ME321

Advanced Mechanics of Solids

Credits:

 

 

2L-0T-1P-0A (7 Credits)

 

Pre-requisite:


ESO 202.

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.


Refernces:

  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.