Analysis of stress-strain state of the metal plate based on discrete data of displacement values

An actual problem of stress-strain state (SSS) analysis of a bent metal plate under an uncertain acting load is solved. A problem in the direct use of spatial interpolation for obtaining the surface of a metal plate, which is realized in the Surfer software product, is formed. It is noted that direct use of existing interpolation methods without considering physical-mechanical properties leads to results distortion. It was noted that spatial interpolation methods have analogy with the finite element method (FEM) in terms of surface display using meshes. This was the basis for comparing the results of surface modelling by FEM and grid-cell interpolation methods. The main difference of the interpolated surface was the absence of spline properties. A new approach to solving the problem was the additional use of second and fourth-order polynomial spline functions, whose expressions are obtained from the initial and boundary conditions of the deformed plate. With its help, lines of smooth curvature, which acted as frame lines, were obtained and plotted on the grid-cell surface. The introduction of the frame lines on the grid-cell resulted in the combination of the initial discrete data with the displacement values calculated using the expressions of polynomial spline functions. A significant increase in the number of point data allowed the spatial interpolation method to extend the spline properties to the grid-cell interframe space as well. As a result, an adequate deformed surface of a metal plate was reproduced, giving it spline properties - smooth radii of curvature.