MATHEMATICAL MODELING OF CYLINDRICAL SHELL STRESS-DEFORMED STATE OF MEMBRANE COATING WITH A REINFORCING ELEMENT

Abstract

This work considers an approach to multidimensional approximation with regard to modeling the stress-strain state of cylindrical shells of membrane coatings with a reinforc-ing element. The proposed approach is characterized by the absence of the need to com-pose and solve a system of linear algebraic equations, in order to determine the polynomi-al coefficients of the approximating function. Instead, in order to minimize the sum of squared deviations between the initial data and those calculated, high-speed numerical al-gorithms to define extreme values are used. They were obtained in the MS Excel software package in the form of the “Find solution” function. The proposed approach to the ap-proximation of multidimensional experimental data is a flexible and effective tool. Never-theless, it has certain disadvantages inherent in the classical least square method in terms of the occurrence of unplanned oscillations between the nodal points of the approxima-tion. Therefore, this paper provides an example of the use of geometric theory of multidi-mensional interpolation, in order to solve the same modeling problems, but using geometric interpolants. As can be seen from the results, in a specific case, the models obtained on the basis of the geometric theory of multidimensional interpolation most accurately reflect the nature of the process. In this regard, they are more preferable in relation to models obtained using the two-dimensional approximation. Approximation models are obtained in the form of explicit functions, and interpolation models are obtained in parametric form.