APPLIED ELASTICITY & PLASTICITY 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
APPLIED ELASTICITY & PLASTICITY
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
Generalized plane stress and plane strain
Complex variable methods
The San Andreas Fault
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
Stress distribution around circular notches
Velocity and acceleration
Generalized plane stress
A spinning disc
A gravitating sphere
Chapter-4 Large deformation theory
Lagrange an and eulerian strain
Material coordinates
The state of stress
Elementary solutions
Incompressible of continua
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