynamic Perturbation of A Propagating Crack: Implications for Crack Stability.- Dynamic Crack Stability.- A Thermoelasticity Problem in aDomain with an Edge Crack: Asymptotic Analysis.- Methods of Assessment of Thermal Striping Fatigue Damage.- Near-Tip Fields of Mode III Steady-State Crack Propagation in Elastic-Plastic Strain Gradient Solids.- Mode III Interface Crack Lying at Thin Nonhomogeneous Anisotropic Interface. Asymptotics Near the Crack Tip.- Fracture Criterion for Cracks with Bridged Zone.- Models of damage in solids.- Dynamics of Damage in Two-Dimensional Structures With Waiting Links.- Local and Non-Local Approaches to Fatigue Crack Initiation and Propagation.- A Variational Approach to Modelling Initiation of Fracture in NonLinear Elasticity.- Modeling Fracture in Nano Materials.- Boundary Elements and Shear Bands in Incremental Elasticity.- Homogenisation analysis and models of composite media.- Spectral Coupling of Effective Properties of a Random Mixture.- Homogenization Techniques Applied to Earthquake Problems.- Stochastic Homogenisation of Fluid Flows in Heterogeneous Porous Media.- On Micromechanics-Based Nonlocal Modeling of Elastic Matrices Containing Non-Spherical Heterogeneities.- Artificial Ferro-Magnetic Anisotropy: Homogenization of 3D Finite Photonic Crystals.- Homogenized Stiffnesses of Periodic Fibre-Reinforced Composites.- Asymptotic Homogenisation in Strength and Fatigue Durability Analysis of Composites.- Models associated with elastic plates, shells, rods and thin-walled composite structures.- On a Kind of Singular Perturbations for Transmission Problems.- Asymptotics of Laminated Shells. Membrane Bending Coupling and Numerical Implementation.- Exact Singular Solutions for an Inhomogeneous Thick Elastic Plate.- Stretch, Flexure and Twist in Finite Elasticity.- Asymptotic Analysis of Heat Transfer in a System of Channels Connected by Thin Conducting Walls.-Asymptotics of fields near non-smooth boundaries.- Effect of a Thin Coating on the Stress Singularity at the Vertex of a Thin Conical Inclusion.- 3D Singularities with Applications to Fatigue Crack Growth.- Mathematical models of gas and fluid flows.- A Diffusing Vortex Circle in a Viscous Fluid.- Low Axial Reynolds Number, High Swirl Ratio, Vortex Breakdown in a Slowly Varying Tube.- Supersonic Leading-Edge Noise.- Non-linear waves.- Envelope Equations for Modulated Non-Conservative Waves.- Nonlinear Waves in a Bi-Layer and Coupled Klein-Gordon Equations.- Combustion models.- Nonmodal Instability as the Mechanism of Acceleration of Cellular Flames.- Catalytic Combustion: Making the Connection between the Physical/Chemical Processes and the Mathematical Model of the Reactor.- Asymptotic approximations for orbital perturbations.- The use of Lie Series Generating Functions to Derive Asymptotic Series Expressions for Orbital Perturbations.- Advanced numerical techniques.- Inverse Iteration for Nonlinear Eigenvalue Problems in Electromagnetic Scattering.- Fast Iterative Solution of Coupled 3-Dimensional Fluid-Structure Interaction Problems.- Preconditioning for Finger Pattern Matrices Arising from Wavelet Discretisations of Boundary Integral Equations.