To learn and be able to formulate the mathematical model of an optimization problem. To acquire fundamental knowledge of topology optimization. To apply topology optimization methods in the design of structural components.

Student responsibilities:

Attendance at lectures and exercises (a maximum of three absences is allowed).

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

Individual assignments and an oral examination.

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

1 . Explain the fundamental concepts of topology optimization and its applications in structural design.

2 . Analyze mathematical models of optimization problems, including objective functions and constraints.

3 . Implement basic topology optimization algorithms using MATLAB and other software tools.

4 . Conduct optimization while considering constraints and evaluate the results.

5 . Validate results using experimental data.

6 . Present optimization results through technical reports and oral presentations.

Lectures

1. Introduction to Topology Optimization - Basic concepts, history, and significance.

2. Mathematical Foundations of Topology Optimization.

3. Problem Formulation, Objective Functions, and Constraints.

4. Application of MATLAB in Topology Optimization: Working with Matrices and Loops.

5. Application of MATLAB in Topology Optimization: Optimization Functions.

6. Domain Discretization Using Finite Elements.

7. The SIMP Method in Topology Optimization.

8. Overview of Available 2D Topology Optimization Methods: TOP and TOP88 Algorithms.

9. Overview of Available 3D Topology Optimization Methods: TOP99neo Algorithm.

10. Specification of Boundary Conditions and Loads in Available Methods.

11. Impact of Algorithm Parameters on Computation Time and Convergence.

12. Verification of Numerical Models of Topology Optimization through Experimentation.

13. Examples from Industrial Practice and Research.

14. Examples from Industrial Practice and Research.

15. Challenges and Limitations in the Experimental Validation of Topology Optimization Results.

Exercises

1. Historical Applications of Topology Optimization.

2. Review of Required Mathematical Concepts.

3. Definition of a Simple Optimization Problem.

4. Introduction to the Programming Interface. Tasks Involving Matrices and Loops.

5. Function Creation and Optimization Problem Implementation.

6. Domain Discretization.

7. Implementation of the SIMP Method on a Simple Example.

8. Assignment of Individual Project. Code Review and Use of TOP and TOP88 Algorithms.

9. Code Review and Use of the TOP99neo Algorithm.

10. Modification of Boundary Conditions and Loads. Multiple Simultaneous Load Cases.

11. Algorithm Parameter Selection for Topology Optimization.

12. Development of a 3D Model of the Optimized Part.

13. Development of a 3D Model of the Optimized Part.

14. Experimental Load Testing of the 3D Printed Optimized Part.

15. Experimental Load Testing of the 3D Printed Optimized Part.

Compulsory literature:

Recommended literature: