Mathematical Modelling of Solids with Nonregular Boundaries (Hardcover)

Preface
Introduction
Equations of Linear Elasticity
Cracks and Inclusions
The Polya-Szego Matrix
The Concept of the Asymptotic Expansions
Exercises
Modelling of Cracks and Thin Inclusions in Elastic Media
Cracks with Smoothly Closed Edges
Thin Rectangular Holes
Formation of a Griffith's Crack in a Nonuniform Stress Field
Generalization of the Novozhilov Problem for Stationary Propagating Cracks
State of Stress in a Plane with a Thin Elastic Inclusion
Exercises
Domains with Conical and Cylindrical Boundaries
Stress-Strain State in a Neighbourhood of Conical Inclusions and Cavities
Asymptotics of Singularity Exponents at the Tip of an Angular Crack
Equations of Linear Elasticity in Thin Domains
Asymptotic Analysis of the Longitudinal Jump in Adhesively Bonded Joints
Lekhnitskii's Problems
Asymptotic Interpretation of Solutions to Lekhnitskii's Problem
Exercises
Stress-Strain State in the Vicinity of Sharp Inclusions
Asymptotic Behaviour of the Stress-Strain State in the Vicinity of Sharp Defects in an Elastic Body
On the Stress Concentration Near Soft and Rigid Cusp-Shaped Inclusions
Exercises
Integral Characteristics in Elasticity Problems for Nonhomogeneous Bodies
Integral Characteristics of Elastic Inclusions and Cavities in Two-Dimensional Theory of Elasticity
Vibration of Elastic Solids with Small Holes
Quasistatic Interaction of a Crack with Small Defects
Exercises
Appendix
References
Index