Approximate Solutions for Displacements in an Elastic Layer Subjected to Circular or Square Loads

This paper presents new approximate formulas for evaluating the maximum displacements of an elastic layer loaded on a circular or square area. The approximate formulas are based on the exact solutions of the theory of elasticity for a half-space and the elastic layer and offer a simple and quick way to obtain the values of displacements. The novelty of these formulas lies in their ease of application while maintaining high accuracy with respect to the exact solution of the theory of elasticity, which can make them useful in engineering practice and allows for the quick and efficient estimation of displacement values without the need for complex numerical methods—merely a pocket calculator is enough. This is beneficial from an engineering point of view, where time and resources may be limited. This article also provides an analysis of the maximum displacements of different elastic layers—slipping on a non-deformable base (a load on a circular or square area) or fixed on a non-deformable base (a load on a circular area).