# 151-0361-00L An Introduction to the Finite-Element Method

Semester | Spring Semester 2018 |

Lecturers | G. Kress, C. Thurnherr |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | The class includes mathematical ancillary concepts, derivation of element equations, numerical integration, boundary conditions and degree-of-freedom coupling, compilation of the system’s equations, element technology, solution methods, static and eigenvalue problems, iterative solution of progressing damage, beam-locking effect, modeling techniques, implementation of nonlinear solution methods. |

Objective | Obtain a theoretical background of the finite-element method. Understand techniques for finding numerically more efficient finite elements. Understand degree-of-freedom coupling schemes and recall typical equations solution algorithms for static and eigenvalue problems. Learn how to map specific mechanical situations correctly to finite-element models. Understand how to make best use of FEM for structural analysis. Obtain a first inside into the implementation of nonlinear FEM procedures. |

Content | 1. Introduction, direct element derivation of truss element 2. Variational methods and truss element revisited 3. Variational methods and derivation of planar finite elements 4. Curvilinear finite elements and numerical integration 5. Element Technology 6. Degrees-of-freedom coupling and solution methods 7. Iterative solution methods for damage progression analysis 8. Shear-rigid and shear compliant beam elements and locking effect 9. Beam Elements and Locking Effect 10. Harmonic vibrations and vector iteration 11. Modeling techniques 12. Implementation of nonlinear FEM procedures |

Lecture notes | Script and handouts are provided in class and can also be down-loaded from: Link |

Literature | No textbooks required. |