Analysis of Stress:
Definition and Notation for forces and stresses. Body force, surface force, components of stresses, equations of equilibrium, specification of stress at a point. Principal stresses, maximum and minimum shear stress, Mohr’s diagram in three dimensions. Boundary conditions. Stress components on an arbitrary plane, stress invariants, octahedral stresses, decomposition of state of stress, deviator and spherical stress tensors, stress transformation.
Deformation and Strain:
Deformation, strain Displacement relations, strain components, The state of strain at a point, Principal strain, strain invariants, Strain transformation, Compatibility equations, Cubical dilatation, spherical and deviator strains, plane strain, Mohr’s circle, and compatibility equation.
Relations and the General Equations of Elasticity:
Generalized Hooke's; law in terms of engineering constants. Formulation of elasticity Problems.
Two Dimensional Problems in Cartesian Co-Ordinates:
Airy's stress function, investigation of simple beam problems. Bending of a narrow cantilever beam under end load, simply supported beam with uniform load, Use of Fourier series to solve two dimensional problems. Existence and uniqueness of solution, Saint -Venant's principle, Principle of super position and reciprocal theorem.
Two Dimensional Problems in Polar Co-Ordinates:
General equations, stress distribution symmetrical about an axis, strain components in polar co-ordinates, Rotatingdisk and cylinder, Concentrated force on semi-infinite plane, Stress concentration around a circular hole in an infinite plate.
Thermal Stresses:
Introduction, Thermo-elastic stress -strain relations, thin circular disc, long circular cylinder.
Torsion of Prismatic Bars:
Introduction, Torsion of circular cross section bars, Torsion of elliptical cross section bars, Soap film analogy, Membrane analogy, Torsion of thin walled open tubes.
Elastic Stability:
Axial compression of prismatic bars, Elastic stability, buckling load for column with constant cross section.
Viscoelasticity:
Linear Viscoelastic behavior. Simple viscoelastic models-generalized models, linear differential operator equation. Creep and Relaxation- creep function, relaxation function, hereditary integrals. Complex modulii and compliances. (Note: No numericals)