Syllabus – Course B7
Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union within the confines of the European Social Fund
and realized under surveillance of Ministry of Science and Higher Education.
Field of studies: CIVIL ENGINEERING First cycle programme Course: COMPUTATIONAL METHODS
Class type: L C D A
Semester(s): IV
Number of hours per semester:
15 30
Prerequisites: Applied Mathematics and Numerical Methods, Strength of Materials Effects of
learning - expertise and competences acquired
The student should understand the theoretical foundations of approximation methods and the algorithm of the finite element method for stationary
problems, especially for statics of bar structures and two-dimensional
configurations. The student should have a basic capability of using typical FEM packages.
DESCRIPTION OF COURSE Lecture:
Mathematical modelling (local and global formulation). Approximation and interpolation. Classical finite difference method (FDM). Variational methods of approximate solution (weighted residual, Galerkin method). Fundamentals of finite element method (FEM). Finite element modelling of bar structures and two-dimensional problems (stationary heat flow, plane stress statics).
lAboratory:
Approximate methods to solve partial differential equations. FEM algorithm for bar structures.
Simulation of heat flow in a plate. Computation of stress distribution in a deep beam. Used software: MATLAB (toolboxes CALFEM and PDETOOL), RMWIN, ROBOT. Assignments:
determination of beam deflection using FDM and FEM, solution of a simple truss and frame, computation of a two-dimensional heat flow problem using PDETOOL, solution of a two- dimensional statics problem using ROBOT.
Bibliography (primary and additional):
1. P.-E. Austrell et al, Calfem - a finite element toolbox, version 3.4, Structural Mechanics, LTH Sweden, 2004
2. R.D. Cook, Finite Element Method for Stress Analysis, J. Wiley & Sons 1995 3. C.A. Felippa, Introduction to Finite Element Methods, University of Colorado,
http://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/Home.html
4. N. Ottosen and H. Petersson, Introduction to the Finite Element Method, Prentice Hall 1992 5. Cz. Cichoń, W. Cecot, J. Krok, P. Pluciński, Metody komputerowe w liniowej mechanice
konstrukcji Skrypt PK, Kraków 2010
6. G. Rakowski, Z. Kacprzyk, Metoda elementów skończonych w mechanice konstrukcji, Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa 2005
Assessment method: passing two written tests and positive grade from laboratory assignments Contact person: Jerzy Pamin, PhD, DSc, Prof.CUT (jpamin@L5.pk.edu.pl )
