Advanced Solid Mechanics Lecture Note

Description

Name of Notes : – Advanced Solid Mechanics Lecture Note

Introduction

This course builds upon the concepts learned in the course “Mechanics of Materials” also known as “Strength of Materials”. In the “Mechanics of Materials” course one would have learnt two new concepts “stress” and “strain” in addition to revisiting the concept of a “force” and “displacement” that one would have mastered in a first course in mechanics, namely “Engineering Mechanics”. Also one might have been exposed to four equations connecting these four concepts, namely strain-displacement equation, constitutive equation, equilibrium equation and compatibility equation. Pictorially depicts the concepts that these equations relate. Thus, the strain displacement relation allows one to compute the strain given a displacement; constitutive relation gives the value of stress for a known value of the strain or vice versa; equilibrium equation, crudely, relates the stresses developed in the body to the forces and moment applied on it; and finally compatibility equation places restrictions on how the strains can vary over the body so that a continuous displacement field could be found for the assumed strain field.

In this course too we shall be studying the same four concepts and four equations. While in the “mechanics of materials” course, one was introduced to the various components of the stress and strain, namely the normal and shear, in the problems that was solved not more than one component of the stress or strain occurred simultaneously. Here we shall be studying these problems in which more than one component of the stress or strain occurs simultaneously. Thus, in this course we shall be generalizing these concepts and equations to facilitate three dimensional analysis of structures.

Modules / Lectures

• 1. Introduction
• 2. Mathematical Preliminaries
• 3. Kinematics
• 4. Traction and Stress
• 5. Balance Laws
• 6. Constitutive Relations
• 7. Boundary Value Problem: Formulation
• 8. Bending of Prismatic Straight Beams
• 9. End Torsion of Prismatic Bars
• 10. Bending of Curved Beams
• 11. Beam on Elastic Foundation
• Bibliography