Mechanics of thin structures : plates and shells

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.

• 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 (energetical approach).

• 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.