- Subject code: 132NAST
- No. of credits: 2 + 2
- Credit and Exam

Short 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.

References:

- J. Fish and T. Belytschko:A First Course in Finite Elements,John Wiley & Sons, 2007 (free access @CTU)
- O. C. Zienkewicz and R. L. Taylor: The Finite Element Method, Volume 1, The Basis, Fifth Edition, Butterworth-Heinemann, 2000
- C. Felippa:Introduction to Finite Element Methods,Department of Aerospace Engineering Sciences,University of Colorado at Boulder
- Z. Bittnar and J. Šejnoha:Numerical Methods in Structural Mechanics, ASCE Press, 1996

MATLAB links:

- G. Strang:Short MATLAB tutorial
- C. Moler:Numerical Computing with MATLAB

- Grading policy (correction 15/11/2022)
- Semester projects (optional)
- Retaining wall (10 points)
- Heat transfer 2D (5 points)
- Homework assignments (optional)
- Mid-term review test (example)
- Exam (example)

- Lectures:
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 5
- Lecture 6
- Lecture 7 + TRIANGULAR ELEMENT WITH LINEAR SHAPE FUNCTIONS
- Lecture 9 + TRIANGULAR ELEMENT WITH LINEAR SHAPE FUNCTIONS
- Lecture 10 (by prof. Zeman)
- Lecture 11
- Lecture 12a - automatic mesh generation (by prof. Rypl)

- Tutorials:
- Tutorial 1:Working in MATLAB and OCTAVE
- Tutorial 2:1D Elastic Bar Element: Localization, Matlab benchmarks Seminar02.m.zip

**New: Tutorial 2 - appendix:**Benchmark with thermal loading, Matlab benchmarks Seminar02_apen.zip

- Tutorial 3:2D Trusses, Solution in Matlab Seminar03.m
- Tutorial 4:Aproximation Functions and Numerical Integration for 1D Problems, Matlab benchmarks Seminar04.zip
- Tutorial 5: One dimensional heat transfer analysis - steady state, Matlab benchmarks Seminar05.zip
- Tutorial 6: One dimensional non-stationary heat transfer analysis, Matlab benchmarks Seminar06.zip
- Tutorial 7+8:Two dimensional steady state heat transfer analysis, Matlab benchmarks Matlab_seminar07.zip
- Tutorial 9:Two dimensional problem - Linear elasticity, Analytical solution, and Matlab benchmarks: Seminar09.zip
- Tutorial 10:Beams, Matlab benchmarks: Seminar10.zip
- Tutorial 11:A posteriori error estimation, Matlab benchmarks: Seminar11.zip

- Course Schedule:

Date | Lecture | Tutorial |
---|---|---|

October 27 | Introduction to FEM, Overview of Direct Stiffness Method - 1D Elasticity | Introduction to Programming - Matlab, Octave, Excel; Localization |

October 4 | Strong and Weak Forms, Weighted Residual Method, Lagrange Principle | 1D Elastic Element: Localization, Benchmarks |

October 11 | Aproximation Functions and Numerical Integration - Gauss Quadrature, Finite Elements | 2D Trusses |

October 18 | Finite Element Formulation for One-Dimensional Problems - Linear Elasticity | Linear and Quadratic Bar Elements, Gauss Quadrature, Natural Coordinates |

October 25 | Dean's Day |
Dean's Day |

November 1 | Finite Element Formulation for One-Dimensional Heat Conduction Problems | 1D Heat Conduction |

November 8 | Finite Element Formulation for One-Dimensional Nonstationary Heat Conduction Problems | 1D Nonstationary Heat Transfer |

November 15 | Two-Dimensional Heat Conduction Problems | 2D Heat Conduction |

November 22 | Finite Element Formulation for Two-Dimensional Problems - Linear Elasticity | 2D Problems - Plane Stress and Plane Strain Problems |

November 29 | Mid-term test |
2D Problems - Plane Stress and Plane Strain Problems |

December 6 | Finite Element Formulation for Beams | Beams |

December 13 | Numerical Aspects of FEM I | Beams |

December 20 | Numerical Aspects of FEM II | A posteriori Error Estimation |

Downloads:

Links:

- Finite Element Method - Wikipedia
- Finite Element Analysis - Wikipedia
- Matlab
- Octave
- Finite Element Analysis of Solids and Fluids (K.J. Bathe, MIT Open Courseware)
- Introduction to Finite Element Methods (C. Felippa, University of Colorado)
- Short matlab tutorial (G. Strang)
- Numerical Computing with MATLAB (C. Moler)
- A First Course in Finite Elements (J. Fish and T. Belytschko) [Free chapter on MATLAB]