PSI - Issue 38

Amaury Chabod et al. / Procedia Structural Integrity 38 (2022) 382–392 Amaury CHABOD / Structural Integrity Procedia 00 (2021) 000 – 000

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3. Strain Gage Position Optimization The strain gage response accuracy is strongly dependent on its placement on the component. First, small radius or sharp edge, source of high stress gradients field, should be avoided ( Hoffman (1989)) . This would indeed imply averaging of stress depending on the strain gage length and on the amplification of errors due to the precision of placement. Generally, for a given load case, representative strain gages are placed where stress field is important, in a smooth region where placement is physically achievable and precise, with their orientation aligned with the principal stress directions. This process can be automatized with nCode DesignLife, where strain gage placement and orientation are optimized, removing sharp edges and small radius areas from possible nodal candidates. In this process, the determinant of the strain matrix [ ] [ ] is maximized (Wickham et al. (1992, 1994) and Wheeler (2011)). As a result, analysis obtains a list of strain gages exact positions and orientations. Importantly, the determinant of matrix [ ] [ ] is made available for a proper definition of the experimental preparation. In addition, the coordinates of FE nodes and their orientations help to create a mask with CAD and 3D printing. This enables us to find exact positions on real components of complex shapes. 4. Load Reconstruction Process 4.1. General process From independent unitary load cases and strain gages measurement, the objective is to reconstruct loads applied to a component. An added value of such a process is to avoid any load transducer interferences with the load path or to measure diffuse and unknown loads, such as reactions due to aerodynamic or hydraulic loads. This principle is used in load/torque transducers based on strain gages technology. In our application, the whole structural component acts as a measuring body, linking the strain response with the load introduced. An important benefit of such a technique is that it is simpler to use simple strain gages measurements than complex transient and multi-physics FE analysis possibly with fluid-structure interaction. From equation (1), we obtain the least mean squares estimator for the applied loads (Munson and Mentley (2015), He and Fu (2001)): { ̂ } = ([ ] [ ]) −1 [ ] { ̂ } (3) The load reconstruction process can be thought of as the reverse, and bijective, operation of the Virtual Strain Gage. Furthermore, the variance of loads is directly linked to strain standard deviation error e: ({ ̂ }) = ([ ] [ ]) −1 (4) These equations allow to propagate the uncertainty resulting from strain measurements on load estimate. Additionally, a load estimator is given for each independent load case from strain measurements. The Load Reconstruction Process can be schematized in Fig. 2.

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