### Course: Modelling and Simulation

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 Course title Modelling and Simulation KTS/MOD Lecture + Lesson Bachelor not specified Winter 4 Czech, English Compulsory Face-to-face Course does not contain work placement None The course is available to visiting students
Lecturer(s)
• Konečný Martin, Ing. Ph.D.
• Žabka Petr, Ing. Ph.D.
• Skřivánek Josef, Ing. Ph.D.
• Komárek Jiří, Ing. Ph.D.
• Baťka Ondřej, Ing.
• Friedrich Ondřej, Ing.
Course content
Lectures: 1. Introduction to numerical simulations: nature and importance of modelling, basic types of simulations; finite element method, types of solved problems, basic principle of FEM. 2. Computational model creation: efficient model, basic rules, domain of model application, linear and non-linear models, frequent sources of non-linearity, pre-processing, processing, post-processing. 3. Creation of FEM mesh: dimensions, basic element types, direct and automatic mesh generation, geometry import. 4. Boundary conditions: degrees of freedom, constrains and loads; symmetry, symmetry conditions, symmetry introduction into the model. 5. Structural analysis: linear algebra revision, block matrix multiplication, definition of static structural problems, overview of parameters, position, displacement, strain, stress. 6. Structural analysis relations: equilibrium equations; Strain-displacement relations, Cauchy relations, their derivation and matrix notation; constitutive equations, generalized Hook's law, impact on 2D tasks. 7. Discretization: mesh concept, mesh requirements, storing in memory; base functions, their properties and derivations. 8. FEM variational principle: calculus of variation main idea, weak and strong formulation, minimum total potential energy principle, basic FEM equation derivation. 9. Basic FEM equation: stiffness matrix, its derivation and properties, spring analogy, stiffness matrix assembling; load vector, its derivation and properties, mass distribution analogy. 10. Introduction of boundary conditions: force boundary conditions, influence of discretization, introduction into equations; geometric boundary conditions, influence on solutions and introduction into equations. 11. Basic element types: overview of element types, coordinate transformation; iso-parametric elements, natural coordinate system, numerical integration, Gaussian points. 12. Effective data handling: stiffness matrix band properties, note numbering effect, memory storage; direct algorithms, Gaussian elimination, frontal method, substructures and macroelements; Iterative methods, their principles and properties. 13. Modelling errors: Error types; numerical error, system conditioning, discretizational error, solution convergence, error estimation. 14. Modelling pitfalls: singularity, singularity sources, elements locking, stability, buckling. Seminars: The seminars are focused on modelling and simulation of linear static problems using the FEM system. Students will become familiar with its basic tools, which are used to create and solve a computational model. Emphasis is placed on solution of assigned tasks and interpretation of achieved results. These are mainly solutions of truss, beam and shell structures. Students are assigned individual tasks, which include the creation of a computational model, calculation and evaluation of results.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing), Practicum, Task-based study method
• Class attendance - 56 hours per semester
Learning outcomes
Introduction to modelling of technical problems. Computer-oriented simulations. Finite Element Method in continuous mechanics. Variation formula of FEM - deformation variant. Fundamentals of computer model creation. Effective data handling. Modelling errors. Problem solving using FEM software products.
Student will get knowledge from this subject.
Prerequisites
Elasticity and strength I.
KMP/PP1

Assessment methods and criteria
Written exam, Practical exam

Active participation in tutorials, completion of assignments.
Recommended literature
• Manuál komerčního softwaru..
• Bathe K.J. Finite element procedures. 2006. ISBN 978-0-9790049-2.
• Cook R. D. Finite element modeling for stress analysis. New York, 1995. ISBN 0471107743.
• Hruš T. Základy metody konečných prvků, Technická Univerzita v Libereci, 2005, Liberec..
• KÁNOCZ, A. - ŠPANIEL, M. Metoda konečných prvků v mechanice poddajných těles. /Skripta/. Praha, ČVUT, 1998.
• Kolar V., Němec I., Kanicky V. FEM: principy a praxe metody konečných prvků. 1997. ISBN 80-7226-021-9.
• Petruška J. MKP v inženýrských výpočtech.
• Petruška, J. Počítačové metody mechaniky II. FSI VUT, Brno, 2001.
• ZIENKIEWITZ, O. - MORGAN, K. Finite Element and Approximation. New York, John Wiley and Sons, 1983.

 Study plans that include the course
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