Thin structures and instabilities

Continuum mechanics, linear elasticity (1^st year Mechanics course)

Acquire the knowledge necessary to understand structural models (hypotheses and application framework), as well as the associated dimensioning methods:
•  Know how to model and analyze structures based on beams and plates
•  Master the dimensioning methods in linear elasticity and buckling

•  Recalls of three-dimensional elastodynamics (kinematics, sthenic, Hooke's law, local equations, integral formulations)
•  Beam models:
-- Euler-Navier-Bernoulli and Timoshenko hypotheses
-- Establishment of models
-- Energetic theorems (Ménabréa and Castigliano)
-- Elasticity dimensioning
•  Plate models (Kirchoff-Love and Reissner-Mindlin)
•  Instabilities of thin structures in compression under moderate rotations (Euler buckling, von-Karmann model).

•  Know how to model and analyze complex structures
•  Master the methods of dimensioning in elasticity
•  Know how to anticipate complex phenomena of instability
•  Propose reduced approaches to minimize computational costs

DS : written assessment, 2h (100%)

•  Course handout (pdf)
•  P. Ballard et A. Millard, Poutres et arcs élastiques, Edition Ecole Polytechnique, 2009.
•  C.R. Calladine, Theory of shell structures, Cambridge University Press, 1983.

Stéphane Bourgeois