A Unified Full-Field Deformation Measurement Approach for Plates With Different Thickness

The plate element with varying thicknesses follows distinct deformation laws. Consequently, the inverse finite element method (iFEM) must be adjusted to meet diverse plate elements. However, a challenge arises because it is difficult to distinguish between the thin and thick regions of most models. Therefore, a unified method is needed to handle the displacement field reconstruction of plate structures, which is an unsolved problem in this field so far. Additionally, the strain sensors are pasted at the center of mass symmetrically in traditional iFEM, limiting computational accuracy. Therefore, it is also necessary to propose a novel sensor optimization layout method to further optimize the robustness and accuracy in the proper region. To tackle these challenges, this article proposes an innovative method for full-field deformation measurement of thick and thin plates. This approach combines the principles of the iFEM, scaled boundary element theory, and the degenerate shell element. Initially, the mathematical model of discrete theoretical and experimental values of single-surface strains based on scaled boundary element theory is established for calculating the surface deformation field of plate structures. A bi-objective particle swarm optimization method is used to obtain the paste location and angle of the sensor distribution. Then, the degraded shell element model based on interpolated shape functions of 16-node spectral elements is proposed. This method solved the problem of pathological equations in the 3-D solid model for calculating thin plates and the problem of excessive stiffness coefficients at the edges for calculating thick plate. Next, the method establishes the relationship between the surface and mid-plane displacement field to realize the reconstruction of the entire domain displacement field. Finally, the simulation and experimental results show the high accuracy and universality of the method in reconstructing deformation field of plate structures with different width-to-thickness ratios under different load cases.