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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

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
  5. ALGORITHMS FOR UNCONSTRAINED OPTIMIZATION: Gradient methods
  6. LINE SEARCH TECHNIQUES
  7. ALGORITHMS FOR UNCONSTRAINED OPTIMIZATION: Newton and quasi-Newton methods
  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. GENERAL CONSTRAINED PROBLEMS
  11. SENSITIVITY ANALYSIS: finite differences, direct and adjoin approaches in static and vibration linear problems, semi analytical sensitivity analysis
  12. FROM OPTIMALY CRITERIA TO SEQUENTIAL CONVEX PRORAMMING: optimality criteria (fully stressed design and OC for a single displacement), generalized optimality criteria, interpretation of optimality criteria, relation between OC and mathematical programming approaches
  13. STRUCTURAL APPROXIMATIONS: Linear approximation, reciprocal approximation, CONLIN, MMA, GCMMA
  14. SOLVING EFFICIENTLY SUB PROBLEMS: Projection methods, linearization methods (SLP, SQP), dual methods
  15. CONLIN and MMA solvers
  16. SHAPE OPTIMIZATION: formulation, velocity field, multidisciplinary optimization, XFEM & Level Set
  17. TOPOLOGY OPTIMIZATION: formulation, homogenization approach, SIMP, perimeter method, stress constraints
  18. COMPOSITE STRUCTURE OPTIMIZATION: formulation, parameterization, solution schemes, examples

 

Projects & Computer works

  • Project 1: Unconstrained constrained minimization
  • Project 2: Topology optimization
    • Work description
    • Fichiers top.m, mmasub.m, subsolve.m
    • Web site to download fundamental paper "A 99 line topology optimization code written in MATLAB®" by Ole Sigmund
  • Project 3: Linearly constrained minimization
    • Work description
  • Project 4: Topology optimization using NX-TOPOL
    • Work description

     

Practical sessions

  • Optimisation des structures: Exercices (livre)