Open AccessA.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
Author(s) -
А В Старов,
Sergei Kalashnikov
Publication year - 2020
Publication title -
international journal for computational civil and structural engineering
Language(s) - English
Resource type - Journals
eISSN - 2588-0195
pISSN - 2587-9618
DOI - 10.22337/2587-9618-2020-16-1-106-129
Subject(s) - parametric statistics , relation (database) , deformation (meteorology) , mathematics , hardening (computing) , yield (engineering) , space (punctuation) , deformation theory , mathematical analysis , geometry , materials science , computer science , composite material , statistics , layer (electronics) , database , operating system
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.