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  • Documentation

    Validation Case: Flange Under Bolt Preload

    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:

    The simulation results from SimScale were compared to test case results presented in [SSNV228]\(^1\).


    The geometry used for the case is shown below:

    flange bolt preload geometry model
    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 pipe sections, flanges, a bolt, nuts, washers, and a gasket.

    Analysis Type and Mesh

    Tool Type: Code Aster

    Analysis Type: Non-linear Static

    Mesh and Element Types:

    Mesh TypeNumber of CellsNumber of
    Element Type
    Standard (structured) 50210623441st Order Hexahedrals and Pyramids
    Table 1: Mesh details

    The mesh was computed using SimScale’s Standard Mesher algorithm. To optimize the performance of the FEA model, Sweep meshing refinement was used on the different parts, resulting in a structured mesh. Such a mesh consists of mapped hexahedral and pyramid elements, as can be seen in the figure:

    structured mesh flange bolt preload validation case
    Figure 2: Finite elements structured mesh used for the simulation generated with the standard algorithm

    Simulation Setup


    • Elastic Modulus \(E = \) 200 \(GPa\)
    • Poison’s ratio \(\nu = \) 0.3

    Boundary Conditions:

    • Constraints:
      • Symmetry plane on the XZ plane faces
      • Symmetry plane on the YZ plane faces
      • 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 \(Pa\), automatically ramped from zero to the 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:

    \(\sigma_{ZZ}\) \((SIZZ)\) \([MPa]\)30.313530.01.05 %
    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:

    stress contours developed due to bolt preload flange
    Figure 3: Deformed shape and stress contour on the bolted flange
    stress on bolt in preload
    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.


    If you still encounter problems validating you simulation, then please post the issue on our forum or contact us.

    Last updated: March 1st, 2023