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The finiterelationship between the forces and moments of plates and shells in the parametric form of the theory of small elastoplastic deformations is investigated of A.A. Ilyushin, to determine the load-bearing capacity of structures from a material without hardening. A geometric image of the exact yield surface in the space of generalized stresses is obtained. In the firstpart of the article the conclusion of the finalrelation is given. In the second and third parts, by introducing other parameters, alternative equivalent dependences of the finalrelationship have been developed and variants of its approximation for application in computational practice are considered. In the fourth part, additional properties of the finalrelationship are considered, the possibility and necessity of its use in problems of plastic deformation of plates and shells is shown.

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Abstract. The paper addresses the problem of plastic deformation of circular membranes and shallow axisymmetric membrane shells under high-intensity loading considering rotary inertia. The resolving equations systems are obtained, the numerical implementation program and algorithms are developed. The research methods used in the paper include finite difference method, differential-incremental method of the second and fourth orders of accuracy, the Fourier series solutions with Bessel functions. The results are obtained confirming reasonability of considering rotary inertia.

The finite relationship between the forces and moments of plates and shells in the parametric form of the theory of small elastoplastic deformations is investigated of A.A. Ilyushin, to determine the load-bearing ca­pacity of structures from a material without hardening. A geometric image of the exact yield surface in the space of generalized stresses is obtained. In the first part of the article the conclusion of the final relation is given. In the second and third parts, by introducing other parameters, alternative equivalent dependences of the final rela­tionship have been developed and variants of its approximation for application in computational practice are considered. In the fourth part, additional properties of the final relationship are considered, the possibility and necessity of its use in problems of plastic deformation of plates and shells is shown.