Line Mesh

Original Post - 30 Nov 2021 - Michael H. Scott

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The DiscretizeMember function, which dates back many years, was recently superseded by the line mesh command, written by Minjie. In addition to creating boundaries for solid meshes, as shown in this post, you can use line meshes to discretize a frame member (2D or 3D) into beam-column elements–just pass the optional element type and arguments to the mesh command.

Below is example code for a portal frame model. First, define nodes for the joints.

import openseespy.opensees as ops

H = 360
L = 144

ops.wipe()
ops.model('basic','-ndm',2,'-ndf',3)

ops.node(1,0,0); ops.fix(1,1,1,1)
ops.node(2,0,L)
ops.node(3,H,L)
ops.node(4,H,0); ops.fix(4,1,1,1)

Corner nodes of frame mesh

Next, define line meshes with the element type and arguments that would come after the nodes in the regular element command–in this case, the transformation tag and beam integration tag for a dispBeamColumn element. The mesh type is 0 (not an FSI analysis) and there are 3 DOFs per node.

E = 29000

# W14x90
A = 26.5
Ic = 999
ops.section('Elastic',1,E,A,Ic)
ops.beamIntegration('Legendre',1,1,2)

# W18x76
A = 22.3
Ig = 1330
ops.section('Elastic',2,E,A,Ig)
ops.beamIntegration('Legendre',2,2,2)

# Corotational transformation
ops.geomTransf('Corotational',1)

# Number of elements/member
Nele = 8

# Columns
c = L/Nele
# tag Npts nodes type dofs size eleType transfTag beamIntTag
ops.mesh('line',1,2,*[1,2],0,3,c,'dispBeamColumn',1,1)
ops.mesh('line',2,2,*[3,4],0,3,c,'dispBeamColumn',1,1)
    
# Beam
c = H/Nele
# tag Npts nodes type dofs size eleType transfTag beamIntTag
ops.mesh('line',3,2,*[2,3],0,3,c,'dispBeamColumn',1,2)

Nodes and elements for frame mesh

And that’s pretty much it.

Compared to DiscretizeMember, the line mesh is easier because it doesn’t require you to keep track of node and element tags to pass into the function–the numbering of nodes and elements is handled internally.

The meshes shown in this post were plotted using the opsvis package developed by Seweryn Kokot.

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Line Mesh