Basic Concepts
Definition of stress and strain at a point, components of stress and strain at apoint, strain displacement relations in Cartesian co-ordinates, constitutive relations, equilibrium equations, compatibility equations and boundary conditions in 2-D and 3-D cases, plane stress, plane strain – Definition.
Two-dimensional problems in Rectangular Coordinates
Airy’s stress function approach to2-D problems of elasticity. Solution by Polynomials – End Effects, Saint – Venant’s Principle – solution of some simple beam problems, including working out of displacement components.
Two - dimensional problems in Polar coordinates
General equation in Polar coordinates –Strain and displacement relations, equilibrium equations - Stress distribution symmetrical about an axis – Pure bending of curved bars – Displacements for sym metrical stress distributions –Bending of a curved bar by a force at the end – The effect of a small circular hole on stress distribution in a large plate subjected to uni-axial tension and pure shear.
Analysis of Stress and Strain in Three Dimensions:
Introduction – Principal stresses –Determination of the principal stresses and principal planes.– Stress invariants – Determination of the maximum shearing stress- Octahedral stress components, Principal strains – strain invariants.
FE approach
FE formulation using CST Elements, Element Nodal load vector- Body force, surface traction, Numerical examples. Isoparametric formulation of General Quadrilateral Elements in Two Dimensions: Strain-displacement matrix, Element stiffness matrix, Numerical examples. Computation of Nodal Loads in rectangular element: Linear and quadratic variation in displacement and load. Finite Element Formulation of Axisymmetric triangular Element.