Course detail
FEM in Engineering Computations I
FSI-RIV Acad. year: 2023/2024 Winter semester
The course presents an introduction to selected numerical methods in Continuum Mechanics (finite difference method, boundary element method) and, in
particular, a more detailed discourse of the Finite Element Method. The relation to Ritz method is explained, algorithm of the FEM is presented together with
the basic theory and terminology (discretisation of continuum, types of elements, shape functions, element and global matrices of stiffness, pre- and
post-processing). Application of the FEM in different areas of engineering analysis is presented in theory and practice: static linear elasticity, dynamics
(modal analysis and transient problem), thermal analysis. In the practical part students will learn how to create an appropriate computational model and
realise the FE analysis using commercial software.
Language of instruction
Czech
Number of ECTS credits
5
Supervisor
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
The course-unit credits award is based on the individual preparation of two semester projects, proving students have mastered the work with a selected FE
package. Examination has the form of a written test.
Attendance at practical training is obligatory. Study progress is checked in seminar work during the whole semester.
Aims
Aim of the course is to present numerical solution of problems of Structural and Continuum Mechanics by Finite Element Method and to give a general view
of the possibilities of commercial FE packages.
Students learn how to formulate appropriate computational models of typical problems of applied mechanics. They will become experienced in preparation,
running and postprocessing of FE models and able to use any of the commercial FE packages after only a short introductory training.
The study programmes with the given course
Programme N-MTI-P: Materials Engineering, Master's, elective
Programme N-SLE-P: Foundry Technology, Master's, elective
Programme N-IMB-P: Engineering Mechanics and Biomechanics, Master's
specialization BIO: Biomechanics, compulsory
Programme N-ETI-P: Power and Thermo-fluid Engineering, Master's
specialization FLI: Fluid Engineering, compulsory
Programme N-IMB-P: Engineering Mechanics and Biomechanics, Master's
specialization IME: Engineering Mechanics, compulsory
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
Discretisation in Continuum Mechanics by different numerical methods
Variational formulation of FEM, historical notes
Illustration of FE algorithm on the example of 1D elastic bar
Line elements in 2D and 3D space – bars, beams, frames
Plane and axisymmetrical elements, mesh topology and stiffness matrix structure
Isoparametric formulation of elements
Equation solvers, domain solutions
Convergence, compatibility, hierarchical and adaptive algorithms
Plate and shell elements
FEM in dynamics, consistent and diagonal mass matrix
Explicit FE solution
FEM in heat conduction problems, stationary and transient analysis
Optimization with FEM
Computer-assisted exercise
26 hours, compulsory
Teacher / Lecturer
Syllabus
Illustration of algorithm of Finite Difference Method on selected elasticity problem
Commercial FE packages – brief overview
ANSYS – Introduction to environment and basic commands
Frame structure in 2D
Frame structure in 3D
Plane problem of elasticity
3D problem, pre- and postprocessing
Post processing with Workbench
Consultation of individual projects
Modal analysis by ANSYS
Consultation of individual projects
Transient problem of dynamics, stress vaves
Problem of heat conduction and thermal stress analysis
Presentation of semester projects