Solution of Basic Problems of Solids Mechanics by FEM (FSI-6KP-A)

Academic year 2020/2021

Supervisor:	doc. Ing. Tomáš Návrat, Ph.D.
Supervising institute:	ÚMTMB	all courses guaranted by this institute
Teaching language:	English
Aims of the course unit:
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.
Learning outcomes and competences:
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.
Course contents:
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.
Teaching methods and criteria:
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:
The graded course-unit credit requirements : - active participation in seminars, - good results in the written test of basic knowledge, - individual preparation and presentation of seminar assignments.
Controlled participation in lessons:
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.
Type of course unit:
Lecture	13 × 2 hrs.	optionally
Computer-assisted exercise	13 × 2 hrs.	compulsory
Course curriculum:
Lecture	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	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. Steady-state thermal analysis. 8. Finding natural frequencies and mode shapes. 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.

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