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 membrane	3D loading of bending	2D loading plane constraints

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:

  

;