Course Content:

Introduction to Cartesian tensors; Strains: Concept of strain, derivation of small strain tensor and compatibility; Stress: Derivation of Cauchy relations and, equilibrium and symmetry equations, principal stresses and directions; Constitutive equations: Generalized Hooke’s law including thermoelasticity, Material symmetry; Boundary Value Problems: Definition of the bvp in linear elasticity including concepts of uniqueness and superposition; 2-d plane stress and plane strain problems, introduction to governing equations in cylindrical and spherical coordinates, axisymmetric problems (examples may include problems on curved beams, thermoelasticity, torsion of non-circular cross sections, contact problems in 2-d, problems on wedges and crack tip fields); 3-d problems by potential methods; Energy methods and problems.

Lecturewise Breakup

I. Introduction to Cartesian tensors: (3 Lectures)

II. Strains: Concept of strain, derivation of small strain tensor and compatibility: (3 Lectures)

III. Stress: Derivation of Cauchy relations and, equilibrium and symmetry equations, principal stresses and directions: (3 Lectures)

IV. Constitutive equations: Generalized Hooke’s law including thermoelasticity, Material symmetry: (3 Lectures)

V. Definition of the bvp in linear elasticity including concepts of uniqueness and superposition: (1 Lecture)

VI. 2-d plane stress and plane strain problems, introduction to governing equations in cylindrical and spherical coordinates, axisymmetric problems (examples may include problems on curved beams, thermoelasticity, torsion of non-circular cross   sections, contact problems in 2-d, problems on wedges and crack tip fields): (8 Lectures)

VII. 3-d problems by potential methods: (2 Lectures)

VIII. Energy methods and problems: (3 Lectures)

Laboratory sessions:

I. Application of strain gauge techniques: Lecture on strain gauge based methods, Cantilever beam and Portal frame experiments.

II. Application of Strain Gauge techniques: Experiment on combined bending and torsion.

III. Applications of photoelasticity: Demonstration of photoelastic techniques.

IV. Applications of photoelasticity: Calibration of the photoelastic constant, Determination of the stress field in a beam under bending.

V. Applications of Digital Image Correlation: Demonstration of DIC techniques, determination of strain fields in the gauge section of a polymeric dogbone specimen under tension.

VI. Applications of DIC: Determination of thermoelastic stress and strain fields using DIC.

References

1. Timoshenko and Goodier, Theory of Elasticity, McGraw Hill Publishing Company, 1970.
2. Bower, Applied Mechanics of Solids, CRC Press, 2009.
3. Saad, Elasticity: Theory Application and Numerics, Academic Press, 2004.