D112 - Finite element method in materials engineering

Course specification
Course titleFinite element method in materials engineering
Study programme
Lecturer (for classes)
Lecturer/Associate (for practice)
Lecturer/Associate (for OTC)
    ConditionОблик условљености
    The goalThe objective of the course is gaining knowledge and mastering the skills of finite element modelling using licensed software.
    The outcomeStudents develop independence in other teaching and working tasks, especially in solving the complex problems.
    Contents of lecturesIntroduction to the finite element method (FEM) theory. Development of FEM. Errors and convergence of the solution. Virtual work principle. Comparison of FEM and other numerical and analytical methods. Application of matrix calculus in representation of stress and strain fields. Discretization of domain and application in materials engineering. Basic shapes and types of finite elements. Determining the stiffness matrix. Interpolation functions - isoparametric formulation. Numerical integration. Solving linear problems in materials engineering. Representation of thermal loads. Influence of material anisotropy, Geometry non-linearity - contact problems. Constitutive equations for nonlinear material behaviour. Heterogeneous materials, problem of porosity. FEM in analysis of material damage - application to components of process equipment exposed to complex thermomechanical loading. Basics of FEM in fluid mechanics - interaction of fluid and deformable body.
    Contents of exercisesLAB and study research work will consist of exercises which include application of different constitutive models of materials exposed to external loading; this part of the course will be conducted using the licensed software package ABAQUS in the laboratory for FEM numerical computations: ; Types of elasticity and plasticity (linear/non-linear, isotropic/anisotropic, etc.); Defining the properties of fiber-reinforced laminate composite materials; Dependence of yield strength on temperature and strain rate (Johnson-Cooke law - application in simulation of material joining by welding); Modelling damage development in the material (crack growth tracking, extended FEM); Examples of failure analyses of process equipment components using FEM; Simulation of fluid flow by the finite element method. Submodelling as a technique for more efficient use of computer resources.
    1. M. Rakin, B. Međo, Finite Element Method in Materials Engineering (in Serbian, under review), Faculty of Technology and Metallurgy, University of Belgrade
    2. K.J. Bathe, Finite Element Procedures, Prentice - Hall, 2007
    3. O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 7th Edition, 2013
    4. S.S. Rao, The Finite Element Method in Engineering, Fourth ed., Pergammon Press, 2004
    5. M. Kojić., Computational Procedures in Inelastic Analysis of Solids and Structures, Center of Sci. Research of SANU, Kragujevac, 1997
    6. M. Kojić, N Filipović, B. Stojanović, N. Kojić, Computer Modeling in Bioengineering, Wiley, 2008
    7. D. Blagojević, D. Ružić, Elements of numerical mechanics (in Serbian), University of Banja Luka, 2006
    8. ABAQUS User s Manuals, Version 6.11, Simulia, 2012
    Number of hours per week during the semester/trimester/year
    LecturesExercisesOTCStudy and ResearchOther classes
    Methods of teachingLectures and practices in the classroom (using the overhead projector, blackboard, computer and video beam). LAB work: solving the examples using the licensed software package ABAQUS in the laboratory for FEM numerical computations.
    Knowledge score (maximum points 100)
    Pre obligationsPointsFinal examPoints
    Activites during lectures10Test paper
    Practical lessons25Oral examination35