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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: 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. GENERALIZED OPTIMALITY CRITERIA: solving subproblems using dual maximization, relation between OC and mathematical programming approaches.
  12. GENERAL NON LINEAR PROGRAMMING I: Dual Methods
  13. GENERAL NON LINEAR PROGRAMMING II: Barrier function, penalty method, augmented lagrangian method
  14. GENERAL NON LINEAR PROGRAMMING II: Projection methods, linearization methods (SLP, SQP),
  15. STRUCTURAL APPROXIMATIONS: Linear approximation, reciprocal approximation, CONLIN, MMA, GCMMA
  16. SENSITIVITY ANALYSIS: finite differences, direct and adjoin approaches in static and vibration linear problems, semi analytical sensitivity analysis
  17. SHAPE OPTIMIZATION: formulation, velocity field, multidisciplinary optimization, XFEM & Level Set
  18. TOPOLOGY OPTIMIZATION: formulation, homogenization approach, SIMP, perimeter method, stress constraints
  19. COMPOSITE STRUCTURE OPTIMIZATION: formulation, parameterization, solution schemes, examples

 

Projects & Computer works

  • Project 3: Linearly constrained minimization
    • Work description
  • Project 4: Topology optimization using NX-TOPOL
    • Work description

     

Practical sessions

  • Optimisation des structures: Exercices (livre)