Pressure constraint

This example illustrate the use the pressure constraint for the simulation of a pipe under internal pressure and external pressure. The problem is treated in 2D with plane strain assumption.

import fedoo as fd

# Pressure in MPa
external_pressure = 0.1
internal_pressure = 2
radius = 200
thickness = 20

fd.ModelingSpace("2D")  # plane strain assumption
mesh = fd.mesh.hollow_disk_mesh(radius, thickness, nr=5, nt=41)

material = fd.constitutivelaw.ElasticIsotrop(200e3, 0.3)

wf = fd.weakform.StressEquilibrium(material)
solid_assembly = fd.Assembly.create(wf, mesh)

To find the nodes belonging to the boundary of the pipe, the fedoo.Mesh.find_nodes() method is used with the “Distance” criterion from the center of pipe whose coordinates is [0, 0].

ext_nodes = mesh.find_nodes("Distance", ([0, 0], radius))
int_nodes = mesh.find_nodes("Distance", ([0, 0], radius - thickness))

The pressure requires to build a weaform over a surface Mesh. To automatically build the required surface mesh from a set of nodes, with use the fedoo.contraint.Pressure.from_nodes() constructor.

Alternatively, we can use the fedoo.contraint.Pressure.from_elements() constructor from a set of element to extract the external surface.

Note

The from_nodes and from_elements constructor can’t be used to apply a pressure over a shell structure because, as the shell mesh is a surface mesh, these constructors will extract linear mesh of the boundaries. To apply the mesh over a shell geometry, the fedoo.contraint.Pressure constructor needs to be called. See the example sphx_glr_examples_01_simple_spherical_shell_compression.py

ext_pressure = fd.constraint.Pressure.from_nodes(mesh, ext_nodes, external_pressure)
int_pressure = fd.constraint.Pressure.from_nodes(mesh, int_nodes, internal_pressure)

Define a problem from the solid and pressure assemblies The 3 assemblies are sumed.

pb = fd.problem.Linear(solid_assembly + ext_pressure + int_pressure)
pb.solve()

pb.get_results(solid_assembly, "Stress").plot("Stress", "pressure", "Node")