23.3.4 Beam element cross-section orientation

Products: ABAQUS/Standard  ABAQUS/Explicit  ABAQUS/CAE  

References

Overview

The orientation of a beam cross-section:

  • is defined in terms of a local, right-handed axis system; and

  • can be user-defined or calculated by ABAQUS.

Beam cross-sectional axis system

The orientation of a beam cross-section is defined in ABAQUS in terms of a local, right-handed (, , ) axis system, where  is the tangent to the axis of the element, positive in the direction from the first to the second node of the element, and and are basis vectors that define the local 1- and 2-directions of the cross-section. is referred to as the first beam section axis, and is referred to as the normal to the beam. This beam cross-sectional axis system is illustrated in Figure 23.3.4–1.

Figure 23.3.4–1 Local axis definition for beam-type elements.

Defining the n1-direction

For beams in a plane the -direction is always (0.0, 0.0, –1.0); that is, normal to the plane in which the motion occurs. Therefore, planar beams can bend only about the first beam-section axis.

For beams in space the approximate direction of must be defined directly as part of the beam section definition or by specifying an additional node off the beam axis as part of the element definition (see Element definition, Section 2.2.1). This additional node is included in the element's connectivity list.

  • If an additional node is specified, the approximate direction of is defined by the vector extending from the first node of the element to the additional node.

  • If is defined directly for the section and an additional node is specified, the direction calculated by using the additional node will take precedence.

  • If the approximate direction is not defined by either of the above methods, the default value is (0.0, 0.0, –1.0).

This approximate -direction may be used to determine the -direction (discussed below). Once the -direction has been defined or calculated, the actual -direction will be calculated as , possibly resulting in a direction that is different from the specified direction.

Input File Usage:           Use the following option to specify the -direction directly for a beam section integrated during the analysis:
*BEAM SECTION
-direction (the data line number depends on the value of the SECTION parameter) 

Use the following option to specify the -direction directly for a general beam section:

*BEAM GENERAL SECTION
-direction (the data line number depends on the value of the SECTION parameter) 

Use the following option to specify an additional node off the beam axis to define the -direction:

*ELEMENT

ABAQUS/CAE Usage: 

Property module: AssignBeam Section Orientation: select region and enter the -direction


Specifying an additional node off the beam axis is not supported in ABAQUS/CAE.

Defining nodal normals

For beams in space you can define the nodal normal (-direction) by giving its direction cosines as the fourth, fifth, and sixth coordinates of each node definition or by giving them in a user-specified normal definition; see Normal definitions at nodes, Section 2.1.4, for details. Otherwise, the nodal normal will be calculated by ABAQUS, as described below.

If the nodal normal is defined as part of the node definition, this normal is used for all of the structural elements attached to the node except those for which a user-specified normal is defined. If a user-specified normal is defined at a node for a particular element, this normal definition takes precedence over the normal defined as part of the node definition. 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. If the angle between the normal defined as part of the node definition or the user-specified normal and is greater than 90, the reverse of the specified normal is used.

Input File Usage:           Use the following option to specify the -direction as part of the node definition:
*NODE
node number, nodal coordinates, nodal normal coordinates

Use the following option to define a user-specified normal:

*NORMAL

ABAQUS/CAE Usage: Defining the nodal normal is not supported in ABAQUS/CAE; the nodal normal calculated by ABAQUS is always used.

Calculation of the average nodal normals by ABAQUS

If the nodal normal is not defined as part of the node definition, element normal directions at the node are calculated for all shell and beam elements for which a user-specified normal is not defined (the “remaining” elements). For shell elements the normal direction is orthogonal to the shell midsurface, as described in Shell elements: overview, Section 23.6.1. For beam elements the normal direction is the second cross-section direction, as described in Beam element cross-section orientation, Section 23.3.4. The following algorithm is then used to obtain an average normal (or multiple averaged normals) for the remaining elements that need a normal defined:

  1. If a node is connected to more than 30 remaining elements, no averaging occurs and each element is assigned its own normal at the node. The first nodal normal is stored as the normal defined as part of the node definition. Each subsequent normal is stored as a user-specified normal.

  2. If a node is shared by 30 or fewer remaining elements, the normals for all the elements connected to the node are computed. ABAQUS takes one of these elements and puts it in a set with all the other elements that have normals within 20 of it. Then:

    1. Each element whose normal is within 20 of the added elements is also added to this set (if it is not yet included).

    2. This process is repeated until the set contains for each element in the set all the other elements whose normals are within 20.

    3. If all the normals in the final set are within 20 of each other, an average normal is computed for all the elements in the set. If any of the normals in the set are more than 20 out of line from even a single other normal in the set, no averaging occurs for elements in the set and a separate normal is stored for each element.

    4. This process is repeated until all the elements connected to the node have had normals computed for them.

    5. The first nodal normal is stored as the normal defined as part of the node definition. Each subsequently generated nodal normal is stored as a user-specified normal.

    This algorithm ensures that the nodal averaging scheme has no element order dependence. A simple example illustrating this process is included below.

Example: beam normal averaging

Consider the three beam element model in Figure 23.3.4–2. Elements 1, 2, and 3 share a common node 10, with no user-specified normal defined.

Figure 23.3.4–2 Three-element example for nodal averaging algorithm.

In the first scenario, suppose that at node 10 the normal for element 2 is within 20 of both elements 1 and 3, but the normals for elements 1 and 3 are not within 20 of each other. In this case, each element is assigned its own normal: one is stored as part of the node definition and two are stored as user-specified normals.

In the second scenario, suppose that at node 10 the normal for element 2 is within 20 of both elements 1 and 3 and the normals for elements 1 and 3 are within 20 of each other. In this case, a single average normal for elements 1, 2, and 3 would be computed and stored as part of the node definition.

In the last scenario, suppose that at node 10 the normal for element 2 is within 20 of element 1 but the normal of element 3 is not within 20 of either element 1 or 2. In this case, an average normal is computed and stored for elements 1, and 2 and the normal for element 3 is stored by itself: one is stored as part of the node definition and the other is stored as a user-specified normal.

Appropriate beam normals

To ensure proper application of loads that act normal to the beam cross-section, it is important to have beam normals that correctly define the plane of the cross-section. When linear beams are used to model a curved geometry, appropriate beam normals are the normals that are averaged at the nodes. For such cases it is preferable to define the cross-sectional axis system such that beam normals lie in the plane of curvature and are properly averaged at the nodes.

Initial curvature and initial twist

In ABAQUS/Standard normal direction definitions can result in a beam element having an initial curvature or an initial twist, which will affect the behavior of some elements.

  • When the normal to an element is not perpendicular to the beam axis (obtained by interpolation using the nodes of the element), the beam element is curved. Initial curvature can result when you define the normal directly (as part of the node definition or as a user-specified normal) or can result when beams intersect at a node and the normals to the beams are averaged as described above. The effect of this initial curvature is considered in cubic beam elements. Initial curvature resulting from normal definitions is not considered in quadratic beam elements; however, these elements do properly account for any initial curvature represented by the node positions.

  • Similarly, nodal-normal directions that are in different orientations about the beam axis at different nodes imply a twist. The effect of an initial twist, which could result from normal averaging or user-defined normal definitions, is considered in quadratic beam elements.

Since the behavior of initially curved or initially twisted beams is quite different from straight beams, the changes caused by averaging the normals may result in changes in the deformation of some beam elements. You should always check the model to ensure that the changes caused by averaging the normals are intended. If the normal directions at successive nodes subtend an angle that is greater than 20, a warning message is issued in the data (.dat) file. In addition, a warning message will be issued during input file preprocessing if the average curvature computed for a beam differs by more than 0.1 degrees per unit length or if the approximate integrated curvature for the entire beam differs by more than 5 degrees as compared to the curvature computed without nodal averaging and without user-defined normals.

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 - and -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 and are made orthogonal to each other by rotating in this plane by an equal and opposite angle.