The methods of specifying the middle surface of an elliptical cylinder in curvilinear coordinate systems are described. An algorithm for discretization of an elliptic cylinder by high-precision quadrangular finite elements with a set of nodal variable parameters, which includes components of the displacement vector, as well as their partial derivatives of the first and second orders, is described. Nodal unknowns in global and local coordinate systems are described. Two types of interpolation procedure are presented: vector interpolation of displacement fields, scalar interpolation. Interpolation expressions for the components of the displacement vector and their first and second derivatives are obtained using the vector version of the interpolation procedure.

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Nowadays, the task of creating and improving computational algorithms for determining the stress-strain state (SSS) of technosphere objects and systems, taking into account the physically non-linear stage of operation of the material of structures and their elements, is quite relevant. A variational approach to the formation of a plasticity matrix at the loading step for a three-dimensional body is presented on the deformation theory of plasticity. A variant of obtaining the plasticity matrix using the operations of differentiating the covariant components of the stress tensor with respect to the covariant components of the strain tensor is considered. As an alternative to it, an option has been developed for the formation of a plasticity matrix at the loading step, based on the hypothesis of proportionality of the components of the deviator of stress increments to the components of the deviator of strain increments for three-dimensional bodies. The use of such option of forming a plasticity matrix at the loading step in software systems can significantly simplify the programming process and make it more understandable to potential users of computing systems in the design and reconstruction of technosphere objects and systems.