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Structural and Multidisciplinary Optimization

 

Educational Commitments

Organization and exams

Lecture notes : Introduction to Numerical Optimization (Prof. P. Tossings)

  1. INTRODUCTION TO MATHEMATICAL PROGRAMMING THEORY: basic concepts, convexity, convergence, KKT conditions, etc.
  2. ALGORITHMS FOR UNCONSTRAINED OPTIMIZATION: Gradient methods
  3. LINE SEARCH TECHNIQUES: + additionnal material
  4. ALGORITHMS FOR UNCONSTRAINED OPTIMIZATION: Newton and quasi-Newton methods
  5. QUASI UNCONSTRAINED MINIMIZATION
  6. GENERAL NON LINEAR PROGRAMMING I: Dual Methods
  7. GENERAL NON LINEAR PROGRAMMING II: Transofrmation methods: Barrier function, penalty method, augmented lagrangian method and linearization methods (SLP, SQP).

 

Lecture notes: Structural optimization (Prof. P. Duysinx)

  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. INTRODUCTION TO THE FINITE ELEMENT METHOD: historical perspective, bar element, linear elasticity
  4. OPTIMALITY CRITERIA: Optimality criteria
  5. SENSITIVITY ANALYSIS: finite differences, direct and adjoin approaches in static and vibration linear problems, semi analytical sensitivity analysis
  6. FROM OC TO STRUCTURAL APPROXIMATION: Berke's expression of displacement is a first order Taylor expansion
  7. STRUCTURAL APPROXIMATIONS: Linear approximation, reciprocal approximation, CONLIN, MMA, GCMMA
  8. GENERALIZED OPTIMALITY CRITERIA: dual maximization to solve efficiently convex seperable subproblems
  9. CONLIN AND MMA SOLVERS: dual solvers for convex linearisation schemes, CONLIN and MMA
  10. SHAPE OPTIMIZATION: formulation, velocity field, multidisciplinary optimization, XFEM & Level Set
  11. TOPOLOGY OPTIMIZATION: FUNDAMENTALS. An introduction to topology optimization
  12. TOPOLOGY OPTIMIZATION: ADVANCED TOPICS. Stress constraint.
  13. TOPOLOGY OPTIMIZATION: ADVANCED TOPICS. Manufacturing constraints, topology optimization and addtive manufacturing.

 

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)