JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisite

Mechanics of solids

Course Objectives

The objectives of this course are to introduce graduate and senor undergraduate’s

students to advanced topics in linear elasticity. Students will build on the knowledge gained through all mechanical related courses of the undergraduate curriculum (statics, mechanics of materials etc)

Course outcomes: After completing this course, the student should be able to:

• Deriving the governing equations for 2D and 3D elastic problems.
• Solve these problems with various solution methodologies.

UNIT - I

Introduction: Elasticity – notation for forces and stress components of stresses - components of strain - Hooks law. Plane Stress and plain strain analysis - plane stress - plane strain- differential equations of equilibrium - boundary conditions – compatibility equations –stress function - boundary condition.

UNIT - II

Two dimensional problems in rectangular co-ordinates-solution by polynomials - Saint-vanant’s principle-determination of displacements-bending of simple beams-application of Fourier series for two dimensional problems-gravity loading.

UNIT - III

Two dimensional problems in polar coordinates - stress distribution symmetrical about an axis - pure bending of curved bars - strain components in polar coordinates – displacements - displacement for symmetrical stress distribution - simple symmetric and asymmetric problems - general solution of two- dimensional problem in polar coordinates - application of general solution in polar coordinates.

UNIT - IV

Analysis of stress and strain in three dimensions - principal stress - stress ellipsoid - director surface - determination of principal stresses - max shear stresses - homogeneous deformation - principal axes of strain rotation. General Theorems. Differential equations of equilibrium - conditions of compatibility - determination of displacement - equations of equilibrium in terms of displacements - principle of super position - uniqueness of solutions - the reciprocal theorem.

UNIT - V

Torsion of Prismatic Bars - torsion of prismatic bars - bars with elliptical cross sections - other elementary solution - membrane analogy - torsion of rectangular bars-solution of torsional problems by energy method - use of soap films in solving torsion problem - hydro dynamical analogies - torsion of shafts, tubes, bars etc.

TEXT BOOKS:

• 1. Theory of Elasticity by Timoshenko, Mc Graw hill Publications

REFERENCE BOOKS:

• 1. Theory of Elasticity by Y. C. Fung.
• 2. Theory of Elasticity by Sadhu Singh. Dhanpat Rai sons Private Limited, New Delhi R19 M.Tech. ENGG. DESIGN M. TECH. I Year I Sem. (ENGG. DESIGN)