Mathematical Modelling of Solids with Nonregular Boundaries: 1st Edition (Hardback) book cover

Mathematical Modelling of Solids with Nonregular Boundaries

1st Edition

By A.B. Movchan, N.V. Movchan

CRC Press

352 pages

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Hardback: 9780849383380
pub: 1995-07-25
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Description

Mathematical Modelling of Solids with Nonregular Boundaries demonstrates the use of asymptotic methods and other analytical techniques for investigating problems in solid mechanics. Applications to solids with nonregular boundaries are described in detail, providing precise and rigorous treatment of current methods and techniques. The book addresses problems in fracture mechanics of inhomogeneous media and illustrates applications in strength analysis and in geophysics. The rigorous approach allows the reader to explicitly analyze the stress-strain state in continuous media with cavities or inclusions, in composite materials with small defects, and in elastic solids with sharp inclusions. Effective asymptotic procedures for eigenvalue problems in domains with small defects are clearly outlined, and methods for analyzing singularly perturbed boundary value problems are examined.

Introductory material is provided in the first chapter of Mathematical Modelling of Solids with Nonregular Boundaries, which presents a survey of relevant and necessary information, including equations of linear elasticity and formulations of the boundary value problems. Background information - in the form of definitions and general solutions - is also provided on elasticity problems in various bounded and unbounded domains. This book is an excellent resource for students, applied scientists, and engineers.

Reviews

"Of interest to advanced graduate students and scientists who work in the area of fracture mechanics."

- Applied Mechanics Reviews, Volume 49, Number 3, March 1996

Table of Contents

Preface

Introduction

Equations of Linear Elasticity

Cracks and Inclusions

The Pólya-Szegö 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

About the Series

Mathematical Modeling

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
TEC021000
TECHNOLOGY & ENGINEERING / Material Science