2. Benchmark solution

2.1. Calculation method used for the reference solution

The embedment at points \(A\) and \(B\) makes it possible to block the following deformations \(x\): \({\varepsilon }_{\mathrm{xx}}=0\).

This blocking associated with the imposed temperature creates an axial compression stress along the \(x\) axis. This constraint has the following expression:

\({\sigma }_{\mathrm{xx}}=E\alpha ({T}_{\mathrm{reference}}-T)\)

2.2. Reference quantities

Constraint \(\mathrm{SIXX}\)

2.3. Benchmark result

For \(T=200°C\) we get \(\mathrm{SIXX}=-0.6\text{E+09}\mathrm{Pa}\)

For \(T=400°C\) we get \(\mathrm{SIXX}=-1.20\text{E+09}\mathrm{Pa}\)

2.4. Uncertainty about the solution

Analytical solution