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 \((\mathrm{0.5,}0.5)\)

\(t=1s\)

DX

\(-0.052734375\mathit{mm}\)

Node PT_ben \((\mathrm{0.5,}0.5)\)

\(t=1s\)

DY

\(0.052734375\mathit{mm}\)

PT_Ben \((\mathrm{0.5,}0.5)\) node

\(t=1s\)

PRES

\(-0.1875\mathit{Pa}\)

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