Calculus of Variations:
Notes
Recorded Notes

• Introduction:   [L1]

• Extremization of Functions:   [L2]

• Extremization of Functionals:   [L3]

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]

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]

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]

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]