The second example demonstrates the application of NX Nastran’s optimization capabilities to transient analyses. The example is a simple portal frame acted upon by an enforced displacement at its base (Figure 5-8). This is a simple representation of a civil engineering structure subjected to seismic loading. The problem was obtained from Reference 9, which demonstrated the possibility of disjoint design spaces when working in the time domain in an analogous fashion to the disjoint design space referred to earlier in the frequency domain. The portal has the following parameters:
Table 5-3. Parameters for the Portal Frame Example
PARAM Meaning Value
E Young’ Modulus 30.0 × 106psi
r Material density 0.28 lbm/in3
Imin Minimum allowable inertia 290.04 in4
NSM Nonstructural mass per unit length 10.0 lbm/in
wmin Minimum allowable fundamental frequency 60 rad/sec
dmax Maximum allowable displacement ±3.0 in
wmax Maximum allowable stress ±3.0 ksi
L Height and width of the portal 180 in
Advanced Dynamic Analysis User’s Guide 5-65
Figure 5-8. The Portal Frame
The frame is subjected to horizontal ground motion in the form of a half sine pulse:
Equation 5-68.
The design task is to minimize the weight of the structure while imposing the limits on structural displacement, stress and natural frequency listed inTable 5-3.
Finite Element Model
The frame was modeled using three finite element bars (the symmetry of the problem could have been used to limit this to two elements). The stress is computed as the ratio of the bending moment in the beam divided by the section modulus.
The weight of the beam is simply its volume times the structural density. One design variable controls the bending moment of inertia of the vertical columns, while a second variable controls the inertia of the horizontal beam. Equations for the section modulus, S, and area, A, in terms of the moment of inertia of the beam, I, are taken fromReference 9in“Selected Bibliography”:
Equation 5-69.
Equation 5-70.
The transient response was performed over a period of 250 msecs at a time step of 1 msec.
Responses were retained at every 5 msecs and the stress and displacement constraints were applied at each of the retained time steps. For the initial design, moment of inertia values of
600 in4were used for both design variables, making the initial objective value 1722.2 lbs (this ignores the weight of the nonstructural mass).
Results
Figure 5-9. Transient Stress Response for the Initial and Final Designs of the Portal Frame
Figure 5-9shows the transient stress response of the end of the horizontal beam for the initial and final designs. It can be observed that the stresses for the initial design are well below the 30 ksi limits, while the response is right at this limit for the final design. Since there is no damping in the structural representation, the structure would continue to sway if a longer record were obtained, but the imposed limits should not be exceeded.
Table 5-4compares the results from this analysis with those given inReference 9in“Selected Bibliography”. Note that the NX Nastran results are somewhat higher than those given in the reference, which can be attributed to differences in the finite elements used in the two analyses.
Table 5-4. Comparison of Results for the Portal Frame
PARAM NX Nastran Reference
X1 (columns) 578.6 in4 498.0 in4
X2 (crossbeam) 301.7 in4 330.0 in4
Objective 1534. lbs 1463. lbs
Advanced Dynamic Analysis User’s Guide 5-67
Although the examples shown here are elementary, it should be apparent that the capabilities they demonstrate are quite powerful. NX Nastran’s capabilities for dynamic response
optimization can be coupled with design tasks that have requirements for static response, natural frequency, and buckling and aeroelastic responses. Note, too, that the models can include superelements. Furthermore, although all the examples here have properties for the design variables, the capability also interacts with NX Nastran’s shape optimization capability.
One additional area in which dynamic response optimization can be applied is the system identification of structures to match modal test results. A modal test can be considered a forced excitation. Therefore, the capability described here could be used modify structural parameters in an NX Nastran analysis so that the responses obtained from an NX Nastran frequency analysis could match test results.
5.10 DDAM
The Dynamic Design Analysis Method (DDAM) is a procedure that is used to determine the shock response of equipment mounted on-board a ship to underwater explosions. The DDAM procedure consists of three distinct phases:
• Phase 1: NX Nastran performs a modal analysis of the equipment structure and calculates the corresponding modal participation factors and modal effective masses for each mode.
• Phase 2: The Naval Shock Analysis (NAVSHOCK) FORTRAN program uses the modal effective masses and natural frequencies calculated by NX Nastran in Phase 1 and user-supplied inputs from either a DDAM control file or command line entry to compute shock design accelerations.
• Phase 3: NX Nastran uses the shock design accelerations computed by NAVSHOCK in Phase 2, and the modal participation factors and natural frequencies calculated by NX Nastran in Phase 1 to compute the shock response of the structure.
Prior to NX Nastran 5, you were required to use dmap alter files to complete a DDAM procedure.
Beginning with NX Nastran 5, the DDAM procedure has been implemented as a new solution sequence, SOL 187, thus eliminating the alter requirement. When you use SOL 187, you can perform a DDAM procedure:
• Automatically from a single NX Nastran input file and a DDAM control file.
• Interactively from two NX Nastran input files (one for Phase 1 and one for Phase 3) and either a DDAM control file or command line entry.
For the automated procedure, NAVSHOCK executes automatically as an ISHELL program after NX Nastran has completed Phase 1. Once NAVSHOCK has completed Phase 2, NX Nastran automatically resumes execution to complete Phase 3.
For the interactive procedure, NX Nastran terminates execution once Phase 1 has completed. To execute NAVSHOCK, you must manually start it from the command line. Once NAVSHOCK has completed Phase 2, you must restart NX Nastran to complete Phase 3.