| Abstract | (semestr ) |
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| 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. |
| Content | |
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1. Course organization. Why study finite elements?
2. One-dimensional elasticity I: Governing equations, boundary conditions
3. One-dimensional elasticity II: Strong and weak forms of boundary value problem, relation to the principle of virtual displacements
4. One-dimensional elasticity III: Galerkin discretization, finite element method as a special case of the Galerkin method, connection to the direct stiffness method
5. One-dimensional steady-state heat transfer I: Governing equations and boundary conditions
6. One-dimensional steady-state heat transfer II: Finite element discretization, information on the mid-term review test
7. Mid-term review test
8. Two-dimensional steady-state heat transfer I: Governing equations and boundary conditions
9. Two-dimensional steady-state heat transfer II: Finite element discretization
10. Two-dimensional elasticity I: Governing equations and boundary conditions
11. Two-dimensional elasticity II: Finite element discretization
12. Convergence of the finite element method and error estimation, information on the final exam
13. Reserve lecture, pre-exam consultations |
| Literature | |
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Compulsory literature:
[1] 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
Recommended literature:
[2] 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
[3] C.B. Moler: Numerical Computing with MATLAB, SIAM, 2004, ISBN: 978-0-898716-60-3, URL: https://doi.org/10.1137/1.9780898717952
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| Prerequisities | |
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| Studijní plány | |
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Předmět je zařazen do následujících studijních plánů:
- studijní plán Civil Engineering (ND2024), skupina Civil Engineering, 1st semester (ND20230100), dop. semestr 1 (valid from 2024/25 )
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