Mechanics of slender structures
Summary
Analysis of the mechanical response and deformation of slender structural elements.
Content
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 (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.
Keywords
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:
- Model Model and analytically solve simple problems of statics and stress analysis, S1
- Solve Analyze and design assemblies of simple mechanical elements in the framework of static and buckling, S2
- Analyze Model with analytical or numerical tools the nonlinear response of structures and materials, S12
- Estimate
- Interpret
- Prove
- Choose
- Formulate
Transversal skills
- Use a work methodology appropriate to the task.
- Set objectives and design an action plan to reach those objectives.
- Plan and carry out activities in a way which makes optimal use of available time and other resources.
- Assess progress against the plan, and adapt the plan as appropriate.
- Continue to work through difficulties or initial failure to find optimal solutions.
- Assess one's own level of skill acquisition, and plan their on-going learning goals.
- Demonstrate the capacity for critical thinking
Teaching methods
Lectures, practical demonstrations, example problems, in-class exercises, and homework.
Assessment methods
The course concludes with a written exam (100% of the grade).
Supervision
| Office hours | Yes |
| Assistants | Yes |
| Forum | Yes |
Resources
Virtual desktop infrastructure (VDI)
No
Bibliography
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).
Notes/Handbook
Printed handouts of the lectures will be provided with material that enhances and complements recommended books.
Moodle Link
Dans les plans d'études
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Mechanics of slender structures
- Cours: 3 Heure(s) hebdo x 14 semaines
- TP: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Mechanics of slender structures
- Cours: 3 Heure(s) hebdo x 14 semaines
- TP: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Mechanics of slender structures
- Cours: 3 Heure(s) hebdo x 14 semaines
- TP: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Mechanics of slender structures
- Cours: 3 Heure(s) hebdo x 14 semaines
- TP: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel