Optimization in Structural Design

Lecturer:

Tutor:

Supervisor:

Department of Mechanics

Synopsis:

Optimization in Structural Design

Requirements:

none

Syllabus of lectures:

1. Short introduction, scope of structures considered in the course

2. Functionals, variational principles, examples

3. Generalized principles, Gateau's differential, Gateau's derivative, examples

4. Variation, minimum of functional, numerical methods starting with variational principles, examples

5. Unconstrained optimization problems, general formulation, examples

6. Methods of solution: Ritz method, steepest descent type methods, conjugate gradients, applications to selected structures

7. Applications of steepest descent method to concrete structural problems

8. Test I

9. Constrained problems, general formulation, examples

10. Penalty method, lagrangian multipliers, indicatrix

11. Applications of Ritz and steepest descend methods

12. Over-relaxation method, Newton-Raphson method, convergence, applications

13. Dual problems, Fenchel transformation, solvability, solution of problems with more local extremums

14. Test II

Syllabus of tutorials:

Study Objective:

Students will get acquainted with different methods of optimisation of structures.

Study materials:

1. Cea, J.: Optimization, DUNOD Paris, 1973., 2. Rockafellar, J.: Convex Analysis, John Willey and Sons, 1972.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: