Stressed state of a two-layer coating of a container with increased internal pressure

Storage of individual bulk materials in containers requires their isolation from external influences, for example, moisture ingress. Waterproofing is provided by maintaining increased pressure in the container. In order to slow down the possible pressure drop, the upper part of the container is made of an elastic two-layer material. One layer provides waterproofing. The second layer provides sufficient strength of the two-layer coating. Its stressed state of the material significantly affects the service life and safety of flexible coatings. Establishing and taking into account the influence of operating conditions, mechanical properties of material layers on the stressed-deformed state of the coating is a relevant scientific and technical problem. Its solution allows to increase the reliability and safety of using pressure vessels. In the article, the layers are considered as isotropic with reduced mechanical characteristics. Using the stress functions (Erie functions) of the classical linear theory of elasticity, a mathematical model of the plane deformed state of the two-layer coating is constructed. The model takes into account the boundary conditions for the external surfaces of a two-layer coating: a uniformly distributed normal load given by Fourier expansion acts on the surface of the first layer. A normal stress acts on the external surface of the second layer. The model also takes into account the conditions for the joint deformation of the layers: equality of the forces of mutual pressure of the layers, tangential stresses arising on the surfaces of interaction of the layers and their displacements. Based on the solution of the mathematical model, an algorithm for determining the stress-strain state of a two-layer coating is formulated. It takes into account the assumption of stress functions, respectively, of the components of the stress-strain state of the material of the coating layers in the form of sums. The dependence of the coating deformations on the mechanical properties of the material of the layers has been established. Thus, an increase from the minimum to practically maximum value of the Poisson's ratio of the layer material that provides waterproofing reduces the coating deflection by almost an order of magnitude.