Finite Element Method

Enable understanding of theoretical foundations and segments of Finite Element Method for the calculation of line and space structures. Develop creativity and ability to understand, formulate and solve engineering problems independently.

Student is able and competent to analyze and solve problems of beams and plates utilizing The Finite Element Method.

Introduction. Fundamental terms.
Strong and weak form of equilibrium.
Bubnov-Galerkin solution of the boundary-value problem problem. Finite element method.
Convergence of the Finite element method.
Stiffness matrix. Coordinate transformation.
The finite element of the Bernoulli-Euler beam. Hermite polynomials.
The finite element of Timoshenko beam. Hierarchical approximative functions.
Basic working principles of software packages based on the Finite element method.
The theory of bending of thin plates - basics.
Isoparametric finite element of a thin plate subjected to bending.
Plate loaded in-plane - basics.
Isoparametric finite element of an in-plane loaded plate.
Isoparametric three-dimensional (brick) finite elements.

1. G.Radenković, Statika linijskih nosača u ravni, Građevinski fakultet, Beograd, 2007

   (Original)

2. M. Sekulović, Metod konačnih elemenata, Građevinska knjiga, Beograd, 1988.

   (Original)

3. Kojić, M., Slavković, R., Živković, M., Grujović, N.: Metod konačnih elemenata, Mašinski fakultet Kragujevac, 1995.

   (Original)

4. J. Fish, T. Belytschko, A First Course in Finite Elements, Wiley, 2007

   (Original)

It is compulsory to solve and defend 2 project assignments during the semester. The projects must be submitted and defended by the start of next semester. If the students do not pass colloquiums during the semester, they can take correctional colloquiums during the regular examination period.

Interactive lectures and exercises with work on individual assignments. Consultations.