VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.

101-0158-01L 5 Credits DR , MSC D-MATL , D-BAUG

Method of Finite Elements I

Lecturers & Examiners: Prof. Dr. Eleni Chatzi, Dr. Adrian Egger, Dr. Konstantinos Vlachas

VVZ CR n/a

Last Updated: 2026-06-04 00:22:55

Abstract

This course introduces the fundamental concepts of the Finite Element Method (FEM), covering element formulations, numerical procedures, and modelling aspects. A key focus is the hands-on implementation of FEM algorithms in Python.Disclaimer: The course is not about commercial software, but about core concepts and numerical foundations.

Objective

The course revisits the Direct Stiffness Method and provides an overview of the basic principles of matrix structural analysis. Students will learn the theoretical foundations of the Finite Element Method and gain insight into practical solution strategies. Upon completion of the course, students will be able to: - Understand and apply the Direct Stiffness Method within a matrix-based structural analysis framework. - Explain and utilise the theoretical building blocks of FEM, including the Principle of Virtual Work and isoparametric formulations. - Develop and implement linear finite element models for truss, beam, and 2D continuum elements. - Apply the Finite Element Method to practical structural engineering problems and interpret results critically. - Program FEM algorithms in Python, enabling transparent, customisable analyses beyond black-box software.

Content

**Contents** 1. Introductory Concepts Motivation for finite element analysis; overview of matrices, linear algebra, and the role of discretisation in computational mechanics. 2. The Direct Stiffness Method (DSM) Principles of DSM and its role as the foundation for FEM. Illustrated demonstrations and programming exercises in Python. 3. Formulation of the Finite Element Method Core ingredients of FEM: Principle of Virtual Work, interpolation and isoparametric concepts. Formulations for: – 1D elements (truss, beam) – 2D elements (plane stress/strain) Accompanied by hands-on programming demos. 4. Practical Application of FEM Transition from theory to practice. Modelling considerations, boundary conditions, mesh refinement, and interpretation of results. Realistic examples from engineering applications illustrate the modelling workflow and typical pitfalls.

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)

Main link
Course Webpage

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