2. Reference solution#
2.1. Calculation method used for the reference solution#
In thermal: we solve the stationary thermal problem:
Note:
The boundary conditions chosen here are not those necessary for the homogenization method: we would in fact find
everywhere.
The solution is then (verifying the conditions defined in [§1.3]):
The potential energy is then in equilibrium:
In mechanics: we solve the elastostatic problem:
for cases:
3D loading
|
3D loading
|
2D loading
|
The solutions are:
in 3D,**membrane* loading and isotropic elasticity:
the potential energy at equilibrium is:
in 3D,**membrane* loading and orthotropic elasticity:
with
either
because the local coordinate system is not confused with the global coordinate system (the nautical angles are all equal to 90°).
where
and
in 3D, loading**flexion*:
;
in 3D,**flexure load* and orthotropic elasticity:
with
either
because the local coordinate system is not confused with the global coordinate system (the nautical angles are all equal to 90°).
where
and
in 2D, plane loading:
;