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

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.

A.A. ILYUSHIN S FINAL RELATION, ALTERNATIVE EQUIVALENT RELATIONS AND VERSIONS OF ITS APPROXIMATION IN PROBLEMS OF PLASTIC DEFORMATION OF PLATES AND SHELLS PART 1: A.A. ILYUSHIN S FINAL RELATION

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.

On a certain version of the multilane turnpike theorem in Gale’s non-stationary economy

In the vast majority of papers concerning asymptotic (main) properties of the optimal growth processes in Neumann-Gale-Leontief’s stationary economies, the geometric image of a turnpike is expressed by a single ray, called von Neumann’s ray. Even though neither the postulate of stationariness nor unambigiousness of a production turnpike are consistent with the observations of real economic processes, the list of papers devoted to the effect of a multilane turnpike in Neumann-Gale-Leontief’s non-stationary economies (with changing technology and multiple lanes) is much more modest. These works include mainly papers by Panek (2017, 2018), where the author replaces a single production turn-pike in Gale’s non-stationary economy with a multilane turnpike. This paper draws directly upon the author’s earlier work (Panek, 2019), where two turnpike theorems were presented. Both of them were based on the assumption signifi-cantly weakened by this paper – that in Gale’s non-stationary economy the optimal pro-duction structure in period ݐ remains optimal also in the future.