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28 Jun 2026 - Michael H. Scott
Before using the PFEM in OpenSees to model wave loading on structures, where what’s “correct” is generally unknown, we should first verify the implementation reproduces fundamental principles in fluid mechanics, e.g., Archimedes’ principle.
In what is likely the simplest fluid-structure interaction problem, a body is submerged in seawater and anchored to the seafloor by a single cable. If the submerged body weighs less than the seawater it displaces, the tension in the cable, T, should equal the difference between the weight of the displaced seawater (buoyant force), FB=γV, and the weight of the body, W. This simple result provides an exact solution against which the PFEM implementation can be verified.
The model is two-dimensional with a 1 inch thickness for both the fluid domain and the submerged object. The specific weight of seawater is γ=64 lb/ft3 and its viscosity is 2.51e-5 lb-sec/ft2.
A rectangular object is used instead of a more realistic circle because its volume is represented exactly, whereas the volume of a circle can only be approximated by the finite element mesh. Using a rectangle eliminates discretization error associated with the object geometry.
The object weighs 10 lb and is 20 inch by 20 inch. In the numerical
model, the object is discretized with tri31 elements. The cable is 0.25
inch diameter and is modeled with a single corotTruss element with
E=29000 ksi. A regular truss element would work just as well for
this problem, but if you eventually move on to mooring lines, a mesh of
corotational elements is one possible approach.
Anyway, it’s a small, light object attached to a stiff cable. But that’s OK for this verification because the response reaches steady state quickly.
The cable force damps out to the expected solution, thus the OpenSees PFEM implementation reproduces Archimedes’ principle. Not a huge win, but a confidence builder for bigger tests. Like when Duke plays Stetson before the ACC regular season gets underway.