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Solid Mechanics

Prof. Ajeet Kumar · IIT Delhi

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About

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 Learners

Prerequisites: 1st year Engineering Mechanics

Lectures

Week 1

  1. Mathematical Concepts: Working with Vectors & Tensors YouTube
  2. Traction Vector YouTube
  3. Stress Tensor & its Matrix Representation YouTube

Week 2

  1. Transformation of Stress Matrix YouTube
  2. Stress Equilibrium Equations : Balance of Linear & Angular Momentum YouTube
  3. Balance of Angular Momentum (contd…) YouTube

Week 3

  1. Principal Planes & Principal stress components YouTube
  2. Maximizing the Shear Component of Traction YouTube
  3. Mohr's Circle YouTube

Week 4

  1. Mohr's Circle (contd…), Stress Invariants, Decomposition of the Stress Tensor YouTube
  2. Concept of Strain Tensor YouTube

Week 5

  1. Longitudinal and Shear Strains YouTube
  2. Local Volumetric Strain & Local Infinitesimal Rotation YouTube
  3. Similarity in Properties of Stress & Strain Tensors YouTube

Week 6

  1. Stress-Strain Relation YouTube
  2. Stress-Strain Relation for Isotropic Materials YouTube

Week 7

  1. Linear Momentum Balance in Cylinderical Coordinate System YouTube
  2. Linear Momentum Balance in Cylinderical Coordinate System (Contd..) YouTube
  3. Strain Matrix in Cylinderical Coordinate System YouTube

Week 8

  1. Extension-Torsion-Inflation in a Hollow Cylinder YouTube
  2. Extension-Torsion-Inflation in a Hollow Cylinder (Contd..) YouTube
  3. Solving Problems Involving Torsion of Shafts YouTube

Week 9

  1. Pure Bending of Rectangular Beams YouTube
  2. Bending of Beams (Contd..) YouTube
  3. Bending of Unsymmetrical Beams YouTube

Week 10

  1. Concept of Shear Center YouTube
  2. Theoy of Beams YouTube
  3. Theoy of Beams (Contd…) & Beam Buckling YouTube

Week 11

  1. Energy Methods YouTube
  2. Energy Methods (contd…) YouTube

Week 12

  1. Theories of Failure YouTube
  2. Theories of Failure (contd…) YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Delhi
Department
Mechanical Engineering
Teacher
Prof. Ajeet Kumar
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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