| Week | Dates Topics Recitations | Notes | Others |
| 1 - 5 | Module 1: Structural design with finite-variable optimization | ||
| 1 |
Aug. 4, 2022:
Overview of the course (Size, shape and topology optimization)
Aug. 5,2022: Template of a structural optimization problem |
Recitation notes 1 |
Article on strctural hierarchy by Prof. Lakes
Article on Eiffel's optimal structures |
| 2 |
Aug. 9, 2022:
No class due to Muharrum holiday.
Aug. 11, 2022: Identifying size, shape, and topology optimization problems (once more) Unconstrained and constrained minimization: theory and its relation to structural optimization Aug. 12,2022: No recitation session |
Lecture notes 3 Lecture notes 4 Lecture notes 5 |
- |
| 3 |
Aug. 16, 2022:
Constrained minimization; duality; two-bar truss optimization
Aug. 18, 2022: Multi-bar truss optimization Aug. 19,2022: Matlab practice |
Lecture notes 6 extra (duality) |
- |
| 4 |
Aug. 23, 2022:
Size (and topology) optimization of trusses and the optimality criteria algorithm
Aug.25, 2022: Dual formulation of truss optimization for statically determinate trusses Concepts of states of self stress and Maxwell's rule Simultaneous geoemtry and material optimization of trusses Aug. 26,2022: Matlab program for truss optimization |
Lecture notes 7b Lecture notes 8a |
FEA theory notes (trusses and beams) Matlab truss analysis code Matlab truss optimization code |
| 5 |
Aug. 30, 2022:
Dual formulation of truss optimization for statically determinate trusses Concepts of states of self stress and Maxwell's rule Sep. 1, 2022: Simultaneous geoemtry and material optimization of trusses Sep. 2,2022: Dual method for statically determinate truss optimization |
Lecture notes 9 Truss optimization using the dual method Dual truss opt code |
Geormetry+material optimization paper |
| 6 - 11 | Module 2: Structural optimization in the framework of calculus of variations | ||
| 6 |
Sep. 6, 2022:
Genesis of calculus of variations Formulating variational problems in geometry and mechanics Sep. 8, 2022: Mathematical preliminaries of calculus of variations: vectors spaces, function spaces, etc. Sep. 9,2022: Demonstration of COMSOL software for topology optimization of stiff structures |
Geometry and mechanics problems cast as calculus of variations problems Mathematical preliminaries to calculus of variations; functional and function spaces Banach, Sobolev, etc., spaces |
- |
| 7 |
Sep. 13, 2022:
Gateaux (first) variation, Frechet differential, etc. Fundamental lemma of calculus of variations Some examples Sep. 15, 2022: Euler-Lagrage equations; multiple functions and multiple derivatives Sep. 16,2022: Practice with Gateaux variation and EL equations |
Fundamental lemma of calculus of variations Euler-Lagrange equations in multiple functions and multiple derivatives but in a single domain variable |
- |
| 8 |
Sep. 20, 2022:
Euler-Lagrange equations when there are two and three independent variables Sep. 22, 2022: Euler-Lagrage equations with global (functional) and local (function) constraints Sep. 23,2022: Example problems in writing Euler-Lagrange equations |
Euler-Lagrange equations with global (functional) constraints Euler-Lagrange equations with local (function) constraints |
- | 9 |
Sep. 27, 2022:
Variable end conditions in Calculus of Variations; transversality conditions; broken extremals; Weirstrass-Erdmann conditions Sep. 29, 2022: Optimization of a bar (a dozen problems) Sep. 30,2022: Bar optimization code in Matlab |
A dozen optimization problems of a bar Solutions of two bar optimization problems |
Bar optimization code | 10 |
Oct. 4, 2022:
Beam optmization problems Oct. 6, 2022: 2D frame optimization problems; stiffness, strength, and flexibility Oct. 7,2022: Beam optimization code in Matlab |
Solution to beam optmization for stiffness and flexibility 2D frame optimization problem Beam optimization for strength |
Beam optimization code | 11 |
Oct. 11, 2022:
Homogenization method and its role in topology optimization; power law and material interpolation Oct. 13, 2022: 1D homogenization using asymptotic expansion method Plating with 99-line code to understand the influence of the penalty parameter and sensitivity filter. Oct. 14,2022: Midterm examination |
|
99-line code for 2D stiff-structure optimization YinSyn 2D code for topology optimization of structures and compliant mechanisms |
| 12 - 15 | Module 3: Multiphysics design problems; Sensitivity analysis for shape and topology optimization | 12 |
Oct. 18, 2022:
Topology optimization of compliant mechanisms in 2D continuum Oct. 20, 2022: Multiphysics design problems Oct. 21,2022: Practice with multiphysics formulations and "material interpolation" |
|
- | 13 |
Oct. 25, 2022:
Pressure load problem and electro-thermal-elastic problem Ananlytical expressions for sensitivity from the Calculus of Variations framework Oct. 27, 2022: Electro-elasto-statics, fluids, protein and other design problems using topology optimization Oct. 29,2022: Topology optimization with COMSOL Multiphysics |
|
- | 14 |
Nov. 1, 2022:
No class--Karnataka Rajyotsava Nov. 3, 2022: Discussion of the midterm questions Nov. 4,2022: Q&A and discussion |
|
- | 15 |
Nov. 8, 2022:
No class--Gurunanak Jayanthi Nov. 10, 2022: Parameters sensitivity analysis Nov. 4,2022: Discussion; Q&A |
Shape derivative with a 1D example Derivatives of the Jacobian and its other forms |
- | 16 |
Nov. 15, 2022:
Shape derivative and optimization with it in 2D Nov. 17, 2022: Topological derivative and optimization with it Nov. 4,2022: Discussion for project-cum-programming assignment, term paper, and HW 4 |
Topological derivative |
- | 17 |
Nov. 22, 2022:
Topological derivative in open and closed loop level-set method Nov. 24, 2022: Convex linearization leading to the method of moving asymptotes (MMA) Nov. 25,2022: Classes ended. |
Instructions for the term paper Project presentation template ConLin, MMA, and GCA papers |
- |