OS-E: 3005 Eigenvalue Maximization

An irregularly shaped plate is optimized to increase its natural frequencies.

Model Files

Before you begin, copy the file(s) used in this example to your working directory.

Model Description

The plate is supported at ten bolt locations around its perimeter. The edge of the plate is turned downward to add stiffness.

Figure 1. Cover Plate Model with Constraints Shown
The red areas are excluded from the design domain. The blue area is open for OptiStruct to add a bead reinforcement pattern. The bead is drawn upward with respect to the plate orientation. The DTPG card used is as follows. Four different runs were made using different values for the draw height. The first run was made with a draw height of 20mm, the second with 40mm, the third with 60mm, and the fourth with 80mm.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
DTPG 1 PSHELL 5            
  20.0 60.0 YES 20.0 NORM     NONE  
The optimization is set up to maximize the frequencies of the first six modes (minimizing the sum of the weighted inverse eigenvalues) and to ensure that the first three modes were above certain design constraints. This is accomplished by placing the following cards in the subcase definition:
The following cards are placed in the Bulk Data section:
DRESP1 11 freq1 FREQ     1  
DRESP1 12 freq2 FREQ     2  
DRESP1 13 freq3 FREQ     3  
DRESP1 1 wfreq WFREQ        
DCONSTR 101 11 400.0        
DCONSTR 101 12 500.0        
DCONSTR 101 13 600.0        
DRESP2 1 wfreq 900        


Setting constraints on the first three modes results in separations between the frequency values of the modes and prevents OptiStruct from falling into local minimums when optimizing the modes. This approach ensures that a minimum performance criterion is satisfied.
Note: For the 40mm, 60mm, and 80mm draw height runs, the constrained frequencies are higher than those shown above.
The solutions generated for the plate runs are:

Figure 2. Solution for Plate with Draw Height Equal to 20mm

Figure 3. Solution for Plate with Draw Height Equal to 40mm

Figure 4. Solution for Plate with Draw Height Equal to 60mm

Figure 5. Solution for Plate with Draw Height Equal to 80mm

The reinforcement patterns have a similar shape, but runs with a higher maximum draw height use more levels of draws throughout the plate. All of the solutions made good engineering sense, connecting the weak areas of the plate with beads running primarily across the short span of the plate. These beads were fluidly connected across the long span of the plate allowing the beads to reinforce each other.