101-0158-01L Method of Finite Elements I
| Semester | Spring Semester 2025 |
| Lecturers | E. Chatzi, A. Egger |
| Periodicity | yearly recurring course |
| Language of instruction | English |
| 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. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning 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. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 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. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Prior basic knowledge of Python is necessary. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
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