• Zavarivanje i zavarene konstrukcije, Semester 3, position 2

Learning the fundamentals of numerical analysis and optimization. Learning the fundamentals of optimization. Students are taught how to formulate optimization problems and identify essential parts of the optimization process. Teaching students how to use optimization methods to optimize constructions. Basic understanding of the reliability of machine components and constructions. Understanding how to determine the reliability of basic and complicated systems. Improving teamwork abilities and linking information and ideas from many fields. Knowing the technical and economic significance of faliure, as well as possessing the knowledge to analyze faliure based on the established cause-manifestation categories.

The student will be able to: 1. Establish the optimization model of the machine system, identify the necessary variables, and describe the functional limitations and criteria for the appropriate optimization assignment after successfully completing the course. 2.Conduct an analysis and simulation of the sensitivity of the established functional constraints to parameter changes. 3. Suggest a procedure for decomposing large construction optimization models into less complex ones, and create a MATLAB application to do so. 4. Use one-dimensional and multidimensional numerical methods in the MATLAB software programme. 6. Use and create new optimization methods to identify the optimal sizes of complicated machine systems on your own or as part of a team. 7. Describe the fundamental markers of reliabilty indicators; 8. Use approximation approaches to calculate the basic reliability indicators of machine parts and structures. 9. Use analytical methodologies to determine the fundamental reliability indicators of machine parts and structures. 10. Determine the parameters of basic distributions using probability paper; 11. Examines the effect of working and critical stress distribution on the safety and reliability of machine parts and structures. 12. Assess the reliability of complicated systems with series, parallel, and combination element connections. 13. Constructs machine parts and assemblies on the reliability basis.

Introduction to modeling and optimization. Optimization problem setting. General mathematical model for optimization. Graphical optimization procedure. Defining the fiesable area. Use of MATLAB program for graphical optimization procedure. Optimization problems without constraints. Optimization problems with constraints. Post optimal analysis: the physical meaning of Langrange multipliers. Engineering optimization examples in the MATLAB program. Non-linear programming. Constraints in the form of equality. Constraints in the form of inequalities. Numerical methods for unconstrained optimization. Numerical methods for optimization with constraints. Method of penalty functions. Optimization examples in MATLAB. The importance of reliability in the process of designing and constructing machine structures. Definition of reliability. Basic indicators of reliability. Estimated and theoretical reliability, confidence level. Reliability of elementary and partial function executors for different failure intensity functions: constant function, linearly increasing and exponentially increasing function. Operating and critical stress distributions. Comparative analysis of construction based on reliability and safety factor. Methodology for dimensioning elements and joints of mechanical construction based on the required reliability. Reliability of machine structures for different connections (structures) of elements: serial, parallel and combined. Statistical analysis of complex tolerances (tolerance chains). Correlation between reliability and safety factor for different ratios of standard deviations and mean values of operating and critical stress.

Using the graphical method to determine the optimal solution to a linear programming issue. Development of suitable MATLAB programming codes and implementation of optimization methods within this package to address optimization challenges. The approximate determination of fundamental reliability indicators. Assessing reliability using analytic reliability functions. Distributions of operating and critical stress. Reliability-based dimensioning of machine construction elements. The reliability of structures with series-parallel and mixed element connection. Statistical analysis of complex tolerances. Corellation between reliabilty and safety factor.

Defined within the module curriculum.

Computer usage: Students are required to use computers and MATLAB programming tools.

Total assigned hours: 75

New material: 20
Elaboration and examples (recapitulation): 10

Auditory exercises: 0
Laboratory exercises: 20
Calculation tasks: 0
Seminar paper: 6
Project: 2
Consultations: 0
Discussion/workshop: 2
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 7
Review and grading of the project: 0
Test: 0
Test: 3
Final exam: 5

Activity during lectures: 5
Test/test: 35
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 30
Project: 0
Final exam: 30
Requirement for taking the exam (required number of points): 35

Singiresu S. Rao "Engineering Optimization Theory and Practice" John Wiley and Sons, inc., 2019.; Владимир Зељковић, Стеван Максимовић, Прорачун поузданости механичких елемената и конструкција, Графокомерц, Београд, 1998.; ; Градимир Ивановић, Поузданост техничких система, Београд, 2011;; Милосав Огњановић, Развој и дизајн машина, Београд, 2000.;; Singiresu S. Rao "Engineering Optimization Theory and Practice" John Wiley and Sons, inc., 2019.