2. Benchmark solution#
2.1. Calculation method#
The reference results are either non-regression values, or the analytical solutions in motion and under pressure, given by the following formulas [1]:
\(U1=\frac{{({x}^{2}-1)}^{2}({y}^{2}-1)y}{4}\) and \(U2=\frac{{({y}^{2}-1)}^{2}(1-{x}^{2})x}{4}\)
\(P=5{x}^{3}(y-1)+{y}^{3}\)
2.2. Reference quantities and results#
The analytical solution gives:
Location |
Instant |
Component (DEPL) |
Value |
|
Node PT_ben \((\mathrm{0.5,}0.5)\) |
|
DX |
\(-0.052734375\mathit{mm}\) |
|
Node PT_ben \((\mathrm{0.5,}0.5)\) |
|
DY |
\(0.052734375\mathit{mm}\) |
|
PT_Ben \((\mathrm{0.5,}0.5)\) node |
|
|
|
2.3. Uncertainties about the solution#
This analytical reference solution is accurate.
2.4. Bibliographical reference#
[1] An analysis of some mixed-enhanced finite element for plane linear elasticity, F. Auricchio, L. Beirao da Veiga, C. Lovadina, C. Lovadina, A. Reali. Compute. Methods Appl. Mech. Engrg. 194 (2005) 2947- 2968