Construction of discrete analogs of differential equations for bending of plates and shells with discontinuous parameters based on spline approximation method

Abstract

A new approach to the construction of discrete analogs of the differential equations of bending of plates with discontinuous parameters based on the two-dimensional spline approximation method is proposed. At its core, it is close to the Finite Element Method, since all constructions at the beginning are carried out for a single cell of a finite element, and then applied to the entire area surrounding the base node. The use of such a technique makes it possible to reduce the number of unknowns in each node of the grid area, and the introduction of parameter gaps into the resolving system makes it possible to take into account their effect on the stress-strain state of the structures. This approach to the construction of discrete analogs of partial differential equations allows developing a universal method for constructing discrete analogs of these equations. This technique will significantly reduce the amount of computation in the strength analysis of buildings and structures of various functional purposes using lamellar and shell elements.