Introduction to Unified Theory of Elasticity. Translational and Rotational Equilibrium of 3D Infinitesimal Element in Cartesian Coordinates. Direct and Shear Strains in terms of Displacements. 3D Equations of Compatibility. Body Forces. Potential Functions. Stress-Strain and Strain-Stress Relations. Airy Stress Function. Biharmonic and Laplacian Equation Development for Plane Stress/Strain. Plane Stress to Plane Strain Transformations. Effect of Non-uniform Temperature Field in an Elastic Body.

Integrated Elasticity Application Solutions using Airy Stress Function Approach. Inverse, Semi-Inverse, Combination of Polynomials of Various Order. Boundary Condition, Equilibrium and Compatibility Criteria Achievement for Cartesian Coordinate Applications. Solution Initiation Assumptions. Comprehensive Stress and Deflection Elasticity Calculation. Comparison with Strength of Materials Solutions.

Equations of Equilibrium, Compatibility, Stress/Strain Relations, Biharmonic and Laplacian equations development in Polar Coordinates. Cartesian/Polar Transformations. Stress Function Solutions in Polar Coordinates. Axisymmetric and Asymmetric Applications – Curved Beams, Solid Shafts, Thick Cylinders. Comparison of Elasticity and Strength of Materials Solutions. Stress Concentration in a Circular Hole in a Tension Field. Stress Concentration Factors. Concentrated Load Line Solutions. Wedge subjected to Axial and Transverse Loads. Neubers Nomograph Design Approach. Un-reinforced and Reinforced Cut-Out Stress Analysis. Design of Neutral Holes.

Semi-Infinite Solid Contact Stress Variation Analysis. Calculation of Contact Area Shape and Size and Maximum Contact Pressure. Cylinders in Contact. Determination of Relative Displacement, Contact Area and Maximum Stress. Pin in Concave. Cylinder on Flat Surface. Hertz Solution for 3D Variable Curvature Contacting Bodies. Sphere to Sphere, Sphere to Flat, Sphere to Concave Contact Design Solutions.

Small Deflection Theory for Homogeneous Uniform Plates. Stress, Curvature and Moment Relations. The Differential Equation of Plate Deflection. Boundary Conditions. Simply Supported Rectangular Plates. Navier’s Solution. Infinite Beam. Applied Solutions including Reaction Distribution Solution and Assumption Assessment. Axisymmetrically Loaded Circular Plates. Elasticity Solutions for various Boundary Conditions, Shape and Loading Configurations. The Finite Difference Solution. The Grid Representation Method. The Finite Element Solution. Assessment of Numerical Methods to achieve Converged Solutions for various Boundary Conditions, Shape, Loading Configurations and Mesh Densities.

Assumptions and Development of Thin Shell Theory. Simple Membrane Action. Bending versus Membrane Stresses as Load Carrying Mechanisms. Local Buckling. Geometry of Shells of Revolution. Meridional and Tangential Equilibrium and Stress and Deflection Analysis of Symmetrically Loaded Shells of Revolution. Comparison of Elasticity and Strength of Material Solutions for spherical, conical and cylindrical shells. Advanced Elasticity Applied Solutions The Finite Element Solution for various Boundary Conditions, Shape, Loading Configurations and Mesh Densities.

Torsion of Prismatic Bars of Arbitrary Cross-section. General Solution of the Torsion Problem. Displacement / Strain / Stress Relations. Development of Equations of Equilibrium and Compatibility. Prandtl Stess Function. Poisson’s Equation. Traction Boundary Conditions for Solid and Multiply Connected Members. Torsion Stress Surface and Contours. Relationship between Torque and Stress. Torsion Elasticity Solution for Elliptical Member. Shear Stress, Angle of Twist and Warpage Determination. Prandtl’s Membrane Analogy. Experimental Application. Torsion of Thin Walled Members of Open Cross-section. Torsion of Multiply Connected Thin Wall Members. Membrane Analogy for Thin Walled Members. Development and Application of Bredt’s Formulae. Fluid Flow Analogy. Torsion of Restrained Thin Walled Members of Open Cross-section. The Finite Element Solution.