Hello all. I’m modeling a plate immersed in fluid, and for that I want to add a pressure \Delta p to the bilinear form of the Kirchhoff-Love plate equation. The pressure is non-locally dependent on the displacement \phi of the plate, i. e. pressure at one cell depends on the displacement of other cells in the cross-section, as
The A-matrix comes from the fundamental solution method to the Navier Stokes Equations.
Does someone have an idea on how to implement this non-local dependent pressure? Or even if it is possible to do that with Fenics?
Ideally, it should look something like this
import fenics as fe mesh = fe.UnitIntervalMesh(10) v_element = fe.FiniteElement("Lagrange", mesh.ufl_cell(), 2) v_space = fe.FunctionSpace(mesh, v_element) phi = fe.TrialFunction(v_space) w = fe.TestFunction(v_space) for k in range(1): for j in range(1): xj = fe.Point(0.5) a_pressure = 1e2*phi(xj)*w*dx(1)
where the dx(1) should be a subdomain of the mesh.
Thanks for any input!