CE-570: Advanced Structural Mechanics 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 HW assignments and MATLAB codes