Generalized Plane Strain

I’m working on a “thermal shock” analysis of piping to investigate the transient stress through the pipe wall when severe convection loads are applied to the inside surface. In this case the stresses vary in the radial direction, but not in the circumferential direction (axisymmetric, assuming convection load htc does not vary around the pipe)). For the axial direction, the pipe is considered to be long. so that it can grow/shrink axially, but a plane cutting through the pipe cross section would remain planar (ie, axial strain is constant but non-zero). This fits the definition of generalized plane strain in the axial direction.

If I analyze this by considering a pie-shaped 3D section of some length in the axial direction (ie a segment of a ring of pipe), the boundary conditions on the circumferential planes are essentially symmetric and is easily done. However, with the boundary conditions available in simscale, I’m having some trouble implementing the axial generalized plane strain condition. Note the direct strain must be constant across the section, so the z displacement of each node on that face must be the same. However, the magnitude of that displacement is not known in advance so a fixed boundary condition is not applicable.

How would one implement appropriate boundary conditions for this scenario?


Hi @fnippard,
if i understand you correctly you need a cyclic symmetry condition and you don’t know how to apply that with SimScale?
Under Contacts for the advanced analysis types you find bonded, sliding and also cyclic symmetry.

You can have a look at this project as an example how to apply it correctly:

Additionally you can have a look at the documentation: SimScale Documentation | Online Simulation Software | SimScale


My query is about how to define appropriate constraints in the “axial” direction. Cyclic symmetry is applicable to constraints in the hoop direction.

Hi Franklin (@fnippard),

I’m going by memory here, so I might be wrong on the details, but you should be able to achieve what you are looking for by using a remote displacement constraint. The remote point should be located on the end face of the pipe, at its centre. Set all three translations (X, Y and Z) to unconstrained. Rotation about the x and y axes should be fixed and rotation about the z axis should be unconstrained. The deformation behavior should be deformable.

This arrangement should keep all the nodes on the end face planar and perpendicular to the axis of the pipe while allowing the pipe to expand and contract in all directions.

I hope this helps.

Regards, Ben

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I think you could try as first attempt:

  • Completely fix one end face
  • The opposite end face unconstrained in the axial direction and constrained in the other two.

This should relieve the axial stress while keeping the model from rigid body motion.

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