Gauss point location
Posted: Thu Dec 07, 2023 5:56 pm
Hi,
I have a simple model of cantilever beam under tip horizontal load, which consists of two displacement-based beam elements. Each displacement-based beam elements have two integration points and following Gauss-Legendre quadrature rule. The location of Gauss points should be inside the beam element (v.s. force-based beam follows Gauss-Lobatto rules that Gauss points are at the beam ends). The beam elements are prismatic and the analysis is elastic. I provided my tcl code below for reference.
When I visulize the result in STKO post-processor, the Gausspoint plot shows the Gauss points are located at beam ends, see the screenshot attached.
And when I plot the beam bending moment diagram, you can see the bending moment is dis-continuous between two elements. I output the bending moments at end of beam element and noticed they equal to the moment value at Gauss points. However, as I mentioned above, the Gauss point for displacement-based element should be inside the element.
Any comments are welcomed
I have a simple model of cantilever beam under tip horizontal load, which consists of two displacement-based beam elements. Each displacement-based beam elements have two integration points and following Gauss-Legendre quadrature rule. The location of Gauss points should be inside the beam element (v.s. force-based beam follows Gauss-Lobatto rules that Gauss points are at the beam ends). The beam elements are prismatic and the analysis is elastic. I provided my tcl code below for reference.
Code: Select all
wipe
model basic -ndm 2 -ndf 3
node 1 0 0 -mass 1.0 1.0 1.0
node 2 0 150 -mass 1.0 1.0 1.0
node 3 0 300 -mass 1.0 1.0 1.0
fix 1 1 1 1
fix 2 0 0 0
fix 3 0 0 0
uniaxialMaterial Elastic 1 29000
section Fiber 1 {
patch rect 1 1000 2 -25.0 -10.0 25.0 10.0
}
geomTransf Linear 1
element dispBeamColumn 1 1 2 2 1 1
element dispBeamColumn 2 2 3 2 1 1
timeSeries Linear 1
pattern Plain 1 1 {
load 3 2.0 0.0 0.0
}
recorder mpco "SKTO_elastic.mpco" \
-N displacement rotation reactionForce reactionMoment \
-E force stress strain material.force material.stress material.strain \
section.force section.stress section.strain section.fiber.stress section.fiber.strain
constraints Penalty 1e15 1e15
numberer Plain
system BandGeneral
test NormDispIncr 1.0e-8 100
algorithm Newton
integrator LoadControl 0.01
analysis Static
analyze 100And when I plot the beam bending moment diagram, you can see the bending moment is dis-continuous between two elements. I output the bending moments at end of beam element and noticed they equal to the moment value at Gauss points. However, as I mentioned above, the Gauss point for displacement-based element should be inside the element.
Any comments are welcomed