2. Reference solution

2.1. Calculation method

The reference results are either non-regression values (values of empirical modes, reduction coefficients) or values (displacements, temperatures, stresses and flows) calculated on a complete model.

Reduced coordinates are also tested. We recall that empirical trends \({\mathrm{\Psi }}_{m}(x)\) are such that:

(2.1)\[ u (x, t)\ approx\ sum _ {m=1} ^ {\ mathit {nbmode}} {\ mathrm {\ Psi}} _ {m} (x)\ times {a} _ {m} (t)\]

For a given \(u(x,t)\) field (temperature, displacement, heat flow, or stress) with \({a}_{m}\) the reduced coordinates.

2.2. Reference quantities and results

For thermal, the results on the complet model:

Location	Moment	Temperature ( TEMP )
Node A in \((\mathrm{1,0,3})\)	\(t=1s\)	\(\mathrm{29,9053048593}°C\)
Node A in \((\mathrm{1,0,3})\)	\(t=4s\)	\(\mathrm{139,462715634}°C\)
Node A in \((\mathrm{1,0,3})\)	\(t=7s\)	\(\mathrm{567,08693147}°C\)
Node A in \((\mathrm{1,0,3})\)	\(t=10s\)	\(\mathrm{999,349943608}°C\)
Node B in \((\mathrm{3,3,3})\)	\(t=1s\)	\(\mathrm{29,90499961}°C\)
Node B in \((\mathrm{3,3,3})\)	\(t=4s\)	\(\mathrm{139,458066818}°C\)
Node B in \((\mathrm{3,3,3})\)	\(t=7s\)	\(\mathrm{567,040457129}°C\)
Node B in \((\mathrm{3,3,3})\)	\(t=10s\)	\(\mathrm{999,12502482}°C\)

Location	Moment	Flow ( FLUX_NOEU )
Node A in \((\mathrm{1,0,3})\)	\(t=7s\)	\(-\mathrm{0,0005673343795326032}W\)
Node A in \((\mathrm{1,0,3})\)	\(t=10s\)	\(-\mathrm{0,003152488515227189}W\)
Node B in \((\mathrm{3,3,3})\)	\(t=7s\)	\(\mathrm{0,0011356797075429094}W\)
Node B in \((\mathrm{3,3,3})\)	\(t=10s\)	\(0.0063191212851786W\)

For mechanics, the results on the complet model:

Location	Moment	Component	Move ( DEPL )
Node A in \((\mathrm{1,0,3})\)	\(t=10s\)	DX	\(\mathrm{0,0696319525128}\,{mm}\)
Node A in \((\mathrm{1,0,3})\)	\(t=10s\)	DY	\(\mathrm{0,199062276741}\,{mm}\)
Node A in \((\mathrm{1,0,3})\)	\(t=10s\)	DZ	\(\mathrm{0,529606351907}\,{mm}\)
Node B in \((\mathrm{3,3,3})\)	\(t=10s\)	DX	\(-\mathrm{0,208992921588}\,{mm}\)
Node B in \((\mathrm{3,3,3})\)	\(t=10s\)	DY	\(-\mathrm{0,208992921588}\,{mm}\)
Node B in \((\mathrm{3,3,3})\)	\(t=10s\)	DZ	\(\mathrm{0,547254495773}\,{mm}\)

Location	Instant	Component	Constraint ( SIEF_NOEU )
Node A in \((\mathrm{1,0,3})\)	\(t=10s\)	SIXX	\(-\mathrm{2739,13961277}\,{MPa}\)
Node A in \((\mathrm{1,0,3})\)	\(t=10s\)	SIYY	\(-\mathrm{2737,51235419}\,{MPa}\)
Node A in \((\mathrm{1,0,3})\)	\(t=10s\)	SIZZ	\(-\mathrm{2612,22311229}\,{MPa}\)
Node C in \((\mathrm{0,0,0})\)	\(t=10s\)	SIXX	\(\mathrm{13992,3974341}\,{MPa}\)
Node C in \((\mathrm{0,0,0})\)	\(t=10s\)	SIYY	\(\mathrm{13992,3974341}\,{MPa}\)
Node C in \((\mathrm{0,0,0})\)	\(t=10s\)	SIZZ	\(\mathrm{14047,6477194}\,{MPa}\)
D knot in \((\mathrm{3,1,0})\)	\(t=10s\)	SIXX	\(\mathrm{13300,4780377}\,{MPa}\)
D knot in \((\mathrm{3,1,0})\)	\(t=10s\)	SIYY	\(\mathrm{13300,3220671}\,{MPa}\)
D knot in \((\mathrm{3,1,0})\)	\(t=10s\)	SIZZ	\(\mathrm{13368,1442621}\,{MPa}\)

2.3. Uncertainty about the solution

The error in the solution depends on the degree of reduction (number of empirical modes and size of the reduced domain).