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Robust topology optimization of a flexural structure considering multi-stress performance for force sensing and structural safety


This paper demonstrates a new robust topology design formulation for a compliant sensor structure considering multi-stress performance. Compliant mechanism design is one of the main applications of topology optimization that can be used to achieve displacement or force requirements based on its elastic deformation. Most compliant mechanisms have hinge joints where high stress is observed and this should be carefully considered in the design formulation. In this paper, we investigate a new design formulation that considers multiple stress components for force measurement and structural safety in a compliant mechanism—a wind tunnel balance. An internal wind tunnel balance is a multi-axis force sensor that measures aerodynamic forces and moments during wind tunnel testing. For the axial section of the balance, it is required to have substantial stress reading (sensor performance) by the axial load. In this paper, two stress measures are used in the design formation: (1) local directional stress to meet the sensor performance by a small axial force, and (2) normalized P-norm stress with a relaxation approach to ensure the safety of the balance by a large normal force. The high force ratio between axial and normal forces (1:10 +) is investigated in this paper. In addition, a robust approach is applied to reflect the manufacturing uncertainties from three different projected design variables. The manufacturable blueprint designs using this approach show satisfactory performance with respect to sensing and structural safety.

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The authors gratefully acknowledge NASA Langley Research Center and the National Institute of Aerospace for their support from Prime Contract No. NNL13AA08B, Subcontract No. T19-601049-UMBC. The authors thank Dr. Julián Norato (University of Connecticut) for his help on the sensitivity analysis on stress measures.

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Correspondence to Soobum Lee.

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All the necessary data to reproduce the results reported in this paper are provided in Sects. 2,3 and 4.

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This appendix section discusses two issues discovered when Condition 2 is considered as highlighted in Fig. 

Fig. 18
figure 18

Design suitability area

18: (1) unnecessary features that do not contribute to the mechanism (dashed line); and (2) void areas even though volume maximization is considered (solid line).

First, to understand the effect of the feature in the dashed line that is attached to the analysis domain, we investigate the performance measure when the feature is removed, as shown in Fig. 

Fig. 19
figure 19

Modified eroded designs for feature verification

19 and Table

Table 6 Stress parameters based on each modification

6. Unexpectedly, there is a slight change in stress performance as reviewed in Table 6, even though this feature does not seem to be connected to the mechanism.

To investigate the second issue, the triangular area for the eroded design is filled manually (Fig. 

Fig. 20
figure 20

Verification for volume maximization

20) and the stress performances are reviewed (Table

Table 7 Stress parameters

7). Again, there is a slight change in the stress performances and the modified eroded design violates the sensor performance constraint (Eq. (9), σs < σ0 = 30 MPa).

From the two studies, it is concluded that the local stress value is affected by the density change around a disconnected feature or a void (white) area even though it does not seem to contribute to the sensor mechanism. Actually, the void area has nonzero density (xmin) and nonzero material properties, so its density change into higher value increases the mechanism stiffness (and vice versa) and changes the stress performance. This is a specific issue when volume maximization is considered—a volume minimization problem will eliminate unnecessary features and the void area expands to save material.

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Sung, M.K., Lee, S. & Burns, D.E. Robust topology optimization of a flexural structure considering multi-stress performance for force sensing and structural safety. Struct Multidisc Optim 65, 6 (2022).

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  • Stress-based topology optimization
  • Force sensor
  • Compliant mechanism
  • Robust topology optimization
  • Wind tunnel balance
  • Wheatstone bridge