| Week | Dates Topics Recitations | Notes | Others |
| 1 - 5 | Module 1: Structural design with finite-variable optimization | ||
| 1 |
Oct. 1, 2020:
Overview of the course (Size, shape and topology optimization)
Oct. 2, 2020: Template of a structural optimization problem |
Recitation notes 1 |
Article on Eiffel's optimal structures |
| 2 |
Oct. 6, 2020:
Unconstrained finite-variable optimization; necessary and sufficient conditions.
Oct. 8, 2020: Constrained finite-variable optimization; KKT necessary conditions Oct. 9, 2020: Example problems |
Lecture notes 2b Lecture notes 3 Recitation notes 2 Recitation notes 2a (principle of minimum potential energy) |
Homework 1 A paper by Harold Kuhn on KKT conditions and duality Matalb fmincon demo files |
| 3 |
Oct. 13, 2020:
Sufficent condition for constrained minimization Duality in constrained optimization; one-bar optimization. Oct. 15, 2020: 2D truss optimization for stiffness Oct. 16, 2020: Truss code in Matlab |
Lecture notes 4b Lecture notes 5 Simple FEA notes for trusses and frames Recitation 3 notes |
Homework 2 Interactive truss design Truss FEA Matlab codes |
| 4 |
Oct. 20, 2020:
Truss optimization (contd.) for stiffness; adjoint method; optimality criterion of uniformly stressed design
Oct. 22, 2020: Algorithm for 2D truss optimization with size constraints Principle of virtual work and its implication in displacement at a point Oct. 23, 2020: Discussion of HW 2 problems |
Lecture notes 7a Lecture notes 7b |
Solution to HW 1 |
| 5 |
Oct. 27, 2020:
Clayperon's theorem, dual problem for maximizing stiffness of statically determinate trusses Oct. 29, 2020: Truss optimization with failure constraints Simultaneous size (topology) optimization and material selection for trusses Oct. 30, 2020: Review for Quiz 1 |
Lecture notes 9 |
Truss topology optimization Matlab codes Matlab codes for DoF and SoSS of trusses A paper on simultaneous geometry and material optimization of statically determinate trusses Solution to HW 2 |
| 6 - 10 | Module 2: Structural optimization using calculus of variations | Sample quiz 1 | Nov. 2, Quiz 1 |
| 6 |
Nov. 3, 2020:
Overview of calculus of variations: Parts 1 and 2
Nov. 5, 2020: Functional, function spaces, norm, inner product, Gateaux variation, Frechet differential, variational derivative Nov. 6, 2020: Discussion of Quiz 1; mathematical preliminaries for calculus of variations |
Lecture notes 10b Lecture notes 11a Lecture notes 11b Lecture notes 11c |
Solution to Quiz 1 |
| 7 |
Nov. 10, 2020:
Writing Gateaux variation; fundamental lemma of calculus of variation; Euler-Lagrange equations and boundary conditions
Nov. 12, 2020: E-L equation for multiple derivatives and functions; two and three independent variables. Nov. 13, 2020: Practice problems for Gateaux variation and Euler-Lagrange equations |
Lecture notes 12b and 13a Lecture notes 13b |
Homework 3 Matlab files for HW 3, Prob. 1 |
| 8 |
Nov. 17, 2020:
Global and local constraints in calculus of variations;
Nov. 19, 2020: general variation for variable end conditions; transversality conditions and Weirstrass-Erdman corner cnditions Size optimization of bars and beams for stiffness Nov. 20, 2020: Example problems for bar and beam optimization |
Lecture notes 14b Lecture notes 15a Lecture notes 15b Lecture notes 15c Lecture notes 15d |
Homework 4 |
| 9 |
Nov. 24, 2020:
Size (topology) optimization of frames for stiffness and flexibility
Nov. 26, 2020: Size optimization of bars and beams for strength and stability Nov. 27, 2020: Clarifying HW 4 problems and more |
Lecture notes 16b Lecture notes 17a Lecture notes 17b |
- |
| 10 |
Dec. 1, 2020:
2D continuum optimization for stiffness; theory of homogenization; SIMP
Dec. 3, 2020: 2D continuum optimization for compliant mechanisms |
Lecture notes 19 |
- |
| 11 - 14 | Module 3: Sensitivity analysis and design parameterization for multi-physics problems | Sample quiz 2 | Dec. 7, Quiz 2 |
| 11 |
Dec. 8, 2020:
Sensitivity analysis: direct and adjoint methods
Dec. 10, 2020: Parameter sensitivity analysis for continuous systems |
Lecture notes 21 |
- |
| 12 |
Dec. 15, 2020:
Parameter sensitivity analysis (contd.)
Dec. 17, 2020: Convex linearization and dual methods |
Lecture notes 23 |
Homework 5 |
| 13 |
Dec. 22, 2020:
Method of Moving Asymptotes vs. optimality criteria methods
Dec. 24, 2020: Design parameterization for topology optimization |
Lecture notes 25 |
Homework 6 |
| 14 |
Dec. 29, 2020:
Shape sensitivity analysis
Dec. 31, 2020: Shape sensitivity (contd.) |
Lecture notes 29 |
- |
| 15 |
Jan. 5, 2021:
Topological sensitivity
Jan. 7, 2021: Level-set optimization with topological sensitivity |
Lecture notes 27 |
- |
| 16 |
Jan. 12, 2021:
Design parameterization for multi-physics problems (contd.)
Jan. 14, 2021: Design parameterization and formulation for multi-physics problems (contd.) |
Lecture notes 29 |
Jan. 20, 2 PM to 5 PM, Quiz 3 |