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Structural and Multidisciplinary Optimization

 

Educational Commitments

The first course will take place on Thursday September 21, 2017 in room O.33 building B37 at 9h00.

Organization and exams

  • Agenda for academic year 2017-2018 : Planning of courses, supervised computer works and practical sessions
  • Infos about exams : Time schedule, rooms and groups:
    • Room TP40 (B52) Institue of Mechanics and Civil Engineering
    • Serie 1: 9h-12h
    • Serie 2: 14h-17h
  • Exams question list : Questions list for oral exams (theory) (January 2018)

Lecture notes

  1. INTRODUCTION : Course objectives and organization, pedagogical contract.
  2. OPTIMIZATION IN ENGINEERING: Formulation of engineering design as an optimization problem, definitions, examples of applications
  3. TOPOLOGY OPTIMIZATION: BASICS. An introduction to topology optimization
  4. INTRODUCTION TO MATHEMATICAL PROGRAMMING THEORY: basic concepts, convexity, convergence, etc.
  5. ALGORITHMS FOR UNCONSTRAINED OPTIMIZATION: Gradient methods
  6. LINE SEARCH TECHNIQUES: + additionnal material
  7. ALGORITHMS FOR UNCONSTRAINED OPTIMIZATION: Newton and quasi-Newton methods + additional material
  8. QUASI UNCONSTRAINED MINIMIZATION
  9. LINEARLY CONSTRAINED OPTIMIZATION:Generalized steepest descent concept, Gradient projected method, Generalized steepest descent for Newton methods, Active constraint strategy, Special treatment of sie constraints.
  10. OPTIMALITY CRITERIA: Optimality criteria and their interpretation as first order approximation
  11. GENERAL NON LINEAR PROGRAMMING I: Dual Methods
  12. GENERALIZED OPTIMALITY CRITERIA: solving subproblems using dual maximization, relation between OC and mathematical programming approaches.
  13. STRUCTURAL APPROXIMATIONS: Linear approximation, reciprocal approximation, CONLIN, MMA, GCMMA
  14. GENERAL NON LINEAR PROGRAMMING II: Barrier function, penalty method, augmented lagrangian method
  15. SOLVING EFFICIENTLY SUBPROBLEMS: Projection methods, linearization methods (SLP, SQP), Dual Solvers
  16. CONLIN AND MMA SOLVERS
  17. SENSITIVITY ANALYSIS: finite differences, direct and adjoin approaches in static and vibration linear problems, semi analytical sensitivity analysis
  18. SHAPE OPTIMIZATION: formulation, velocity field, multidisciplinary optimization, XFEM & Level Set
  19. TOPOLOGY OPTIMIZATION: Advanced techniques. Perimeter method, stress constraint, multiphysics applications, multibody systems...
  20. COMPOSITE STRUCTURE OPTIMIZATION: formulation, parameterization, solution schemes, examples

 

Further resources to help you

  1. Introduction to Math Programming (C. Fleury)
  2. Unconstrained and linearly constrained minimization (C. Fleury)
  3. General non linear programming (C. Fleury)
  4. Reconciliation of MP and OC (C. Fleury)
  5. Dual methods for structural optimization (C. Fleury)
  6. Convex approximations for structural optimization (C. Fleury)

 

Projects & Computer works

Practical sessions

  • Optimisation des structures: Exercices (livre)
  • Tutorial of NX-TOPOL