At the end of this course, the students; 1) To learn approximation techniques to solve nonlinear systems. 2) Students should be able to derive and analyze the boundary value problems for a variety of simple deformations involving homogeneous, isotropic materials. 3) An ability to identify, formulate, and solve engineering problems. 4) Gaining presentation skill.
MODE OF DELIVERY
Face to face
PRE-REQUISITES OF THE COURSE
No
RECOMMENDED OPTIONAL PROGRAMME COMPONENT
None
COURSE DEFINITION
Strain geometry, Stresses, Balance of an element in continuum media, Strain Energy, Boundary conditions, Constitutive equations, Expression of elastic problems types of stresses, Elastic stability, Deformation of elastic materials.
COURSE CONTENTS
WEEK
TOPICS
1st Week
Introduction
2nd Week
Tensors, the divergence theorem, material time derivatives
3rd Week
Principles of linear and angular momentum, the stress tensor
4th Week
Piola-Kirchhoff tensors
5th Week
Cauchy stress, principal stresses, stress invariants
6th Week
Constitutive equations, material symmetry
7th Week
Hyper-elasticity and hypo-elasticity
8th Week
Midterm
9th Week
Incompressibility, forms of the strain-energy function.
10th Week
Homogeneous deformations, inverse methods
11th Week
Simple shear, pure homogeneous deformations
12th Week
Non-homogeneous deformations
13th Week
Simple torsion
14th Week
Extension and Torsion
RECOMENDED OR REQUIRED READING
o P. Chadwick, Continuum Mechanics, Dover Publications, 1999. o R. W. Ogden, Non-linear Elastic Deformations, Dover Publications, 1997. o G. A. Holzapfel, Nonlinear Solid Mechanics: A Continuum Approach for Engineers, John Wiley and Sons, 2000. o M. E. Gurtin, An Introduction to Continuum Mechanics, Academic Press, 1981.
