Mechanics of Solids - CE6302

Mechanics of Solids

Types of Linearity
Displacements- Vectors and Tensors
Finite Linear Transformation
Symmetric and Asymmetric Components
Principal or Eigen value Representation
Field Theory
Deformation (Relative Displacement)
The Strain Tensor
The Stress Tensor
Components at an Arbitrary Orientation (Tensor Transformation)
Isotropic and Deviatoric Components
Principal Space and the Octahedral Representation
Two Dimensional Stress or Strain
Mohr's Circle for a Plane Tensor
Mohr's Circle in Three Dimensions
Stress-Strain Relationships (Rheology)
Linear Elastic Behavior
Equilibrium of a Differential Element
Orthogonal Coordinate Systems
Linear Viscous Behavior
Simple Viscoelastic Behavior
Fitting Laboratory Data with Viscoelastic Models
Elastic Viscoelastic Analogy
Elasticity and Plasticity
Yield of Ductile Materials
Yield(Slip) of Brittle Materials
Rational Mechanics
Strategies for Elastic Analysis and Design
Tactics for Analysis
St. Venant’s Principle
Two Dimensional Stress Formulation
Types of Partial Differential Field Equations
Properties of Elliptic Equations
The Conjugate Relationship Between Mean Stress and Rotation
The Deviatoric Field and Photoelasticity
Solutions by Potentials
Linear Free Fields: Isotropic Stress
Uniform Stress
Geostatic Fields
Uniform Acceleration of the Half space
Pure Bending of Prismatic Bars
Pure Bending of Plates
The Classic Stress-Function Approach
Airy’s Stress Function in Cartesian Coordinates
Polynomial Solutions and Straight Beams
Polar Coordinates and Airy’s Stress Function
Polar Coordinates and Airy’s Stress Function
Simplified Analysis of Curved Beams
Pure bending of a Beam of Circular Arc
Circular Beams with End Loads
Remarks for Two Dimensional Solutions for Straight and Circular Beams
Lame’s Solution for Rings under Pressure
Small Circular Holes in Plates, Tunnels, and Inclusions
Harmonic Holes and the Inverse Problem
Harmonic Holes for Free Fields
Harmonic Holes for Biaxial Fields
Harmonic Holes for Gradient Fields
Neutral Holes
Solution Tactics for Neutral Holes- Examples
Concentrated Loadings at the Apex
Uniform Loading Cases
Uniform Loading over a Finite Width
Non uniform Loadings on the Half-Space
Line Loads within the Half Space and Diametric Loading of a Circular Disk
Wedges with Constant Body Forces
Corner Effects Eigen function Strategy
St. Venant’s Formulation (Noncircular Cross Sections)
Prandtl’s Stress Function
Torsion: Membrane Analogy
Thin Walled Tubes of Arbitrary Shape
Hydrodynamic Analogy and Stress Concentration
Plastic Material Behavior
Plastic Structural Behavior
Plasticity Field Equations and Thick Ring
Limit Load by a “Work” Calculation
Theorems of Limit Analysis
The Lower Bound Theorem
The Upper Bound Theorem
The Bearing Capacity (Indentation) Problem
Plastic Bending
Plastic “Hinges”
Limit Load (Collapse) of Beams
Limit Analysis of Frames and Arches
Limit Analysis of Plates
Plastic Torsion
Combined Torsion with Tension and/or Bending
Slip Line Analysis
Mohr-Coulomb Criterion (Revisited)
Lateral “Pressures” and the Retaining Wall Problem
Graphic Analysis and Minimization
Slip Line Theory
Purely Cohesive Materials (?=0)
Weightless Material (? = 0)
Retaining Wall Solution for (EPS Material)
Comparison to the Coulomb Solution (?=0)
Slopes and Footings
Solutions for Weightless MohrCoulomb Materials
Slip Line Analysis: The General Case
An Approximate “Coulomb Mechanism”

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