Course detail

Introduction to FEM

FSI-KFEAcad. year: 2017/2018

The course is using mostly direct elasticity problems that can be solved also analytically. Aside from ANSYS Mechanical APDL user skills, the students will also learn differences between analytical solutions and various FEM approaches. This is a foundation for correct application of FEM, result evaluation and interpretation in cases where the analytical approach is not convenient or may not be possible at all.

Learning outcomes of the course unit

The students will acquire basic principles of FEM and will be able to make decisions about correct application of this method for design evaluation of process equipment. They will be also familiar with analysis result evaluation using stress categories, which is adopted by most standards for pressure vessel design in Europe and worldwide.


Basic knowledge about elasticity and stiffness of materials, mechanics, limit states and material properties.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Schneider, P.; Vykutil, J.: Aplikovaná metoda konečných prvků: lineární elastická analýza rotačních skořepinových konstrukcí. PC-DIR, Brno, 1997. (CS)
Lee, H.-H.: Finite element simulations with ANSYS workbench 14: Theory, applications, case studies. Schroff Development Corp., Mission, KS, USA, 2012. (EN)
Tu, J.; Yeoh, G.H.; Liu, C.: Computational fluid dynamics. Elsevier, Amsterdam, Netherlands, 2013. (EN)
Huebner, K. H.; Dewhirst, D. L.; Smith, D. E.; Byron, T. G.: The finite element method for engineers, 4th ed. John Wiley & Sons, Inc., Hoboken, NJ, USA, 2001. (EN)
Anderson, J. D.: Computational fluid dynamics: The basics with applications. McGraw-Hill, New York, NY, USA, 1995. (EN)
Uruba, V.: Turbulence, 2. přepracované vydání. České vysoké učení technické v Praze, 2014. (CS)
Versteeg, H. K.; Malalasekera, W.: An introduction to computational fluid dynamics: The finite volume method. Pearson Education Ltd., Harlow, UK, 2007. (EN)

Planned learning activities and teaching methods

The course unit is taught using exercises, which are focused on practical topics.

Assesment methods and criteria linked to learning outcomes

Seminars will be graded with regard to active participation in seminars as well as accomplishment of partial tasks.

Language of instruction


Work placements

Not applicable.


Finite element method (FEM) is widely used for process equipment evaluation. This course is the first part of a two-semester series and its purpose is teaching the students basic principles and restrictions of FEM. The students will learn common procedures for working with ANSYS Mechanical APDL software that is very good aid in learning of FEM principles, whose knowledge is necessary for correct application of FEM . Sequel of this course, Practical application of FEM, builds on these foundations and teaches the students application of FEM for solving real problems according to standards.

Specification of controlled education, way of implementation and compensation for absences

Attendance at seminars will be checked and absences will be compensated by self-study of the missed topic.

Classification of course in study plans

  • Programme M2I-P Master's

    branch M-PRI , 1. year of study, summer semester, 3 credits, compulsory-optional
    branch M-PRI , 1. year of study, summer semester, 3 credits, compulsory-optional

Type of course unit


Computer-assisted exercise

39 hours, compulsory

Teacher / Lecturer


1. Introduction and basics of FEM
- theoretical introduction to FEM: basic terms and equation, element types, boundary conditions
- getting familiar with graphic user interface and basic workflow in ANSYS Mechanical APDL using simple 2D frame analysis
2. Beam bending
- modelling using beam elements
- modelling using 2D plane elements (triangle vs. quad)
- modelling using 3D solid elements
- result comparison with analytical approach
3. Piping branch
- using special pipe elements
- linear elastic analysis and result evaluation
4. Axisymmetric shells I
- comparison of membrane and shell elements
- result comparison with analytical approach
5. Axisymmetric shells II
- special structures and loads
6. Modelling shell structures
- advantages and restrictions of shell elements
7. Flat ends under pressure
- comparison of linear elastic analysis with analytical approach
- limit analysis
- comparison with EN 13445
8. Shell model of a pressure vessel (SMPV)
- geometry import
- geometry adjustments and meshing
9. SMPV – load cases
- preparation of components for boundary conditions and loads
- solution and result evaluation
10. SMPV –stress caused by temperature distribution
- thermal analysis
- application of thermal analysis results into structural analysis as a boundary condition
11. SMPV – submodelling
12. SMPV – linear elastic analysis result evaluation
- using stress categories according to EN 13445
13. SMPV – graphical outputs
- rendering of representative images
- model, boundary conditions and loads
- analysis results