Numerical Analysis of Structures
Code  Completion  Credits  Range  Language 

132NAST  Z,ZK  5  2P+2C  English 
 Garant předmětu:
 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 onedimensional elasticity equations. Galerkin method, Gauss integration, principle of the Finite Element method. Steady state heat conduction in one dimension. Twodimensional heat conduction problem, triangular finite elements. Twodimensional elasticity problems. Convergence of FEM, error estimates.
 Requirements:

no prerequisities
 Syllabus of lectures:

* Course organization. Why study finite elements?
* Onedimensional elasticity I: Governing equations, boundary conditions
* Onedimensional elasticity II: Strong and weak forms of boundary value problem, relation to principle of virtual displacements
* Onedimensional elasticity III: Galerkin discretization, finite element method as a special case of the Galerkin method, connection to the direct stiffness method
* Onedimensional steadystate heat transfer I: Governing equations and boundary conditions
* Onedimensional steadystate heat transfer II: Finite element discretization, information on the midterm review test
* Midterm review test
* Twodimensional steadystate heat transfer I: Governing equations and boundary conditions
* Twodimensional steadystate heat transfer II: Finite element discretization
* Twodimensional elasticity I: Governing equations and boundary conditions
* Twodimensional 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
* MATLABbased analysis of planar truss structures, Homework #1
* Finite element method for onedimensional elasticity I (hand calculations)
* Finite element method for onedimensional elasticity II (MATLABbased analysis), Homework #2
* Finite element method for onedimensional heat conduction I (hand calculations)
* Finite element method for onedimensional heat conduction II (MATLABbased analysis), Homework #3
* Finite element method for twodimensional heat conduction I (hand calculations)
* Finite element method for twodimensional heat conduction II (MATLABbased analysis), Homework #4
* Finite element method for twodimensional elasticity I (hand calculations)
* Finite element method for twodimensional elasticity II (MATLABbased analysis), Homework #3
* Convergence of finite element method for twodimensional elasticity (MATLABbased 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 MATLABoriented exercises.
 Study materials:

!J. Fish and T. Belytschko: A First Course in Finite Elements, John Wiley & Sons, 2007, ISBN:9780470035801, 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: 9789812568762, URL: https://doi.org/10.1142/6169
?C.B. Moler: Numerical Computing with MATLAB, SIAM, 2004, ISBN: 9780898716603, URL: https://doi.org/10.1137/1.9780898717952
 Note:
 Further information:
 Course Moodle space, hosted at https://moodlevyuka.cvut.cz/
 Timetable for winter semester 2023/2024:

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  Timetable for summer semester 2023/2024:
 Timetable is not available yet
 The course is a part of the following study plans:

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