Mechanics of thin structures : plates and shells

Lecturer(s): Hélène MAGOARIEC, Cécile NOUGUIER
Course ⋅ 14 hTC ⋅ 10 hPW ⋅ 4 hAutonomy ⋅ 4 h


Thin structures, light and allowing optimization of the weight / performance ratio, feature prominently in many industries (aeronautics, civil engineering, chemical engineering, etc.). The main objective of this course is to provide the future engineers with elements required for modeling and design of buildings based on thin structural elements by analyzing the behavior of 2D thin structures, flat or curved. In consideration of the material gain conferred by the thinness, the risk of instability is amplified: phenomena such as buckling of plates and shells have to be accounted for. The second objective of this course is to provide the future engineers with the bases to study instabilities of elastic thin structures.


Solid mechanics, Thin plates and shells, Love-Kirchhoff model, Love model, Dimensioning, Elastic instability, Extensometry, Comparison theory/experiments


Part 1 - Elastic behavior of plates: 4 Lectures, 2 Tutorials, 1 Practical work; Definition, schematization, hypotheses, and mechanical forces ; internal forces; local balance ; LoveKirchhoff thin plates model ; boundary conditions. Practical work: experimental validation of the Love-Kirchhoff model and study of an approximate solution. Part 2 - Elastic behavior of shells of revolution: 2 Lectures, 2 Tutorials; Geometry of surfaces, definition, schematization, mechanical forces ; internal membrane forces ; local balance for shells of revolution ; usual loadings ; Elastic stress, strain, and displacements. Part 3 - Elastic stability of thin structures: 2 Lectures/Tutorials; Buckling of thin plates and shells; critical load.

Learning Outcomes

  • Being able to design plates and shells (stress, displacements, and elastic instabilities)
  • Being able to determine predominant elastic effects in thin structures (stress, strain, displacements)
  • Being able to build a model for 2D thin structures, following the way of modeling used for 1D structures during the previous semesters
  • Being able to compare theory and experiment: engage a critical analysis to validate a model or an approximation (by an energy approach)


Final mark = 50% Knowledge + 50% Know-how Knowledge = 100% final exam Know-how = 100% continuous assessment