In Abaqus documentation (Beam section 29.3.4–5), it states:
“In Abaqus/Explicit initial curvature of the beam is not taken into account: all beam elements are assumed to be initially straight. The element’s cross-section orientation is calculated by averaging the n1- and n2-directions associated with its nodes. These two vectors are then projected onto the plane that is perpendicular to the beam element’s axis. These projected directions n1 and n2 are made orthogonal to each other by rotating in this plane by an equal and opposite angle.”
In modelling of curved geometry (even with a very fine mesh to ensure element straightness), Abaqus issue the following warnings for bean section orientations in the local 1-direction, local 2-direction and beam tangent:
- For xxx beam elements either the average curvature about the local 1-direction differs by more than 0.1 degrees per unit length as compared to the default curvature or the approximate integrated curvature for the entire beam differs by more than 5 degrees as compared to the approximate integrated default curvature. This may be due to a user-specified normal or due to the nodal averaging routine used by Abaqus. This difference may cause unexpected behavior of the beam and you may want to verify that the beam normals are correct for your problem. The elements have been identified in element set WarnBeamCurvature1.
Any idea on how to evaluate the effect of this averaging routine on the behaviour of the beams? Abaqus documentation states that “Appropriate beams’ normals are needed to ensure proper application of loads that act normal to the beam cross-section”. But how can we evaluate these loads and check how they affected by the above warnings?
Hi Hassan Al-Budairi,
Also try to model your beam using several beam parts with sufficiently small curvature (and twist if any).
Thanks Fabian Dwenger & Victor J. Аdlucky for your contributions to this disscussion; as I mentioned (even with a very fine mesh .....), mesh refinement would not solve the issue as these warnings are related to section orientations that are affected by the geometrical curvature.
To shade more light about this discussion:
The beam cross-section orientation is defined in Abaqus in terms of a local, right-handed (t,n1,n2) axis system.
t: the tangent to the axis of the element, positive in the direction from the first to the second node of the element.
n1: basis vector that define the local 1-direction of the cross-section. It referred to as the first beam-section axis.
n2: basis vector that define the local 2-direction of the cross-section. It referred as the normal to the beam.
For beams in space, the tangent direction t is define by the nodes (as described above), the n1-direction is defined by finding an approximate direction of n1 first by:
1- Direct approach as part of the beam section definition by following the first beam cross section axis.
2- Specify an additional node off the beam axis as part of the element definition. The approximate n1-direction is defined by the vector extending from the first node of the element to the additional node.
3- By a default value (0.0, 0.0, −1.0) if none of the above is considered.
This approximate n1-direction may be used to determine the n2-direction (discussed below). Once the n2-direction has been defined or calculated, the actual n1-direction will be calculated as n2xt, possibly resulting in a direction that is different from the specified direction.
The nodal normal (n2-direction) is defined by:
1- Giving its direction cosines as the fourth, fifth, and sixth coordinates of each node definition.
2- Giving them in a user-specified normal definition.
3- Calculated by Abaqus if none of the above is considered.
If the specified normal subtends an angle that is greater than 20° with the plane perpendicular to the element axis, a warning message is issued in the data (.dat) file. This is what is happening in this case.
I have attached a number of pictures to show the initial geometry for a small section of my model and the section orientations for course and fine mesh. As mentioned above, further refinement will not remove the warnings but, instead, would violate the slenderness ratio of the beams.
The question is still on how we can evaluate the effect of these warnings on the beam behaviour?
Regards;
Hi Hassan Al-Budairi,
It seems to me that beam considered is such that "... the approximate integrated curvature for the entire beam differs by more than 5 degrees as compared to the approximate integrated default curvature."
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