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101-0158-01L 5 Credits DR , MSC D-MATL , D-BAUG
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Method of Finite Elements I

Lecturers & Examiners: Prof. Dr. Eleni Chatzi, Dr. Adrian Egger
VVZ CR n/a

Last Updated: 2026-06-01 11:32:59

Abstract

The course introduces students to the fundamental concepts of the Method of Finite Elements, including element formulations, numerical solution procedures and modelling details. We aim to equip students with the ability to code algorithms (based on Python) for the solution of practical problems of structural analysis.DISCLAIMER: the course is not an introduction to commercial software.

Objective

The Direct Stiffness Method is revisited and the basic principles of Matrix Structural Analysis are overviewed. The basic theoretical concepts of the Method of Finite Elements are imparted and perspectives for problem solving procedures are provided. Linear finite element models for truss and continuum elements are introduced and their application for structural elements is demonstrated. The Method of Finite Elements is implemented on practical problems through accompanying demonstrations and assignments.

Content

Contents: – Introductory concepts In this introductory section, we discuss the background motivating adoption of finite element analysis and offer an overview of matrices and linear algebra. – The Direct Stiffness Method In this section, we overview the basic principles of the DSM method. We offer illustrative demos and exercises in Python. – Formulation of the Method of Finite Elements In this section, we overview the main ingredients to the formulation of the FE method, namely the Principle of Virtual Work; Isoparametric formulations. We discuss these formulations for both 1D Elements (truss, beam) and 2D Elements (plane stress/strain). We offer illustrative demos and exercises in Python. – Practical application of the Method of Finite Elements This section is concerned with use of the method into practice. We discuss practical considerations and move onto results interpretation onto realistic examples from actual use cases.

Resources

Lecture Notes

The lecture notes are in the form of slides, available online from the course webpage:https://chatzi.ibk.ethz.ch/education/method-of-finite-elements-i.html

Literature

Structural Analysis with the Finite Element Method: Linear Statics, Vol. 1 & Vol. 2 by Eugenio Onate (available online via the ETH Library) Supplemental Reading Bathe, K.J., Finite Element Procedures, Prentice Hall, 1996.

Learning Materials (Links)

General Information

Language
English
Levels
DR , MSC
Frequency
Yearly recurring

Examination

Type
end-of-semester examination
Mode
written 120 minutes
Aids
Two pages of personal notes (one sheet filled out front and back, or two individual sheets filled out only on the front side). These might include sketches, diagrams, or text that has been personally created and no templates/copies/screenshots of material. The summary can be created by any means (e.g., a pen, pencil, typed content in Microsoft Word etc.) but it has to be printed for the exam.
The final grade comes by 45% from a compulsory continuous performance assessment task (i.e. 3 graded Homeworks (15% each)) and by 55% by a written examination, which will be on the last day of the course. The compulsory continuous performance assessment task need not be passed on its own; it is awarded a grade which counts proportionally towards the total course unit grade.

Course Components

Type Title Time & Place Hours
lecture with exercise Method of Finite Elements I
  • Mon 12:45-13:30 (HCI J 4)
  • Mon 13:45-15:30 (HCI J 4)
3 h weekly

Offered In