Analysis of Stress and Strain: Stress at a point; stress tensor; stress transformations; principal stresses; octahedral stress; geometrical representation of stress at a point; equations of equilibrium.
Infinitesimal affine transformation for deformation; strain tensor; principal strains; strain-displacement relations for finite and infinitesimal strains; compatibility conditions. Constitutive Equations: General theory; generalized Hooke’s law for anisotropic and isotropic materials.
Equations of Elasticity: Common equations of elasticity theory like Mitchel-Beltrami and Navier equations, formulation of the general elasticity problem; boundary conditions
Solution of Some Special Boundary Value Problems: Simplifications; two-dimensional problems in rectangular and polar coordinates; Airy’s stress function; a few problems like stress concentration around a circular hole and Boussinesq problem.
A few representative three-dimensional problems; torsion and bending of non – circular prismatic bars (Saint- Venant’s solution); membrane analogy, Simple Plate bending