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APPLIED ELASTICITY

 

Table of contents

Preface

Chapter-1 Matrix methods

Summary of matrix properties

Vector representation

Coordinate transferation

Differential operators

The strain matrix

The stress matrix

Isotropic elasticity

Linear anisotropic behavior

Engineering theory of beams

Engineering theory of plates

Applications and worked examples

Graphical representation of failure criteria for isotropic materials

Prandti ‘s stress function for uniform torsion

Bulk modulus

A tension test

Problems

2 Chapter Cartesian tensors

Vector and matrix representation

Coordinate transformation

Differentiation

Representation of strain

Representation of stress

Thermoplastic behavior  

Isotropic materials

Applications and worked examples

Generalized plane stress and plane strain

Complex variable methods

The San Andreas Fault

Problems

Chapter-3 Curvilinear tensors

Base vectors

Metric tensors

Higher order tensors

Vector products

Orthogonal coordinate systems

Covariant differentiation

Strain and stress tensors

Elastic behavior

Membrane theory of thin shells

Applications and worked examples

Stress distribution around circular notches

Velocity and acceleration

Generalized plane stress

A spinning disc

A gravitating sphere

Problems   

Chapter-4 Large deformation theory

Lagrange an and eulerian strain

Material coordinates

The state of stress

Elementary solutions

Incompressible of continua

Problems