Advances in Mechanics and Mathematics

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.