## 3 Calculation of Mechanical Variables Using a Strong Form-Based Meshfree Method
### TP Displacement Tracking Using Synthetic Structural Analysis  
For the target used in the bending test, a similar rubber material was sprayed on the surface of the specimen to prevent detachment while effectively reflecting the deformation of the specimen. The size of the target was 10 \(\times\) 10 mm, and 42 targets were attached at a center distance of approximately 20 mm, as shown in Figure 13a. From Equation (2), the size of the unit pixel according to the scale factor was approximately 0.063 mm. As the size of the unit pixel is the smallest unit for tracking the displacement, it is causally related to the size of the error that occurs in the synthetic structural analysis. In this study, images were extracted every 20 s from the image set to improve the computation efficiency and were used for the displacement tracking using DIP and stress calculation using the PDM. Figure 13a,c,e shows the experimental images acquired at 0, 220, and 460 s, respectively. Figure 13b,d,f shows the nodal deformed shapes processed using DIP and the PDM, indicating the deformation of the beams obtained from the synthetic structural analysis for each corresponding time (i.e., 0, 220, and 460 s). The displacement information of the 42 TPs extracted using DIP from the experimental image was distributed between 671 (\(61\times 11\)) PDM nodes using Equation (11). It can be seen that the actual deformation of the specimen and the shape of the deformation simulated by the PDM nodes were in close agreement. To verify the effectiveness of the algorithm in calculating the kinematic variables of the synthetic structural analysis, the results were compared with the experimental results and the simulation results obtained using only the PDM. The simulation results using PDM were obtained by applying a concentrated load, similar to that in an actual experiment, on the PDM model beam, and by performing an elastic analysis on the rubber deformation process in a quasi-static state. In this case,  
Figure 13: Comparison of the mechanical test and numerical analysis. (**a**) Trimmed image at t = 0 s, (**b**) PDM model at t = 0 s. (**c**) Trimmed image at t = 220 s. (**d**) PDM model at t = 220 s. (**e**) Trimmed image at t = 460 s. (**f**) PDM model at t = 460 s.  
the displacement value was obtained through the PDM analysis without the use of TP displacement through DIP. In the synthetic structural analysis, the method of utilizing the centroid of the target as the TP was first applied. Figure 13b,d,f illustrates the deformed shapes of the 42 TPs obtained through DIP in a particular interval, indicating that the displacement information of the TPs is successfully converted to the node displacement of the PDM model. Later, these nodal displacements were used to calculate various kinematic or kinetic variables. Ass the PDM analysis was performed under the assumption of static and linear elastic states, the results should be compared with the experimental results within the linear elastic range. Figure 14a-d displays the surface plots of the displacement and stress calculated by the synthetic structural analysis and the simulation using only PDM after 60 s of loading. Figure 14a,b compares the displacement calculation results in the \(x\)-direction for the two cases, whereas Figure 14c,d compares the displacement calculation results in the y-direction. The displacement in the \(x\)-direction indicates that a flexural compressive stress is generated above the neutral axis and a flexural tensile force is generated below it. The displacement in the \(y\)-direction is also in the downward direction between the points, tracing a shape similar to the deflection shape of the specimen. In addition, because no displacement constraint exists outside the support points, as shown in Figure 14c,d, the displacement in the \(y\)-direction is upward at the end sides of the beam, similar to that in the experiment.