Development of a procedure for calculating problems in the mechanics of elastomers based on the open modeling language

The object of the study is the stress-strain state of elastomeric structures. When solving practical problems in elastomer mechanics, the issue of selecting an effective computational scheme based on computational mathematics methods arises. However, due to the insufficient number of studies, it is difficult to assess the optimality of a particular methodology, which necessitates an analysis of computational algorithms followed by a comparison of their advantages and disadvantages. In the design of elastomeric structures, the numerical analysis of their stress-strain state is a relevant issue. One of the key characteristics is the compressibility of the material, which is not taken into account by equations for incompressible media. In thin-layer rubber elements, this effect becomes more pronounced as the ratio of one of the geometric dimensions to the thickness of the structure increases. The use of the finite element method in displacements, despite its convenience, encounters computational errors. When the Poisson's ratio approaches 0.5, numerical instabilities arise, complicating the attainment of reliable computational results. This study proposes a new approach to organizing computational schemes in specialized automated design systems, which ensures more accurate modeling of the stress-strain state of structures. The foundation is the use of Open Modeling Language, which simplifies the description of mechanics problems and corresponding numerical schemes within a unified variational framework. The key result is the derivation of universal formulas for determining the potential energy of the system based on the moment finite element scheme. The proposed approach eliminates the “false shear” effect and improves the accuracy of numerical calculations for weakly compressible materials, which is confirmed by numerical analysis and experimental data