Course detail

FEM for Energy Simulations

FSI-LIVAcad. year: 2025/2026

The course focuses on theoretical and practical aspects of using the finite element method (FEM) in linear strength calculations of structures in the field of energy and fluid engineering. Students will master the basics of formulating FEM problems from the point of view of elasticity and strength, including modeling loading conditions by mechanical and pressure effects of flowing fluid. Advanced attention is paid to the assessment of stresses, deformations, linear stability and fatigue of mechanically loaded structures. Lectures are primarily theoretical, with emphasis on understanding the FEM formulation and analysis of results. Exercises include practical calculations and examples of solutions related to typical technological units and devices in sustainable energy.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Petr Koňas, Ph.D.

Department

Energy Institute (EÚ)

Entry knowledge

Matrix notation, linear algebra, function of one and more variables, calculus, differential equations, elementary dynamics, elasticity and thermal conduction.

Rules for evaluation and completion of the course

Credits: active participation in exercises, submission of a semester project (FEM model with strength and possibly fatigue analysis of the assigned component), minimum 75% participation + control task.
- Exam: written part (theoretical questions + computational example) + oral exam (FEM concepts, interpretation of results). The exam may be based on the completed semester project.

Aims

The learning objectives of this course are:

  • To introduce students to the methodology of linear FEM analysis in the context of mechanical problems related to hydrodynamic/thermohydraulic loading of structures.
  • To emphasize the mathematical and physical foundations of FEM formulation in relation to the theory of linear elasticity.
  • To understand the importance of boundary conditions, load modeling and interpretation of results (stress, deformation, safety).
  • To demonstrate the principles of fatigue assessment of structures under cyclic loading induced by a fluid environment.
  • To prepare students for the effective application of strength calculations in the design or analysis of energy equipment.

 

After completing the course, the student will be able to:

  • Describe and derive the weak form of equilibrium equations and their subsequent formulation in FEM.
  • Apply knowledge of continuum mechanics to the solution of 2D and 3D elasticity problems using FEM.
  • Correctly specify boundary conditions, physical properties and loads corresponding to real situations in the energy industry (e.g. pressure pulsations, thermal expansion, force effects of the medium).
  • Perform your own assessment of the linear elasticity problem - determination of stresses, deformations, principal stresses and critical areas.
  • Determine the stability of structures and stress properties in connection with shape and geometric optimization.
  • Apply a basic analytical approach to assessing fatigue damage and service life of exposed parts under conditions of hydrodynamic stress.

Study aids

ZIENKIEWICZ, O. C.; TAYLOR, Robert L. a NITHIARASU, Peruma. The finite element method for fluid dynamics. 7th ed. Oxford: Butterworth-Heinemann, 2014. ISBN 978-1-85617-635-4.

ZIENKIEWICZ, O. C.; TAYLOR, Robert L. a ZHU, J. Z. The finite element method: its basis and fundamentals. 7th ed. Amsterdam: Butterworth-Heinemann, 2013. ISBN 978-1-85617-633-0.

ZIENKIEWICZ, O. C.; TAYLOR, Robert L. a NITHIARASU, Peruma. The finite element method for fluid dynamics. 7th ed. Oxford: Butterworth-Heinemann, 2014. ISBN 978-1-85617-635-4.

Ansys Help. Online. 2024. Dostupné z: https://ansyshelp.ansys.com/.

Prerequisites and corequisites

Not applicable.

Basic literature

K.-J.Bathe: Finite Element Procedures, K.-J.Bathe, 2014
R.D.Cook: Concepts and Applications of Finite Element Analysis, J.Wiley, 2001
Zienkiewicz, O. C., Taylor, R. L., The Finite Element Method for Solid and Structural Mechanics, Elsevier, 2013

Recommended reading

J.Petruška: MKP v inženýrských výpočtech http://www.umt.fme.vutbr.cz/images/opory/MKP%20v%20inzenyrskych%20vypoctech/RIV.pdf
M.Španiel, Z.Horák: Úvod do metody konečných prvků, Nakladatelství ČVUT, 2011
V.Kolář, I.Němec, V.Kanický: FEM principy a praxe metody konečných prvků, Computer Press, 2001

Classification of course in study plans

  • Programme N-ETI-P Master's

    specialization FLI , 2 year of study, winter semester, compulsory

  • Programme N-SUE-P Master's 1 year of study, winter semester, compulsory

  • Programme C-AKR-P Lifelong learning

    specialization CZS , 1 year of study, winter semester, elective

Type of course unit

 

Lecture

26 hod., compulsory

Teacher / Lecturer

doc. Ing. Petr Koňas, Ph.D.

Syllabus

1. Introduction to strength calculations in energy systems. The role of FEM in mechanical analysis under the action of fluids.
2. Formulation of the linear elasticity problem – basic equations of continuum mechanics, constitutive relations.
3. Weak (variational) formulation of elasticity equations. Principle of virtual work.
4. Finite element method – discretization, element shapes, basis functions, solution of systems of equations.
5. Modeling of structural loads – volume, area, linear loads; effects of fluid pressure, overload, impact forces.
6. Boundary conditions – rigid connections, simple support, symmetry, contact problems, ...
7. Analysis of FEM results – primary and secondary quantities (stress, deformation), strength hypotheses.
8. Loads in a fluid environment – ​​effects of pressure pulsations, turbulence, without inertial loading.
9. Stability of structures in terms of flow effects – elasticity and critical loads, risks of vibration excitation.
10. Stress analysis in rotating machines (turbines, pumps); structures subjected to cyclic loading.
11. Introduction to material fatigue – basic concepts, S-N curves, Goodman diagram, Miner’s rule.
12. Linear fatigue assessment in the FEM environment – ​​assumptions, computational approaches, geometric details, risk areas.
13. Verification of FEM results, validation procedures, agreement with analytical calculations

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

doc. Ing. Petr Koňas, Ph.D.

Syllabus

Projektově orientovaná výuka v prostředí ANSYS

1. Seznámení s MKP rozhraním (ANSYS), tvorba modelu, jednoduchá 2D nosná konstrukce.
2. Simulace lineární elastické úlohy – jednoduché tažení, porovnání s analytickým výpočtem.
3. Vliv různých typů zatížení(síla, moment, tlak). Přenos zatížení z kapalného média.
4. Okrajové podmínky v 3D konstrukčních prvcích – modelování upnutí, souměrnosti, omezení pohybu.
5. Posouzení napětí a deformace ve strojních součástích – turbínové lopatky (zjednodušený model).
6. Pružnostní analýza potrubí a výměníků – příklady, tlakové zatížení.
7. Výpočet základních napěťových hypotéz – Tresca, HMH, výpočet bezpečnostních faktorů.
8. Analýza lokálních koncentrací napětí – vliv otvorů, svarů, přechodů.
9. Analýza napětí v rotačních částech vystavených odstředivým silám – rotor čerpadla.
10. Úvod k únavové analýze – výpočet životnosti podle Minerova pravidla.
11. Modelování cyklického zatížení – časová historie zatížení.
12. Posouzení únavy konstrukce vystavené hydrodynamickým vlivům – ukázka typického výpočtu.
13. Samostatná práce – zadání určeného úkolu, zpracování komplexního příkladu.