The objective of the course is to show analytically -in simple cases- and numerically how to model and solve an important class of

so-called planar structures, i.e. such that their mechanical problem is reduced to two space dimensions.


The problems involve " long " solids under plane strain, " thin " solids under plane stress and thin or thick plates under bending loads.


For each class of problems, appropriate formulations will be developed, together with their finite element discretization, in view of

their numerical resolution using a specialized software.

Some rather simple problems will also be solved analytically in order to better understand the theory.

Content :

Chapitre 1 : Plane strain and plane stress in Cartesian coordinates.

Chapitre 2 : Plane strain and plane stress in cylindrical coordinates.

Chapitre 3 : Kirchhoff-Love plate theory in Cartesian coordinates.

Chapitre 4 : Kirchhoff-Love plate theory in cylindrical coordinates.

Chapitre 5 : Reissner-Mindlin plate theory.

Chapitre 6 : Finite element formulations of plate theories.