AMOS MODULE BASED SYLLABUS

 

MODULE 1

Introduction to stress analysis in elastic solids - stress at a point — stress tensor — stress components in rectangular and polar coordinate systems - Cauchy’s equations — stress transformation — principal stresses and planes - hydrostatic and deviatoric stress components, octahedral shear stress - equations of equilibrium

Displacement field — engineering strain - strain tensor (basics only) - analogy between stress and strain tensors - strain-displacement relations (small-strain only) — compatibility conditions

MODULE 2

Constitutive equations — generalized Hooke’s law — equations for linear elastic isotropic solids - relation among elastic constants — Boundary conditions — St. Venant’s principle for end effects — uniqueness theorem

2-D problems in elasticity - Plane stress and plane strain problems - stress compatibility equation - Airy’s stress function and equation - polynomial method of solution — solution for bending of a cantilever with an end load

MODULE 3

Equations in polar coordinates (2D) — equilibrium equations, strain- displacement relations, Airy’s equation, stress function and _ stress components (only short derivations for examination)

Application of stress function to Lame’s problem and _ stress concentration problem of a small hole in a large plate (only stress distribution)

Axisymmetric problems — governing equations — application to thick cylinders, rotating discs.

MODULE 4

Unsymmetrical bending of straight beams (problems having c/s with one axis of symmetry only) — curved beams (rectangular c/s only) – shear center of thin walled open sections (c/s with one axis of symmetry only)

Strain energy of deformation — special cases of a body subjected to concentrated loads, moment or torque - reciprocal relation — strain| energy of a bar subjected to axial force, shear force, bending moment and torque.

MODULE 5

Maxwell reciprocal theorem — Castigliano’s first and second theorems — virtual work principle — minimum potential energy theorem.

Torsion of non-circular bars: Saint Venant’s theory - solutions for circular and elliptical cross-sections

 MODULE 6

Prandtl’s method - solutions for circular and elliptical cross-sections - membrane analogy.

Torsion of thin walled tubes, thin rectangular sections, rolled sections and multiply connected sections.

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