Week
1: Introduction and
Mathematical Preliminaries: Tensor algebra and indicial notation,
Transformation of tensors, Tensor calculus.
Week
2: Deformation and Strain: Lagrangian
and Eulerian descriptions of deformation, Deformation gradient tensor,
Green-Lagrange and Eulerian strain tensors, Infinitesimal strain tensor,
Dilation, Strain compatibility equations.
Week
3: Stress Measures and Balance Laws:
Surface traction vector, Cauchy stress tensor at a point, Cauchy stress
formula, First and second Piola Kirchhoff stress tensors, Mass, momentum,
angular momentum, and energy balance, Stress power.
Week
4: Constitutive Relations: Generalized
Hooke’s law for linear elastic solids, Concept of material symmetry, Elastic stiffness
tensors for monoclinic, orthotropic, transversely isotropic and isotropic
materials, Strain energy density function, Hyperelasticity.
Week
5: Field Equations of Elasticity:
Problem formulation using field equations of elasticity, Stress and
displacement based solution techniques, Lame-Navier equations and
Beltrami-Michell equations, Different elasticity theorems.
Week
6: Stress
Functions and Planar Elastic Problems: Stress
functions, Plane stress formulation, Plane strain formulation, Anti-plane
strain problems, Effect of body forces, Different forms of stress functions.
Week
7: Planar Bending Problems: Stress
functions for solving bending of straight beams, Pure bending problem, Beams
subjected to concentrated and distributed transverse loading.
Week
8: Torsional Problems: Torsion of
prismatic shaft using Prandtl’s stress function, Solution for elliptical,
triangular, and rectangular shafts, Torsion of hollow sections.
Week
9: Problems in Polar Coordinates I:
Field equations in polar coordinates, Stress functions in polar coordinate,
General Michell solution, Axisymmetric problem solution, Bending of curved
beams.
Week
10: Problems in Polar
Coordinates II: Semi-infinite domain problems involving elastic half space,
quarter plane, and plane elastic wedge under different loading conditions.
Week
11: Problems in Polar
Coordinates III: Notch and crack problems, Rotating disc problems, Stress
concentration around a hole within a plate subjected to tension.
Week
12: Advanced Topics: Disk
under diametrical compression, Plane elastic contact problem solution,
Thermo-elastic deformation problems.
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