Numerical Analysis of Structures

Garant předmětu:

Jan Zeman

Přednášející:

Tomáš Krejčí, Jan Zeman

Cvičící:

Tomáš Krejčí, Jan Zeman

Předmět zajišťuje:

katedra mechaniky

Anotace:

Overview of direct stiffness method of structural mechanics. Weak solution of one-dimensional elasticity equations. Galerkin method, Gauss integration, principle of the Finite Element method. Steady state heat conduction in one dimension. Two-dimensional heat conduction problem, triangular finite elements. Two-dimensional elasticity problems. Convergence of FEM, error estimates.

Požadavky:

no prerequisities

Osnova přednášek:

* Course organization. Why study finite elements?

* One-dimensional elasticity I: Governing equations, boundary conditions

* One-dimensional elasticity II: Strong and weak forms of boundary value problem, relation to principle of virtual displacements

* One-dimensional elasticity III: Galerkin discretization, finite element method as a special case of the Galerkin method, connection to the direct stiffness method

* One-dimensional steady-state heat transfer I: Governing equations and boundary conditions

* One-dimensional steady-state heat transfer II: Finite element discretization, information on the mid-term review test

* Mid-term review test

* Two-dimensional steady-state heat transfer I: Governing equations and boundary conditions

* Two-dimensional steady-state heat transfer II: Finite element discretization

* Two-dimensional elasticity I: Governing equations and boundary conditions

* Two-dimensional elasticity II: Finite element discretization

* Convergence of the finite element method, information on the final exam

Osnova cvičení:

* Overview of direct stiffness method for planar truss structures

* Gentle introduction to MATLAB(R) Online

* MATLAB-based analysis of planar truss structures, Homework #1

* Finite element method for one-dimensional elasticity I (hand calculations)

* Finite element method for one-dimensional elasticity II (MATLAB-based analysis), Homework #2

* Finite element method for one-dimensional heat conduction I (hand calculations)

* Finite element method for one-dimensional heat conduction II (MATLAB-based analysis), Homework #3

* Finite element method for two-dimensional heat conduction I (hand calculations)

* Finite element method for two-dimensional heat conduction II (MATLAB-based analysis), Homework #4

* Finite element method for two-dimensional elasticity I (hand calculations)

* Finite element method for two-dimensional elasticity II (MATLAB-based analysis), Homework #3

* Convergence of finite element method for two-dimensional elasticity (MATLAB-based analysis)

Cíle studia:

Students will understand all essential steps of FEM and will be able to apply it to the basic problems of structural mechanics and heat transfer problems. A basic understanding of FEM implementation principles will be ensured by MATLAB-oriented exercises.

Studijní materiály:

!J. Fish and T. Belytschko: A First Course in Finite Elements, John Wiley & Sons, 2007, ISBN:978-047-003-580-1, URL: https://dx.doi.org/10.1002/9780470510858

?P. Krysl: A Pragmatic Introduction to the Finite Element Method for Thermal and Stress Analysis, World Scientific Press, 2006, ISBN: 978-981-256-876-2, URL: https://doi.org/10.1142/6169

?C.B. Moler: Numerical Computing with MATLAB, SIAM, 2004, ISBN: 978-0-898716-60-3, URL: https://doi.org/10.1137/1.9780898717952

Poznámka:

Další informace:

Course Moodle space, hosted at https://moodle-vyuka.cvut.cz/

Rozvrh na zimní semestr 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
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Pá	místnost TH:A-228 08:00–09:50 (přednášková par. 1) Thákurova 7 (budova FSv) A228místnost TH:A-228 10:00–11:50 (přednášková par. 1 paralelka 101) Thákurova 7 (budova FSv) A228

Rozvrh na letní semestr 2024/2025:

Rozvrh není připraven

Předmět je součástí následujících studijních plánů:

• Civil Engineering (povinný předmět)
• Civil Engineering (povinný předmět)