1. Reference problem#

1.1. Geometry#

N4

Y

Z

N3

X

NO. 1

N2

We consider a square with side \(\mathrm{1mm}\).

1.2. Material properties#

The material is orthotropic elastic (defined via DEFI_COMPOSITE). Orthotropy is of thermal origin, i.e. the longitudinal, transverse and normal expansion properties are:

  • \({E}_{L}={E}_{T}={E}_{N}=E=100E9;{\nu }_{LT}={\nu }_{LN}={\nu }_{TN}=\nu =\mathrm{0,3};{G}_{LT}={G}_{LN}={G}_{TN}=E/2(1+\nu )\)

  • \({\alpha }_{LL}=1.E-5;{\alpha }_{\mathit{TT}}=1.E-6;\)

1.3. Boundary conditions and loads#

Block:

The boundary conditions are such that only the thermal membrane effect is allowed. In addition, the plate is blocked so that the effects of plane shear are negligible compared to the effects of longitudinal and transverse deformations:

  • The points N1, N2, N3, N4 are such that: DZ=0.0: which results in zero bending,

  • The points N1, N2 are blocked: DY=0.0 which makes the plane shear negligible,

  • The points N1 is such that: DX=0 which completely encloses this point,

  • Nodes N3, N4 are free from movement in the plane.

Loading:

No mechanical loading is applied. The consequence is that purely elastic deformations are zero. A loading differential is applied all over the plate:

\(T-{T}_{\mathit{ref}}=\Delta T=1°C\)

1.4. Initial conditions#

Néant