14IIM37 - Introduction to the finite element method

Course specification
Course titleIntroduction to the finite element method
Study programme
Lecturer (for classes)
Lecturer/Associate (for practice)
Lecturer/Associate (for OTC)
    ConditionMathematics 1Облик условљености
    The goalThe objective is to get the students familiar with the basics of the finite element method (FEM), as the most often applied numerical method for solution of problems in materials engineering, as well as to understand the role of FEM in determining the material properties, tracking the behaviour of the material exposed to external loading and development of new materials.
    The outcomeAbility of students to successfully apply the knowledge gained through this course for better understanding of the contents of other courses on the materials engineering study program and capability for solving theoretical and practical problems using software packages.
    Contents of lecturesBasis for application of FEM: Interpolation functions - application of interpolation polinomials in one-dimensional, two-dimensional and three-dimensional problems. Numerical integration in FEM - significance and influence on obtained reults. Application of sooftware packages in materials engineering: Stress and strain field analysis using FEM; simulation of elastic deformation, application of different criteria for plastic yielding of materials. Possibilities for simplification of the analysis - application of symmetry conditions and 2D representation in plane strain and plane stress state. Application of FEM in simulation of steady-state and transient heat conduction. Solving the coupled thermo-mechanical problems.
    Contents of exercisesPractice includes solving of the excercises which illustrate the concepts and their interrelations covered in the theoretical part. Overview of the software packages for FEM computations, overview of the modules of the licensed software package ABAQUS. LAB work in the laboratory for FEM numerical computations. Solving the examples: defining the geiometry (or importing the geometry from another software), forming the mesh in two-dimensional and three-dimensional analysis, selection of the appropriate finite element type, defining the boundary conditions, material properties and model processing. Defining the loading, boundary conditions and initial conditions in thermal problems. Visualization and (postprocessing) manipulation of the computation results: variable fields, diagrams showing change of a variable change during time, along a path or depending on another variable. Postprocessing calculations, analysis of results and report creation.
    1. M. Rakin, B. Međo, Metoda konačnih elemenata u inženjerstvu materijala, udžbenik (na recenziji) Tehnološko-metalurški fakultet, Univerzitet u Beogradu (Original title)
    2. J. Fish, T. Belytschko, A First Course in Finite Elements, Wiley, 2007 (Original title)
    3. G.R. Liu, S.S. Quek, The Finite Element Method - a practical course, 2nd edition, 2013. (Original title)
    4. T. Saito (Editor), Computational materials design, Springer, 1999. (Original title)
    5. M. Sekulović, Metod konačnih elemenata, Građevinska knjiga, Beograd, 1988. (Original title)
    6. ABAQUS User s Manuals, Version 6.11, Simulia, 2012. (Original title)
    Number of hours per week during the semester/trimester/year
    LecturesExercisesOTCStudy and ResearchOther classes
    Methods of teaching
    Knowledge score (maximum points 100)
    Pre obligationsPointsFinal examPoints
    Activites during lectures10Test paper40
    Practical lessons30Oral examination