Advanced Mechanics of Solids (ME60402), Spring 2021

Mechanical Engineering Department, Indian Institute of Technology Kharagpur

Instructor:

Email: jeevan@mech.iitkgp.ac.in; jeevanjyoti4@gmail.com

Policies and Guidelines:

All policies and guidelines regarding attendance, grades, assignment submission, absence from exams are laid out in detail in the Policies and Guidelines tab.

Learning Resources

Topics	Problem Sheets
Calculus of Variations: Notes Recorded Notes Introduction: [L1] Extremization of Functions: [L2] Extremization of Functionals: [L3]	None
Energy Methods Notes Recorded Notes Preliminary Concepts: [L4] Virtual Displacement: [L5] Law of Kinetic Energy and Fourier’s Inequality: [L6] Work Function and Principle of Virtual Work: [L7] Principle of Virtual Work Applied to Deformable Body: [L8] 1st Law of Thermodynamics and Potential Energy: [L9] Strain Energy: [L10] Complementary Energy: [L11] Modified Complementary Energy: [L12] Castigliano’s Theorem on Deflections: [L13] Prelude to Problems: [L14] Problems (Parts 1 – 6): [L15], [L16], [L17], [L18], [L19], [L20]	PS1
Bending and Buckling of Beams Notes Recorded Notes Overview and Prelude: [L21] Lateral Loading – Bending: Using Principle of Stationary Potential Energy: [L22] Using Principle of Virtual Work: [L23] Lateral and Axial Loading – Bending and Stretching: Using Principle of Stationary Potential Energy: [L24] Using Principle of Virtual Work: [L25] Buckling: Buckling – 1: [L26] Buckling – 2: [L27] Buckling – 3 (Example): [L28] Buckling – 4 (Alternative Formulation): [L29] Buckling – 5 (Elastica): [L30] Buckling – 6 (Elastica Example Solution, Part 1): [L31] Buckling – 7 (Elastica Example Solution, Part 2): [L32] Buckling – 8 (Elastica Solution, Using Jupyter Notebook): [L33]	PS2
Classical Plate Theory Notes Recorded Notes Derivation (Parts 1 – 5): [L34], [L35], [L36], [L37], [L38] Examples: Circular Plate, Uniform Loading, Clamped Periphery [L39] Circular Plate, Point force at origin, Clamped Periphery [L40] Interpretation of effective shear: [L41] Corner points: [L42]	PS3
Föppl von Karman Plate Theory Notes Recorded Notes Derivation (Parts 1 – 4): [L43], [L44], [L45], [L46] Föppl-von Kármán examples: Example 1, Example 2, Example 3
Torsion Notes Recorded Notes Introduction and Derivation (Part 1): [L47] Derivation (Part 2): [L48] Derivation (Part 3): Prandtl Stress Function: [L49] Simply-Connected Region: [L50] Multiply-Connected Region: [L51]
Unsymmetric Bending Recorded Notes Unsymmetric Bending (Part 1): [L52] Unsymmetric Bending (Part 2): [L53]
Shear Centre Recorded Notes Shear Centre (Part 1): [L54] Shear Centre (Part 2): [L55] Shear Centre (Part 3): [L56]

Textbook

The primary textbook for this course is:

Solid Mechanics – A Variational Approach by Clive L. Dym and Irving H. Shames (Springer).

The ebook is available through IIT Kharagpur’s subscription to Springer at this link (You will need to access it through the Institute proxy.)

Additionally, I use bits and pieces from the following references:

Energy Methods in Applied Mechanics by Henry L. Langhaar (for general theory of energy methods)
Theory of Elastic Stability by Timoshenko and Gere (for problems on beams and plates)
Advanced Mechanics of Materials by Boresi and Schmidt (for problems on energy methods and plates)
Advanced Mechanics of Solids by L. S. Srinath (for theory and problems on shear centre and unsymmetric bending)
Theory of Elasticity by Landau and Lifshitz (for problems on plates)