Learn the methodologies, concepts and techniques of modern optimization theory and practice with applications to mechanical engineering design, product development and structural design. How to create an appropriate mathematical description (a simulation model) of the design problem, how to formulate the optimization problem and finally how to use numerical optimization techniques to solve the problem. Acquire the fundamental knowledge of global and topology optimization.

Student responsibilities:

Attendance at lectures and exercises (maximum three absences). Creating and defending the program task. Oral examination.

Grading and evaluation of student work over the course of instruction and at a final exam:

Individual tasks, oral examination.

Upon successful completion of the course, students will be able to (learning outcomes):

1 . apply rules of the mathematical model scheme to problems of optimal design of the mechanical devices;

2 . use the classical optimization methods (Lagrange multipliers, optimality conditions) for solving problems with restrictions;

3 . create mathematical optimization models for joints calculation, design and analysis of constructions and for optimal synthesis of the planar mechanisms;

4 . apply appropriate numerical methods and algorithms in the solution to problems of nonlinear and linear optimization;

5 . use appropriate numerical methods in the solution of global optimization problems;

6 . apply principles and methods of topology optimization to examples of 2D constructions;

7 . evaluate optimization results;

Lectures

1. Introduction. Conventional and optimum design process. The optimum design problem formulation. Design space, variables, objective function, design constraints. Examples.

2. General mathematical model of optimization. The formulation rules of mathematical models. Classical optimization techniques. Graphical optimization methods in 2D design space.

3. Unimodal optimization problems. The methods of solution and algorithms. Nonlinear programming: one-dimensional minimization, Fibonacci and Golden section method.

4. Unconstrained and constrained design space. The method of Lagrange multipliers, optimality conditions. Examples.

5. Numerical methods in optimum design. Basic idea and algorithm. Algorithms and computer programs for constrained problems. Direct search methods, flexible polyhedron (simplex) method. The methods of sequential unconstrained optimization. Penalty function method.

6. Introduction to linear programming. The methods, application, algorithms. Sequential linear programming.

7. Multiobjective optimization. Pareto optimum. Examples.

8. Practical optimization examples of structures. Optimum design of joints and construction elements.

9. Applying the optimization methods in calculation of statically undetermined structures. Application to frames and crane girders.

10. Optimal design of mechanisms using nonlinear programming. Chebyshev polynomials. Minimization of the structural error. Chebyshev lambda-mechanism, Watt and Evans mechanisms.

11. Optimum design of mechanisms in mobile machinery. Vehicles, lifting and crane mechanisms.

12. Optimal design of structures. Minimum weight, dimensional and structural truss optimization. Fully-stressed design.

13. Global optimization, application and algorithms. The method of differential evolution. Examples - test functions.

14. Introduction to topology optimization. Goals, area of application, theoretical background, problem formulation.

15. The discretization of the design domain. Algorithms and computer programs of the topology optimization. Topology design of truss structures. Examples.

Exercises

1. Illustrative examples. Optimum design problem formulation.

2. Illustrative Examples. Graphical optimization in 2D space.

3. Graphical optimization in 2D space. Illustrative examples: Fibonacci and Golden section method.

4. Illustrative examples. Lagrange multipliers.

5. Illustrative examples. Flexible polyhedron (simplex) method.

6. Illustrative examples. Linear programming.

7. Seminar work - set problems to be solved. Individual work. Consultations.

8. Individual work. Consultations. Individual problem-solving.

9. Individual work. Consultations. Individual problem-solving.

10. Individual work. Consultations. Individual problem-solving.

11. Introduction to topology optimization and the application of the related software.

12. Defining the topology optimization domain.

13. Generating the final 3D model of the topology-optimized structure. Reviewing the available software.

14. Applying the measurement tools to experimentally evaluate the previously optimized structure.

15. Presentation of solved problem. Preliminary exam.

Compulsory literature:

1. Introduction to optimum design, J. S. Arora, McGraw-Hill, 2017, p. 0-0

Recommended literature:

2. Topology Optimization: Theory, Methods and Applications, M. P. Bendsoe, O. Sigmund, Springer, 2003, p. 0-0

3. Differential Evolution, A Practical Approach to Global Optimization, K.V. Price, R.M. Storn, J.A. Lampinen, Springer-Verlag, 2005, p. 0-0