Discrete model of the pile foundation
The solid pile foundation is modeled by elastic vertical bars distributed over the area of the base in a uniform grid. It was assumed that the body of the structure is rigid, its weight is offset from the geometric center. The solution of statically indeterminate systems was obtained by the force method with the help of the Maxwell-Mohr formula. The method of induction made it possible to find a solution for an arbitrary number of piles. The dimensions of the foundation, the weight of the structure, the elastic characteristics of the piles (generalized stiffness), the number of the nodes in the grid of piles on both sides, the center of gravity coordinates were all the parameters of the solution. The computer algebra system Maple generated an analytical expression for the deformation and rotation angles of the foundation. The established dependencies exhibited limit (on the number of the piles) properties, allowing to estimate the deformation characteristics of the foundation and to optimize its design.