Fiches de cours

Mechanics of slender structures


Enseignant(s) :

Nunes Pereira de Almeida Reis Pedro Miguel




Analysis of the mechanical response and deformation of slender structural elements


Through this course, students will learn how to rationalize, analyze, and predict the mechanics of deformation of slender structural elements. The acquired knowledge will build upon, and further specialize material from, previous SGM courses in solids and structures (Introduction to structural mechanics, Structural mechanics, Continuum mechanics, Solid mechanics). The focus will be given to fundamental problems in mechanical systems comprising beams, rods, plates, and shells, primarily in their elastic regime. Methods of analysis will cover both scalings and analytical modeling. Students will recognize the specificities of slender structures, e.g., geometric nonlinearities, buckling, and the possibility of large deformations (albeit under linear material strains). Throughout, concrete examples of slender structures will be provided across a wide range of modern application scenarios and from the recent literature, including biological structures, micro-nano mechanical systems, robotics, and large engineering structures.

The course may contain, but not exclusively, the following elements: [1] Elasticity and dimensional reduction of elastic bodies; [2] Dimensional analysis and scalings; [3] Euler's Elastica; [4] Strings and Rods; [5] Plates; [6] Thin films, Multilayers and Coatings; [7] Shells; [8] Buckling of slender structures.


Thin structures, Mechanics, Elastic deformation, Buckling, Geometric nonlinearities.

Learning Prerequisites

Required courses

ME-232 (Structural Mechanics), ME-201 (Continuum Mechanics), and ME-331 (Solid Mechanics), or equivalent from other institutions.

Recommended courses

ME-202 (Mechanical Systems); ME-373 (Finite element modeling and simulation).  It will be beneficial for students to have taken ME-437 (Advanced Solid Mechanics), or to be taking it in parallel to this course, even if this is not required.

Important concepts to start the course

Familiarity with structural analysis of elastic systems (bars, trusses, beams, trusses, frames, and mechanisms) and boundary value problems in elasticity. The emphasis of the course is primarily on analytical methods to rationalize and model the mechanics of slender structure, hence, an affinity to mathematical and theoretical approaches in problem solving is expected.

Learning Outcomes

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

Transversal skills

Teaching methods

Lectures, practical demonstrations, example problems, in-class exercises, and homework.

Assessment methods

The course concludes with a written exam.


Office hours Yes
Assistants Yes
Forum Yes



The following books are not required but may be useful and complement to the material provided during the course:

L.D. Landau and E.M. Lifshitz 'Theory of Elasticity (3rd Edition)' Elsevier (1986).

O.M. O'Reilly 'Modeling Nonlinear Problems in the Mechanics of Strings and Rods' Springer (2016).

S.P. Timoshenko and S. Woinowsky-Krieger 'Theory of plates and shells' McGraw Hill (1956).

M. R. Begley and J. W. Hutchinson 'The Mechanics and reliability of films, Multilayers, and Coatings' Cambridge University Press (2017).

B. Audoly and Y. Pomeau 'Elasticity and Geometry: From hair curls to the non-linear response of shells' Oxford University Press (2010).

E. Ventsel and T. Krauthammer 'Thin Plates and Shells: Theory, Analysis and Applications' Marcel Decker (2001).

Ressources en bibliothèque

Printed handouts of the lectures will be provided with material that enhances and complements recommended books.

Moodle Link

Prerequisite for


Dans les plans d'études

Semaine de référence

8-9   CM010 
14-15 MED21522   
      Exercice, TP
      Projet, autre


  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand