| Week | Dates Topics Recitations | Notes | Others |
| 1 - 5 | Module 1: Structural design with finite-variable optimization | ||
| 1 |
Aug. 3, 2021:
Overview of the course (Size, shape and topology optimization)
Aug. 5, 2021: Structural optimization with continuous and discrete variables; design parameterization Aug. 6,2021: Template of a structural optimization problem |
Lecture notes 2 Recitation notes 1 |
Article on Eiffel's optimal structures
Design of lattice models of proteins with two variables Design of lattice models of proteins with twenty variables |
| 2 |
Aug. 10, 2021:
Unconstrained finite-variable optimization; necessary and sufficient conditions.
Aug. 12, 2021: Unconstrained problem (contd.) Aug. 13, 2021: Example problems |
Lecture notes 4 Recitation notes 2 Recitation notes 2a (principle of minimum potential energy) |
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| 3 |
Aug. 17, 2021:
Constrained finite-variable optimization; KKT necessary conditions 2D truss optimization for stiffness Aug. 19, 2021: Sufficent condition for constrained minimization Duality in constrained optimization; one-bar optimization. Aug. 20, 2021: Quiz 1 |
Lecture notes 6 Lecture notes 6 extra |
A paper by Harold Kuhn on KKT conditions and duality Matalb fmincon demo files |
| 4 |
Aug. 24, 2021:
Truss optimization for stiffness; adjoint method; optimality criterion of uniformly stressed design Algorithm for 2D truss optimization with size constraints Aug. 26, 2021: Energy methods; Maxwell's rule and static determinacy Dual formulation of truss optimization Aug. 27, 2021: Truss FEA code |
Lecture notes 8a Lecture notes 8b Recitation 4 notes Simple FEA notes for trusses and frames |
Interactive truss design Truss FEA Matlab codes |
| 5 |
Aug. 31, 2021:
Clayperon's theorem, dual problem for maximizing stiffness of statically determinate trusses form and force diagrams of Maxwell Sep. 2, 2021: Truss optimization with failure constraints Shape optimization of trusses using form and force diagrams Sep. 3, 2021: Truss optimization |
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Truss topology optimization Matlab codes Matlab codes for DoF and SoSS of trusses William Baker's paper on form and force diagrams |
| 6 - 11 | Module 2: Structural optimization using calculus of variations | - | - |
| 6 |
Sep. 7, 2021:
Simultaneous size (topology) optimization and material selection for trusses
Overview of calculus of variations: Part 1 Sep. 9, 2021: Overview of calculus of variations: Part 2 Sep. 10, 2021: Holiday for Vinakaya Chaviti |
Lecture notes 10a Lecture notes 10b |
A paper on simultaneous geometry and
material optimization of statically determinate trusses
YinSyn files |
| 7 |
Sep. 14, 2021:
Mathematical preliminaries for calculus of variations: vector space, norm, Banach
and Hilbert spaces, Lebegue and Sobolev norms, energy spaces
First variation of a functional Fundamental lemma of calculus of variations Sep. 16, 2021: Euler-Lagrange equations Sep. 17, 2021: COMSOL demonstration |
Lecture notes 11b Lecture notes 11c Lecture notes 11d - |
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| 8 |
Sep. 21, 2021:
Euler-Lagrange equations for multiple derivatives and functions
Sep. 23, 2021: Euler-Lagrange equations for two and three independent variables Sep. 24, 2021: Practice for writing Euler-Lagrange equations and Zoom quiz on concepts of calculus of variations |
Lecture notes 14 - |
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| 9 |
Sep. 28, 2021:
Global and local constraints in calculus of variations General variation; Transversality conditions; Weirstrass-Erdmann corner conditions Sep. 30, 2021: Bar optimization Oct. 1, 2021: Matlab code for bar optimization |
Lecture notes 16 Lecture notes 17 Lecture notes 18a Lecture notes 18b Solutions of many bar optimization problems by Rahul Pratap Singh Bar optimization Matlab code |
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| 10 |
Oct. 5, 2021:
Beam optimization for stiffness, flexibility, and strength
Oct. 7, 2021: Topology optimization of 2D and 3D continua for stiffness and strength. Oct. 8, 2021: Quiz 4 on concepts of optimization of continuous structures |
Lecture notes 19b (solution of one beam optimization problem) Lecture notes 19c (optimization of 2D frames) Lecture notes 19d (beam optiization for strength) Beam optimization Matlab code |
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| 11 |
Oct. 12, 2021:
Sensitivty filter and more on SIMP
Oct. 14, 2021: Miscellaneous topics in calculus of variations: general variation with variable end conditions; integrals of Euler-Lagrange equations; inverse calculus of variations problems or writing the functional from the differential equation and self-adjointness Oct. 15, 2021: Holiday (Vijaya Dasami); email enquiries are welcome. |
Lecture notes 22 (Self-adjointness and writing the functional from differential equations) |
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| 12 - 15 | Module 3: Sensitivity analysis (parameter, shape, and topology); multiphysics problems in topology optimization | - | - |
| 12 |
Oct. 19, 2021:
Holiday for Milad un Nabi
Oct. 21, 2021: Sensitivity analysis for topology optimization of compliant mechanisms for continuous and discrete formulations Oct. 22, 2021: Conceptual quiz on the content of Lecture notes 17, 21, and 22 |
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| 13 |
Oct. 26, 2021:
Parameter sensitivity analysis: direct and adjoint methods
Oct. 28, 2021: Shape sensitivity analysis: material and shape derivatives; 1D examples Jacobian derivatives Oct. 29, 2021: Discussion of parameter and shape sensitivity derivations; Quiz 6 (simple, conceptual) |
Lecture notes 25 (Shape sensitivity analysis 1D) Lecture notes 26 (Jacobian derivatives) |
Offline Midterm examination |
| 14 |
Nov. 2, 2021:
Shape sensivity analysis and shape optimization Topological derivative and related topology optimization Nov. 4, 2021: Holiday for Deepavali Nov. 5, 2021: Hands-on demonstration of COMSOL |
Lecture notes 28a (Jacobian derivatives) Lecture notes 28b (Topological derivative-based optimization) |
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| 15 |
Nov. 9, 2021:
Electro-thermal-elastic actuator optimization Transient elastic problem Nov. 11, 2021: Electrostatic actuator optimization Pressure load problems Nov. 13, 2021: Hands-on demonstration of COMSOL |
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| 16 |
Nov. 16, 2021:
Convex linearization; dual methods; method of moving asymptotes
Nov. 18, 2021: More on MMA Nov. 19, 2021: Holiday for Gurunank Jayanthi |
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| 17 | Nov. 23, 2021: Where to go from here... |
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| Examinations week |
Dec. 14th, 2021:
Course project presentations (pdf or ppt file)
Dec. 4th, 2021: Term paper due (about two-page pdf file) |
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