Link to YouTube Lecture Videos
Listing of Lecture Topics:
- 01 Lecture 01 - Syllabus; Introduction
- 02 Lecture 02 - Mathematical preliminaries
- 03 Lecture 03 - Vectors, Indicial Notation
- 04 Lecture 04 - Indicial Notation, Tensors
- 05 Lecture 05 - Tensor operations
- 06 Lecture 06 - Transformation due to change of coordinate system
- 07 Lecture 07 - Tensor Invariants
- 08 Lecture 08 - Computation of Eigenvalues and Eigenvectors
- 09 Lecture 09 - Spectral decomposition, Calculus of Scalar, Vectors and Tensors
- 10 Lecture 10 - Directional Derivative, Gradient
- 11 Lecture 11 - Divergence, Curl and Gradient of vector fields
- 12 Lecture 12 - Tensor field and Divergence
- 13 Lecture 13 - Divergence and Integral Theorems ; Kinematics
- 14 Lecture 14 - Deformation map, Deformation Gradient F
- 15 Lecture 15 - Stretch of curves, Deformation tensor C, Strain tensor E
- 16 Lecture 16 - Visualization of Deformation gradient, Principal strains
- 17 Lecture 17 - Polar decomposition of F, Psuedo-spectral decomposition of F
- 18 Lecture 18 - Displacement gradient
- 19 Lecture 19 - Changes in Lengths, Areas and Volumes due to deformation
- 20 Lecture 20 - Time-dependent motion
- 21 Lecture 21 - Material-frame indifference, Objectivity ; Equilibrium and Free-body diagrams
- 22 Lecture 22 - Tractions, Stress tensor, Cauchy stress-traction relationship
- 23 Lecture 23 - Components of stress tensor, Principal stresses
- 24 Lecture 24 - Governing Partial Differential Equation for Equilibrium
- 25 Lecture 25 - First and Second Piola-Kirchhoff Stress tensors
- 26 Lecture 26 - Material behavior, Hyperelasticity
- 27 Lecture 27 - Isotropy, Uniaxial and Triaxial tests
- 28 Lecture 28 - Material Moduli, Plane stress, Plane strain problems
- 29 Lecture 29 - Boundary value problem of structural mechanics, 1D little BVP
- 30 Lecture 30 - Analytical solution of 1D BVP, Method of weighted residuals (MWR) Weak form
- 31 Lecture 31 - Principle of virtual work (PVW) Weak form
- 32 Lecture 32 - Boundary conditions in Weak forms, Variational (energy) Methods
- 33 Lecture 33 - Energy functional for 1D BVP, Vainberg's theorem
- 34 Lecture 34 - Variational Principles for dynamics, Weak form in 3D, Approximate Numerical solution
- 35 Lecture 35 - Ritz method, computer implementation in MATLAB
- 36 Lecture 36 - Gram-Schmidt orthogonalization for functions, Introduction to 1D finite elements (FE)
- 37 Lecture 37 - Element-wise computation of FE matrices, 2D / 3D Ritz method and FE method
|