Description:

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.

Contents:

* 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

Seminar contents:

* 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)

Recommended literature:

!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

Keywords:

matrix methods of structural mechanics, weak solution, Galerkin discretization, elasticity, heat transfer, FEM coding

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar