Overview

Mechanics and mathematics have been complementary partners since Newton's time and the history of science shows much evidence of the beneficial influence of these disciplines on each other. Driven by increasingly elaborate modern technological applications the symbiotic relationship between mathematics and mechanics is continually growing. However, the increasingly large number of specialist journals has generated a duality gap between the two partners, and this gap is growing wider. This volume is intended to bridge this gap. It should be suitable for scientists, engineers and mathematicians, including advanced students (doctoral and post-doctoral level) at universities and in industry interested in modern mechanics and applied mathematics.

Full Product Details

Author:   Gao David Yang ,  Raymond W. Ogden
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2003 ed.
Volume:   4
Dimensions:   Width: 15.50cm , Height: 1.90cm , Length: 23.50cm
Weight:   0.730kg
ISBN:  

9781402076459

ISBN 10:   1402076452
Pages:   314
Publication Date:   31 October 2003
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Fracture Mechanics of Functionally Graded Materials.- 1 Introduction.- 2 Mechanics Models.- 3 Crack Tip Mechanics.- 4 Stress Intensity Factor Solutions.- 5 Fracture Toughness and Crack Growth Resistance Curve.- 6 Thermofracture Mechanics.- 7 Stationary Cracks in Viscoelastic FGMs.- 8 Fracture Dynamics.- 9 Fracture Simulation Using a Cohesive Zone Model.- 10 Concluding Remarks.- References.- 2 Topics in Mathematical Analysis of Viscoelastic Flow.- 1 Introduction.- 2 High Weissenberg number asymptotics.- 3 Instabilities in viscoelastic flows.- 4 Breakup of viscoelastic jets.- References.- 3 Selected Topics in Stochastic Wave Propagation.- 1 Basic Methods in Stochastic Wave Propagation.- 2 Towards Spectral Finite Elements for Random Media.- 3 Waves in Random 1-D Composites.- 4 Transient Waves in Heterogeneous Nonlinear Media.- 5 Acceleration Wavefronts in Nonlinear Media.- 6 Closure.- References.- 4 Periodic Soliton Resonances.- 1 Introduction.- 2 N-periodic soliton solutions to the KP equation with positive dispersion.- 3 Periodic soliton resonances I: solutions to the KP equation with positive dispersion.- 4 Periodic soliton solutions to the DS I equation.- 5 Periodic soliton resonances II: solutions to the DSI equation.- 6 Soliton stability theory due to periodic soliton resonance solution.- 7 Summary.- References.- 5 Nonconvex Semi-Linear Problems and Canonical Duality Solutions.- 1 Nonconvex Problems and New Phenomena.- 2 Canonical Duality Theory: A brief Review.- 3 Canonical Dual Theory and Solutions.- 4 Applications to Unconstrained Global Optimization.- 5 Application to Constrained Quadratic Programming.- 6 Quadratic Programming Over a Sphere.- 7 Concluding Remarks.- References.

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