Abstract：During the manufacturing process of a rough workpiece, the non-uniformity of material mechanical properties can result in the generation of residual stresses within the workpiece. The residual stresses can lead to structural failure. During the cutting removal process of the workpiece, the residual stresses will gradually release and then cause deformation. The "birth-death element" technique of finite element analysis was used to simulate the material's cutting removal process. And then we transformed this process into the release of residual stresses. This study proposed a novel analytical method that combined radial basis function interpolation with geometric and physical equations. It was based on the plate shell theory, small deformation theory, elasticity theory, and the superposition principle. The method aimed to invert the residual stress field and calculate the resulting deformation.The paper was divided into two parts. In the first part, the influence of stress equilibrium equations was neglected. We used the radial basis function interpolation method to invert the release of residual stresses in thin plates according to the initial residual stress field and the residual stress field after material removal. Next, the stresses were substituted into the physical equations to calculate the strain. The strain was substituted into the geometric equations and then the plane displacement was calculated by strain integration from geometric equations. Based on plate shell theory equations, the buckling deformation was inverted according to the plane displacement. In the second part, the reverse process of the first part was performed. Firstly. we inverted the buckling deformation caused by material removal in the thin plate. Then, the buckling deformation was substituted into the plate shell theory equations. We used them to invert the release of residual stress and the reconstructed residual stress field. The results demonstrated the reversibility of these two processes. Furthermore, the analytical solutions showed high agreement with the finite element solutions. This suggested that the analytical method of this paper is applicable to thin plate structures under elastic conditions. It is expected to estimate the residual stress distribution and predict the deformation in the thin plate cutting removal process.
2024, Vol. 45 
