Since this is a transient dynamic analysis, it is natural to consider how
the results compare with those obtained using direct integration of the
equations of motion. Direct integration can be performed with either implicit
(Abaqus/Standard)
or explicit (Abaqus/Explicit)
methods. Here we extend the analysis to use the explicit dynamics procedure.
Context:
A direct comparison with the results presented earlier is not possible since
the B33 element type and direct modal damping are not available in
Abaqus/Explicit.
Thus, in the
Abaqus/Explicit
analysis the element type is changed to B31 and Rayleigh damping is used in place of direct modal damping.
Copy the Dynamic model to one named
explicit. All subsequent changes should be
made to the explicit model.
Delete the modal dynamics step. When
Abaqus/CAE
warns you that deleting a step also deletes step-dependent objects, click
Yes.
Replace the remaining frequency extraction step with an explicit
dynamics step, and specify a time period of 0.5
s. In addition, edit the step to use linear geometry (toggle off
Nlgeom).
This will result in a linear analysis.
Rename the step to Transient dynamics.
Create two additional history output requests. In the first, request
displacement history for the set Tip-a; in the
second, request reaction force history for the set
Attach.
Add mass proportional damping to the bracing section properties. To do
this, double-click BracingSection underneath the
Sections container in the
Model Tree;
in the section editor that appears, click the Damping
tab.
In the Stiffness Proportional Material Damping
region, enter a value of 15 for
Alpha and 0 for the
remaining damping quantities.
These values produce a reasonable trade-off in the values of critical
damping at low and high frequencies of the structure. For the three lowest
natural frequencies the effective value of
is greater than 0.05; but as was shown in
Figure 1,
the first two modes do not contribute significantly to the response. For the
remaining modes, the value of
is less than 0.05. The variation of
as a function of natural frequency is shown in
Figure 1.
Figure 1. Variation of damping ratio with frequency corresponding to the
specified Rayleigh factors (
= 15,
= 0).
Repeat the above step for the main member section properties.
Redefine the tip load at set Tip-b.
Specify CF2 = −10000, and
use the amplitude definition Bounce.
Change the element library to Explicit, and
assign element type B31 to all regions of the model.
Create a new job named expDynCrane, and
submit it for analysis.
When the job completes, enter
the Visualization module
to examine the results. In particular, compare the tip displacement history
obtained earlier from
Abaqus/Standard
with that obtained from
Abaqus/Explicit.
As shown in
Figure 2,
there are small differences in the response. These differences are due to the
different element and damping types used for the modal dynamic analysis. In
fact, if the
Abaqus/Standard
analysis is modified to use B31 elements and mass proportional damping, the results produced by
the two analysis products are nearly indistinguishable (see
Figure 2),
which confirms the accuracy of the modal dynamic procedure.
Figure 2. Comparison of tip displacements obtained from
Abaqus/Standard
and
Abaqus/Explicit.
