# Solid Mechanics

Por: Swayam . en: ,

## Overview

This is the first course where deformation of solid bodies and the underlying concepts are introduced to undergraduate students. The course begins by building foundation of the concepts of stress and strain in three-dimensional deformable bodies. It further uses these concepts to study extension, torsion and bending of beams. The one-dimensional theory of beams are also introduced. We also discuss various theories of failure which are critical for design of machine elements in industry.
INTENDED AUDIENCE: Any Interested LearnersPREREQUISITES: 1st year Engineering Mechanics

## Syllabus

### COURSE LAYOUT

Week 1: Mathematical preliminaries and notation; Kinematics of deformation: rigid vs deforming solids; Lagrangian and Eulerian descriptions; Concept of Traction vectorWeek 2: Stress tensor and its representation in Cartesian coordinate system; Transformation of stress matrix; Equations of equilibrium; Symmetry of stress tensor
Week 3: State of stress in simple cases ; Principal stress components and principal planes; Maximizing shear componentof traction at a point; Mohr’s circle
Week 4: Stress invariants; Octahedral Plane; Decomposition of stress tensor; Concept of strain and strain tensor; ongitudinal,shear and volumetric strains
Week 5: State of strain in simple cases; Strain compatibility condition; Local infinitesimal rotation; Linear stress-strain relation:isotropic and orthotropic cases; Relation between material constants
Week 6: Stress and strain matrices in cylindrical coordinate system; Equations of equilibrium in cylindrical coordinate system, Axisymmetric deformations: combined extension-torsion of a cylinder
Week 7: Belt friction, Review of particle dynamics, Circular motion
Week 8: Bending of beams having non-symmetrical cross-section; Shear center, Shear flow in thin and open cross-section beams
Week 9: Deflection of a beam: Euler Bernouli and Timoshenko beam models; Buckling of beams
Week 10: Reciprocal relations, Castigliano’s theorem, Deflection of straight and curved beams using energy method
Week 11: Various theories of failure and their application
Week 12: Brief introduction to plasticity, Yield surface