Trends in Applications of Mathematics to Mechanics

In many areas of mechanics the interplay between mathematics and physics is crucial for understanding not only underlying principles but also practical applications. This is particularly the case in hydrodynamics and elasticity. Over thirty articles in this volume discuss various aspects including perturbation methods and applications, instability, bifurcations and transition to chaos, multibody dynamics and control, mechanics and mathematics of non-classical materials, and new interactions of mathematics and mechanics. The book addresses scientists and engineers working in these areas including those interested in applied mathematical analysis.

I Perturbation Methods and Applications.- Asymptotic Analysis of Stabilizing Fronts.- Boundary Layer Analysis for Some Problems of Singular Domain Perturbation.- Global Behaviour of Very Thin Cellular Structures. Applications to Networks.- Nonlinear Diffusion in Stellar Magnetic Loops.- Perturbation Solutions of Magnetomechanical Signal Processing Devices.- An Asymptotic Theory for a System of Weakly Nonlinear Wave Equations.- II Instability, Bifurcations and Transition to Chaos.- Quasi-Codimension 3 Bifurcation of Invariant T2 Tori for Maps.- Generalized Lieb-Thirring Inequalities and the Dimension of Attractors Associated to the Ginzburg-Landau p.d.e..- Low Order Spectral Models in Hydrodynamics.- Asymptotical Behaviour of Solutions to Quasi-Linear Schrödinger Equations.- Lyapounov Stability of Electro-Magneto-Elastic Systems.- Criticality of an Exothermic Reaction-Diffusion System of nth-Order.- Flow Induced Bifurcations to Three-Dimensional Motions of Tubes with an Elastic Support.- Local and Global Bifurcations of a Three Particle System.- III Multibody Dynamics and Control.- Multibody System Dynamics Mathematical Theory and Industrial Applications.- A Finite Element Dynamic Analysis of Robotic Manipulators with Flexible Links.- IV Mechanics and Mathematics of Non-Classical Materials.- Mathematical Modelling for Non-Classical Materials.- Nonstandard Modelling of Certain Quasi-Stationary Debonding Processes in Laminates.- Multilevel Model of Micro-Macro Interactions and Residual Stresses in Physical Systems.- Hemivariational Inequalities and Their Applications to Composite Material Structures.- Poiseuille Flows of Incompressible Simple Fluids.- Properly Posed Boundary Condition and the Existence Theorem for Supefluid He4.- Mathematical Aspects of the Theory of Viscoelasticity.- V New Interactions of Mathematics and Mechanics.- On Saint-Venant's Problem and Saint-Venant's Principle in Nonlinear Elasticity.- Hypermembrane Shells.- On the Problem of Constructing the Mathematical Theory of Plates and Shells.- Application of Extremum Principles to Mixed Boundary-Value Problems in Non-linear Elasticity.- Application of Bivariate B-Splines to a Plate Bending Problem.- Entropy and Dynamical Stability - a Method Due to Lagrange-Formalism as Applied to Thermodynamics of Irreversible Processes.- A Thermodynamic Theory for Turbulence.- Approach to Lower Dimensional Dynamical Systems: Thermodynamical Aspects.- A Functional Analytic Approach to an Optimization Problem of Hydrodynamic Propulsion.- Nonlinear Problems in the Kinetic Theory of Gases.- Index of Contributors.