CE231/MSE211 : Mechanics of Solids

Handouts

  1. Definitions of some useful spaces.
  2. Determinants of second order tensors in dimensions higher than 3.
  3. Misc. results from linear algebra.
  4. Extra Exercises on vector/tensor algebra plus solutions.
  5. Extra Indicial Exercises on converting from symbolic to indicial notation plus solutions.
  6. Linearization of the determinant function
  7. Mapping of tangent vectors by the deformation gradient
  8. Deformation gradient in polar coordinates
  9. Volume changes and the determinant expression
  10. Linearization of angle change
  11. Cauchy's Theorem
  12. Geometry of the pi-plane (octahedral plane)
  13. Fourth order symmetric identity tensor
  14. Linear Operator Representation Theorem (finite dimensions)
  15. Basics of steady-state forced linear systems
  16. Steady State Response of the SLS
  17. Introduction to Curvilinear Coordinates
  18. Elastic-Plastic Sphere
  19. Cesaro's Integral
  20. Uniqueness in Linear Elasticity
  21. Michell's Solution to the Bi-Harmonic Equation
  22. Infinite plate with a hole
  23. Saint Venant Effect
  24. Estimation of the first resonant mode of a radial disk resonator
  25. Fitting Prony series and Prony's Method
  26. Mode III crack tip singularities