Numerical Analysis of Structures

Course guarantor:

Jan Zeman

Lecturer:

Tomáš Krejčí, Jan Zeman

Tutor:

Tomáš Krejčí, Jan Zeman

Supervisor:

Department of Mechanics

Synopsis:

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.

Requirements:

no prerequisities

Syllabus of lectures:

* 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

Syllabus of tutorials:

* 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)

Study Objective:

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.

Study materials:

!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

Note:

Further information:

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

Time-table for winter semester 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
Mon
Tue
Wed
Thu
Fri	roomTH:A-228 08:00–09:50 (lecture parallel1) Thákurova 7 (budova FSv) roomTH:A-228 10:00–11:50 (lecture parallel1 parallel nr.101) Thákurova 7 (budova FSv)

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Civil Engineering (compulsory course)
• Civil Engineering (compulsory course)