Course detail

Solution of Basic Problems of Solids Mechanics by FEM

FSI-6KP-AAcad. year: 2024/2025

Students during lectures become familiar with the theoretical foundations of the finite element method, with the essence of numerical computational modelling and with fundamental practical knowledge, which are applied to typical problems of solid mechanics. Practical tasks are divided by 1D, 2D, and 3D level of geometry. Dominantly, the subject is focused on linear static structural analysis, but also an introduction to dynamic analyses and analyses of heat conduction will be presented. The above will be practiced in the ANSYS Workbench computing software. The necessary knowledge of the subject is:

  1. ability to work with ANSYS Workbench software,
  2. understanding of the correct level of the computational model (inclusion of essential variables),
  3. analysis/assessment/verification of the obtained results,
  4. theoretical basement of FEM.

Language of instruction

English

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

doc. Ing. Tomáš Návrat, Ph.D.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Offered to foreign students

Of all faculties

Entry knowledge

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

Rules for evaluation and completion of the course

The graded course-unit credit requirements :

- active participation in seminars,

- knowledge check in the form of a test task,

- individual preparation and presentation of seminar assignments,

- good results in the written test of basic knowledge.


The teacher will specify the specific form of assessment in the first week of the semester.

Attendance at practical training is obligatory. Attendance is checked systematically by the teachers, as well as students’ active participation in the seminars and fundamental knowledge. Unexcused absence is the cause for not awarding the course-unit credit.

Aims

The objective of the course is to present theoretical background of FEM and its practical application to various problems of continuum mechanics. Practical training is done with the commercial FE system ANSYS, which is frequently used at universities, scientific institutions and industrial companies worldwide.

Students gain basic theoretical and practical knowledge of the Finite Element Method. They learn how to use it for solving continuum mechanics problems in complicated two- and three dimensional regions. The acquired knowledge is applicable in all areas of solid mechanics, for students of all branches of engineering study.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Hinton, E. - Owen, D. R. J.: Finite Element Programming
Huebner, K. H. - Thornton, E. A. - Byrom, T. G.: The Finite Element Method for Engineers, 3d ed.
LI, Hua a Shantanu S. MULAY. Meshless methods and their numerical properties. Boca Raton: CRC Press, 2017. ISBN 978-1-138-07231-2. (EN)
Szabó Barna, Babuska, Ivo, Finite Element Analysis : Method, Verification and Validation. John Wiley & Sons, Incorporated, 2021 (EN)
Zienkiewicz, O. C.: The Finite Element Method, 3rd ed.

Recommended reading

Petruška, J: Počítačové metody mechaniky II. FSI VUT, Brno, 2001
Moaveni, S.: Finite Element Analysis: Theory and Applications with ANSYS Prentice Hall; 2nd edition, 2003

Classification of course in study plans

  • Programme B-STI-Z Bachelor's 1 year of study, summer semester, recommended course

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Tomáš Návrat, Ph.D.

Syllabus

  • Introduction to finite element method
  • Theory of finite element method
  • Beam elements: frames, truss structure
  • Plane elements: Plane stress, plane strain and axisymmetric
  • Solid and shell elements
  • Creation of mesh, control of mesh density, influence of discretization on results
  • Solution of dynamic problems - modal, harmonic and transient problems
  • Introduction to program system ABAQUS
  • Thermal conduction problems in ANSYS
  • Basic knowledge on the "art of modelling"

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

doc. Ing. Tomáš Návrat, Ph.D.

Syllabus

1 - 7

  • Introduction of ANSYS Workbench
  • Beam element, truss
  • Plane elements (plane-stress, plane-strain, axisymmetric body)
  • Solid and shell elements
  • Steady-state and transient thermal analysis
  • Finding natural frequencies and mode shapes
  • Dynamic analysis

8 - 12

  • Solving of a given project under the supervision of lecturer

13

  • Presentation of project work by students