Appendix A. Example Analyses with Multiple Imposed Rotations
The examples shown here demonstrat e how the results change when the order of imposed rotations
is changed in a large defection analysis.
A.1. Problem Description
A robotic arm, modeled with one BEAM188 element, is initially aligned along the global Z-axis with one
end at the origin. On the node at the origin displacements are fixed, and non-zero rotations are applied
in all three directions. Two ways of applying rotations are shown: sequential and simultaneous. Animations
are provided to show the differences in results.
The rotations are applied in the following manner:
Sequential rotations - The beam is first rotated by 60° clockwise about the X-axis, followed by a
90° counterclockwise rotation about the local z-axis, and finally another 90° counterclockwise rotation
about the local x-axis. The rotations about each axis are imposed in separat e load steps.
Simultaneous rotations - The total values for the compound rotations are the same as the sequential
case, but the rotations are imposed in a single load step. The beam is rotated by 60° clockwise
about the X-axis, by (90°)(sin(60°)+cos(60°)) counterclockwise about the Y-axis and by (90°)(sin(60°)-
cos(60°)) clockwise about the Z-axis.For the case of sequentially applied rotations, two sample inputs are given: one with imposed rotations
and the other with imposed rotational velocities. This demonstrat es that the use of imposed rotations
and imposed rotational velocities both achieve the same results in a static analysis.
A.2. Sample Inputs for Imposed Rotations
The following input listing shows the model setup, including node and element definitions, material
definitions, and section definitions. This PREP7 input was used for all the examples in this discussion.
Beam Model Setup
/BATCH,LIST
/PREP7
!Parameters
PI=3.1415926536
!Element type definitions
ET,1,188 !Beam element
!Node definitions
N,1,0.,0.,0.
N,2,0.,0.,0.6
!Material properties
MP,EX,1,2.01E11 !Young's modulus for Steel
MP,NUXY,1,0.3 !Poisson's ratio
!Section properties
SECTYPE,1,BEAM,RECT
SECDATA,0.1,0.2 !Beam cross-sectionRelease 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information