ME621A

Introduction to Solid Mechanics

Credits:


3L0T0L0D (9 Credits)



Course Content:
Mathematical Preliminaries: Vector and tensors calculus, Indicial notation. Strain: Definition of small strain, StrainDisplacement relations in 3D, Physical interpretation of strain components, Principal Strains. Stress and equilibrium: Stress components in 3D, Principal Stresses, Cauchy’s principle, stress equilibrium. Constitutive law, Navier’s equations, compatibility equations. Formulation of boundary value problems and solution methods: Plane Problems – plane stress, plane strain, antiplane shear. Fourier transform methods. Superposition principle. Additional topics from: Examples  Torsion of prismatic shaft, Contact problems, Wedge problems, Dislocations and inclusions, Cracks, Thinkfilm problems; Advanced transform methods  Complex variable techniques, Potential methods; Advanced ideas  Energy method, Numerical approaches, Finite elements, Eigenstrains, Micromechanics.
Lecturewise Breakup (based on 75min per lecture)
I. Introduction: (1 Lectures)
II. Mathematical Preliminaries: (4 Lectures)
III. Strains: (1 Lectures)

Definition of small strain, StrainDisplacement relations in 3D, Physical interpretation of strain components, Principal Strains.
IV. Stress and equilibrium: (4 Lectures)

Stress components in 3D and their physical interpretations. [1 Lecture]

Principal Stresses. [1 Lecture]

Cauchy’s principle and derivations of stress equilibrium equations in stress components. [2 Lectures]
V. Constitutive law, Navier’s equations, compatibility: (4 Lectures)

Constitutive law for general linear elastic solid, Discussions on isotropic, orthotropic and transversely isotropic solid.

Navier’s equations.

Stress and displacement approaches.

Compatibility equations.
VI. Formulation of boundary value problems and solution methods: (15 Lectures)

Formulation of boundary value problems. [1 Lecture]

Plane Problems – plane stress, plane strain, antiplane shear (also in axisymmetric coordinates). [2 Lectures]

Examples of plane problems: Stress function approach, Series solutions. [6 Lectures]

Fourier transform methods with examples. [3 Lectures]

Superposition principle: Flamant’s solutions; Kelvin’s solution; Boussinesq’s solution. [3 Lectures]
VII. Additional topics – a few topics to be selected from below: (1113 Lectures)

Further examples: Torsion of prismatic shaft; Contact problems; Wedge problems; Dislocations and inclusions; Cracks; Thinfilm problems.

Further methods: Advanced transform methods; Complex variable techniques; Potential methods.

Further ideas: Energy methods; Numerical approaches; Finite elements; Eigenstrains; Micromechanics.
References:

Elasticity, J. R. Barber

The Linearized Theory of Elasticity, W. L. Slaughter

Continuum Mechanics for Engineers, G. T. Mase and G. E. Mase

Theory of Elasticity, S. Timoshenko and J. N. Goodier

Elasticity: Theory, Applications and Numerics, M. H. Sadd

Applied Mechanics of Solids, A. Bower
