1. Reference problem#

1.1. 3D geometry#

The structure is a straight parallelepiped with a square base, its dimensions (see Figure) are as follows:

\(\mathit{Lx}=\mathrm{1m}\), \(\mathit{Ly}=\mathrm{1m}\), and \(\mathit{Lz}=\mathrm{5m}\)

The interface is defined by level sets directly in the command file using the DEFI_FISS_XFEM [U4.82.08] operator. It is introduced in the middle of the structure by an equation level set \(\mathit{LSN}\) (see Figure):

\(\mathit{LSN}\): \(z\)

_images/10000000000002C2000004407D5FFE3DE81AA07F.png

Figure 1.1-1: Bar geometry and interface positioning

1.2. 2D geometry#

The structure is a rectangle; its dimensions (see Figure) are as follows:

\(\mathit{Lx}=\mathrm{1m}\) and \(\mathit{Ly}=\mathrm{5m}\)

The interface is defined by level sets directly in the command file using the DEFI_FISS_XFEM [U4.82.08] operator. It is introduced in the middle of the structure by an equation level set \(\mathit{LSN}\) (see Figure):

\(\mathit{LSN}\): \(y\)

_images/1000000000000268000003E8718D1684009183FC.png

Figure 1.2-1: Bar geometry and interface positioning

1.3. Material properties#

  • \(\lambda \mathrm{=}1W\mathrm{.}{m}^{\mathrm{-}1}°{C}^{\mathrm{-}1}\)

  • \(\rho {C}_{p}=2J/{m}^{-3}°{C}^{-1}\)

1.4. Boundary conditions and loads#

A temperature \(\text{}\stackrel{̄}{T}{\text{}}^{\text{inf}}=10°C\) is imposed on the knots at the lower edge of the bar, and \(\text{}\stackrel{̄}{T}{\text{}}^{\text{sup}}=20°C\) on the knots at its upper edge.

1.5. Initial conditions#

None (the problem is stationary)