Section numbers and problem numbers given below refer to the textbook.

AS5900: Elasticity

No. Date Lecture topic(s) Section(s) Problem(s)
1. 1 February Course information; Index notation. (notes) 1.1, 1.2
2. 2 February Index notation for partial derivatives. Gradient, divergence, and curl in index notation. Dyadic product. (notes) 1.3
3. 8 February Objective vs subjective quantities = Tensors vs matrices. Rotation matrix Qij between two coordinate systems. (notes) 1.4
4. 9 February Coordinate transform of 1-tensors. (notes) 1.4
5. 10 February Coordinate transform of 2-, 3-, ..., k-tensors. An example. (notes) 1.5
6. 11 February Invariance of the length of a 1-tensor. Invariance of the principal directions of a 2-tensor. (notes) 1.6
7. 15 February Finding the invariants, principal directions, and principal values of a 2-tensor. An example. (notes) 1.6
8. 16 February An example with two eigenvalues equal. Tensor algebra, and calculus. (notes) 1.6-1.8 Exercises 1-1 to 1-17 at the end of chapter 1.
9. 17 February Kinematics. Displacement gradient, strain, and rotation. (notes) 2.1-2.2
10. 18 February An example to illustrate the notions of rotation, and strain. Strain transformation, volumetric and deviatoric parts. (notes) 2.2-2.6 Exercises 2.1-2.12, at the end of Chap 2
11. 22 February Strain compatibility: motivation. Relation between gradients of rotation, ωij, and strain εij. 2.6
12. 23 February Strain compatibility: derivation of the 81 compatibility conditions. notes 2.6
13. 24 February Reduction of the 81 compatibilty conditions to 6 non-trivial ones. Incompatibility tensor, ηij. (notes) 2.6
14. 25 February Establishing the connection ηij,j = 0 between the compatibility equations. Strain in curvilinear coordinate systems. (notes) 2.6, 1.9
15. 1 March Orthogonal curvilinear coordinate systems: unit vectors, and scale factors. Rate of change of unit vectors. (notes) 1.9
16. 2 March Derivation of ∇u in cylindrical coordinates. Strain components in cylindrical coordinates. (notes) 2.7
17. 3 March Traction vector, and its dependence on the plane orientation. The concept of a linear function of the plane orientation. The notion of stress. Cauchy's theorem. (notes) 3.1, 3.2
18. 4 March Coordinate transformation of the stress tensor. The physical meaning of the eigenvalue problem for stress in terms of traction. Normal and shear stress. Planes of maximum normal stress. notes) 3.3, 3.4
26. 22 March (notes)
27. 23 March Derivation of the Beltrami-Mitchell equations. Principle of superposition, and principle of St. Venant. (notes) 5.3, 5.5, 5.6 All the exercises at the end of Chapter 5.
28. 24 March Storage of energy in an elastic solid. Quasistatic loading of a linear elastic solid. Strain energy. (notes) 6.1
29. 24 March Expression for the strain energy U in a Hookean solid. U ≥ 0. Major symmetry of Cijkl. Bounds on elastic moduli. (notes) 6.1, 6.3
30. 25 March Theorems based on strain energy density. Uniqueness of solution of linear elastic boundary value problems. Clapeyron's theorem. Reciprocal theorem. notes) 6.2, 6.4