Determination of the Kernel of a Deformable Foundation Model from Experimental Data

We propose a method for determining the kernel of a deformable foundation model based on the inverse solution of plate bending on an elastic foundation. The results of contact pressure and displacement measurements are approximated by a Gaussian curve, following which the inverse problem for the Fredholm equation of the first kind is solved by the methods of operational calculus using the Fourier integral transform. The solution of the inverse problem represents the kernel of a foundation model, which can be further used to determine deflections and bending moments of beams and plates by solving the corresponding differential bending equation. The obtained model clarifies the distribution and magnitude of the bending moment and eliminates the difficulties arising when solving the elasticity theory problem with a bending moment reduction of 15% or greater.