 
Numerical Analysis of Structures 
Abbreviation: NUANKON  Load: 30(L)
+ 0(E)
+ 15(LE)
+ 0(CE)
+ 0(PEE)
+ 0(FE)
+ 0(S)
+ 0(DE)
+ 0(P)
+ 0(FLE)
+ 0()

Lecturers in charge:  prof. dr. sc. Zdenko Tonković 
Lecturers:  dr. sc. Lana Virag
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Laboratory exercises
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Course description: Course objectives: The purpose is to provide students with application of the finite element method in analysis and design of complex mechanical structures. Besides statical analysis, the basics of dynamical and thermal analysis are presented. The computer exercises include use of commercially finite element software package. The efficiency and accuracy of the numerical computations are demonstrated by examples from engineering practices.
Enrolment requirements and required entry competences for the course: Numerical Analysis of Structures is a continuation of the course Finite Element Method. Upon successful completion of this course (course taken but not necessarily passed), students may enroll in Numerical Analysis of Structures (Finite Element Method passed requirement for taking the exam). Students should also have good background in the basic courses of Solid Mechanics, Structural Dynamics, Mechanical Vibrations, Thermodynamics and Structural Stability.
Student responsibilities: Students are expected to attend and actively participate in every lecture and lab. Lecture and exercise attendance is monitored. Each student need to complete course work that requires both hand calculation and computer simulations. Computer simulations should be performed by using finite element program. After students have successfully completed their course work, they have to take the written exam and achieve a score of 50% to pass and to take the oral exam.
Grading and evaluation of student work over the course of instruction and at a final exam: Assessment: 5% attendance, 35% course work, 35% written examination (a twohour written examination at the end of the course), 25% oral examination (a 30 minutes oral examination at the end of the course).
Methods of monitoring quality that ensure acquisition of exit competences: The teaching and learning methods provide knowledge and understanding as well as intellectual and practical skills. The learning outcomes relating to this course are assessed by course work and examination. The course work is used to assess the student"s ability to use advanced Finite Element Analysis (FEA) techniques to model and to solve practical problems. The learning outcomes related to FEA knowledge, understanding and use of numerical principles are tested in the written and oral examination. In order to improve the quality of teaching of the course, all students fill out a teachercourse evaluation questionnaire at the end of semester.
Upon successful completion of the course, students will be able to (learning outcomes): Apply Finite Element Methods to the analysis of complex engineering structures. Understand a number of advanced topics relevant in computational mechanics (locking phenomena, adaptivity, eigenvalue problem, error estimation, integration methods). Analyze and solve problems associated with buckling. Analyze and solve problems associated with dynamics and vibrations. Analyze and solve problems associated with heat transfer. Interpret results from a finite element analysis. Perform Finite Element analysis using appropriate computer packages.
Lectures 1. Finite Element Analysis procedure. Real structurecomputational model. Classification of elements of structures. Idealization errors. Definition of symmetry types in computational model. 2. Presentation of commercially finite element software package. Creating model geometry. Finite element types. 3. Modeliranje materijala. Linearno elastični (izotropni, ortotropni, kompozitni) i elastoplastični modeli. 4. Boundary conditions modelling. Kinematics constraints. Rigid links. 5. Loads modelling. Static, dynamic and thermal loads. 6. Finite element mesh generation. Discretization errors. Convergence of solution. Adaptivity procedure. 7. h, p and hp version of finite elements. 8. Results analysis. Accuracy estimation of results. Locking phenomena. 9. Types of analysis. Static analysis. 10. Eigenvalue analysis. Basics of linear stability. 11. Basics of dynamic analysis. Basic equations. Free vibrations. Modal equations. Forced Vibrations. 12. Basics of thermal analysis. Basic equations. Thermal stress analysis. 13. Contact elements and contact analysis. 14. Modelling of engineering problems: stiffened plates and shells, resolve and nonresolve joints in structures. 15. Finite element method in mechanical design. Numerical analysis and European regulations for structures.
Exercises 1. Examples of real structure idealization with computational model. Presentation of elements of structures. Examples of symmetric and nonsymmetric structures. 2. Creating model geometry using line, area and volumetric elements. Examples of selection of proper finite element. 3. Examples of different technical materials modelling. 4. Examples of different boundary conditions in models. 5. Examples of different loads modelling. 6. Examples of finite element mesh generation. 7. Comparison of results obtained by h, p, and hp version of finite elements. 8. Introduction to the analysis of finite element results. 9. First preliminary examination. 10. Determination of eigenvalues and critical load of structures. 11. Examples of structural dynamic analysis. 12. Examples of thermal stress analysis. 13. Examples of contact analysis. 14. Examples of stiffened plates and shells, resolve and nonresolve joints modelling. 15. Examples of finite element method application in mechanical design. 
Compulsory literature: 
1.  Sorić, J.: Metoda konačnih elemenata. Golden marketing, Zagreb, 2004. 
2.  R.D. Cook, Concepts and Applications of Finite Element Analysis, John Wiley & Sons, 1981. 
3.  Rao, S.S.: The Finite Element Method in Engineering, ButterworthHeinemann, Boston, 1999. 
Recommended literature: 
4.  K.J. Bathe, Finite Element Procedures in Engineering Analysis, PrenticeHall, 1996 
 