A.A. ILYUSHIN'S FINAL RELATION, ALTERNATIVE EQUIVALENT RELATIONS AND VERSIONS OF ITS APPROXIMATION IN PROBLEMS OF ELASTIC DEFORMATION OF PLATES AND SHELLS. PART 2: ALTERNATIVE EQUIVALENT RELATIONS OF A.A. ILYUSHIN

Abstract

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.

Keywords

• the plasticity theory, plastic deformation of plates and shells, a surface of fluidit, a plasticity condition