Stress-strain state of a plate located on an inhomogeneous base

Abstract

At present, the problems of calculating structures on an elastic foundation are very relevant. In this regard, the influence of the inhomogeneity of the base on the stress-strain state of thin plates is investigated. Plates located on the Winkler elastic foundation and having hinged supports along the contour are considered. It is assumed that the value of the foundation bed coefficient has a symmetrical character of change relative to the middle of the plate, and within its limits is described by a quadratic law. The Ritz-Timoshenko variational method was used to study the stress-strain state of the plate. The calculation was performed in the Excel environment, while trigonometric functions were taken as approximating ones. Plates with different relative lengths are presented: short, medium length and long. It is shown that the effect of base inhomogeneity on the stress-strain state is most noticeable for long plates.