This validation case belongs to structural analysis, with the case of a pipe flange under the effect of bolt preload. The aim of this test case is to validate the following parameters:
Bolt preload boundary condition
The simulation results from SimScale were compared to test case results presented in [SSNV228]\(^1\).
Figure 1: Only one quarter of the flange, corresponding to one bolt is modeled.
It represents a quarter section of a pipe bolted flange pair. The bolt shaft is simplified as a cylinder, as well as the nut. The model includes the pipes sections, flanges, a bolt, nuts, washers, and a gasket.
The mesh was computed using SimScale’s standard mesher algorithm.
Figure 2: Finite elements tetrahedral mesh used for the simulation generated with the standard algorithm
Simulation Setup
Material:
Elastic Modulus \(E = \) 200 \(GPa\)
Poison’s ratio \(\nu = \) 0.3
Boundary Conditions:
Constraints:
XZ plane symmetry faces \( d_y = \) 0 \(m\)
YZ plane symmetry faces \( d_x = \) 0 \(m\)
Symmetry plane on pipe end faces
Contacts:
Bonded contact between the pipes and flange necks
Bonded contact between the flange faces and washers
Bonded contact between the washers and nuts
Bonded contact between the nuts and bolt shaft
Physical contact between the flanges and seal ring
Load:
Bolt preload of 3393 \(N\)
Pressure on internal pipe, flange and seal faces \(P = \) 1e-6 \(Pa\), ramped from zero to maximum value
Reference Solution
The reference solution is of the numerical type, as presented in [SSNV228]\(^1\). It is given in terms of the mean stress on the bolt shaft:
$$ \sigma_{bolt} = 30\ MPa $$
Result Comparison
Comparison of the axial bolt stress \(\sigma_{ZZ}\) at a point data result control item located on the bolt shaft with the theoretical solution is presented below:
FIELD
COMPUTED
REF
ERROR
\(\sigma_{ZZ}\) \((SIZZ)\) \([MPa]\)
30.2624
30.0
0.87 %
Table 2: Results comparison and computed errors
Illustration of the deformed shape and stress distribution on the flange under bolt preload condition is presented in Figure 3, while the overall distribution of the axial stress on the bolt \(\sigma_{ZZ}\) is presented in Figure 4:
Figure 3: Deformed shape and stress contour on the bolted flange.
Figure 4: Stress contour plot for \(\sigma_{ZZ}\) \((SIZZ)\), showing the distribution of the axial stress in the bolt. Stress concentrations can be seen varying from the reference value of 30 MPa.
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