Dynamic finite element analysis of structures

Summary

The course focuses on the dynamic analysis of 3D structures using the finite element method in the context of linear elasticity. Students will gain proficiency in numerical techniques widely employed in static and dynamic structural analysis, and apply these methods to address real-world problems.

Content

Keywords

Finite element, Beam and shell elements, Structural dynamics, Subspace method, Newmark methods

Learning Prerequisites

Required courses

Mechanics:

• Mechanics of structures (for GM)
• Mechanical vibrations
• Solid mechanics

Numerics:

• Numerical analysis
• Finite element method

Recommended courses

Finite element modelling and simulation

Learning Outcomes

By the end of the course, the student must be able to:

• Apply the concepts of structural dynamics to predict the vibratory behaviour, free or forced, conservative or damped, of continuous systems. (S3)
• Derive a finite element formulation of a physical problem from its strong-form using the principle of virtual work or a variational approach. (S9)
• Implement the theoretical concepts of the finite element method to carry out a complete study of a real-world problem based on a project specification, and provide a critical analysis of the results obtained. (S10)

Transversal skills

• Use both general and domain specific IT resources and tools
• Assess one's own level of skill acquisition, and plan their on-going learning goals.
• Make an oral presentation.
• Plan and carry out activities in a way which makes optimal use of available time and other resources.

Teaching methods

Ex cathedra lectures, exercises in the classroom and computer lab sessions.

Expected student activities

Attendance in class.
Solving theoretical and practical problems presented in exercise series.
Complete of several mini-projects.

Write scientific reports.

Assessment methods

50% mini-projects during the semester and 50% final oral exam.

Supervision

Resources

Bibliography

• Thomas Gmür, Méthode des éléments finis en mécanique des structures, Presses polytechniques et universitaires romandes (PPUR), Lausanne, 2018, ISBN 978-2-88915-158-5.

• Thomas Gmür, Dynamique des structures - analyse modale numérique, Presses polytechniques et universitaires romandes (PPUR), Lausanne, 2014 (2ème édition), ISBN 978-2-88074-813-5

• Thomas J. R. Hughes, The Finite Element Method - Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1987 (Dover Publications, 2000), ISBN 978-0-48641-181-1

Ressources en bibliothèque

• The Finite Element Method - Linear Static and Dynamic Finite Element Analysis / Hughes
• Dynamique des structures - analyse modale numérique / Gmür
• Méthode des éléments finis en mécanique des structures / Gmür

Moodle Link

• https://go.epfl.ch/ME-473