Course detail

# Solution of Basic Problems of Solids Mechanics by FEM

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.

Learning outcomes of the course unit

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 and fluid continuum mechanics, for students of all branches of engineering study.

Prerequisites

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

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Zienkiewicz, O. C.: The Finite Element Method, 3rd ed.
Moaveni, S.: Finite Element Analysis: Theory and Applications with ANSYS Prentice Hall; 2nd edition, 2003
Hinton, E. - Owen, D. R. J.: Finite Element Programming
Petruška, J: Počítačové metody mechaniky II. FSI VUT, Brno, 2001
Huebner, K. H. - Thornton, E. A. - Byrom, T. G.: The Finite Element Method for Engineers, 3d ed.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Course unit credist will be awarded based on evaluation of the project. In the project the student has to prove the ability to solve given problem by using FEM.

Language of instruction

English

Work placements

Not applicable.

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.

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

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.

Classification of course in study plans

• Programme B3S-Z Bachelor's

branch B-STI , 1. year of study, summer semester, 4 credits, recommended

• Programme B3S-A Bachelor's

branch B-STI , 3. year of study, summer semester, 4 credits, compulsory-optional

• Programme M2I-Z Master's

branch M-STI , 1. year of study, summer semester, 4 credits, recommended

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

1. Introduction to finite element method.
2. Beam elements. Truss structure.
3. Beam elements. Frames.
4. Plane elements. Plane stress, plane strain and axisymmetric.
5. Theory of finite element method.
6. Solid and shell elements.
7. Creation of mesh, control of mesh density, influence of discretization on results.
8. Solution of dynamic problems - modal, harmonic and transient problems.
9. Introduction to program system ABAQUS.
10. Thermal conduction problems in ANSYS.
11. Programming macro (APDL).
12. Basic knowledge on the "art of modelling".
13. Hardware for FEM jobs.

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

Syllabus

1. Introduction of ANSYS Workbench.
2. Beam element. Truss.
3. Beam element. Beams, frames.
4. Plane elements (plane-stress and plane-strain).
5. Plane elements (axisymmetric body).
6. Solid and shell elements.
7. Connecting bodies, contact.
8. Solution of dynamic problems.
9. Solving of a given project under the supervision of lecturer.
10. Solving of a given project under the supervision of lecturer.
11. Solving of a given project under the supervision of lecturer.
12. Solving of a given project under the supervision of lecturer.
13. Presentation of Project work by students.

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