Thin Shell Foundation Resting on Stochastic Soil

The paper presents an approximate elastic solution to the statical problem of a thin concrete shell foundation. The soil‐structure interaction follows the Winkler concept of soil with random subgrade modulus. The randomness of the soil subgrade modulus renders the problem stochastically nonlinear. The method of statical solution is based on the finite difference procedure in the variational formulation and, to account for the probabilistic nature of the problem, is combined with the method of realizations in one approach, and with the perturbation method (small random parameter method) in the other case. The shell foundation that is dealt with in this paper consists of four hyperbolic‐paraboloid (in short hypar or HP) shells and a set of straight ribs. For the illustrative problem, the results consist of the estimates for the expectations and standard deviations of the discrete values of the structural displacement and internal force fields.