Arkhipov O. Solution of the problem of elastic-plastic bending of arbitrary shaped plane plates by using the R-function method (RFM)

Object of research of a thesis is the stress-strained state of homogeneous isotropic material at an elasto-plastic bending. The purpose of activity - mining of a universal computational method of laminas of an arbitrary plane shape behind elastic limit, and also creation mathematical and software for problem solving of an elasto-plastic plating under lateral loads of a uncanonical plane form at composite boundary conditions. Methods of researches are the theory of R-functions, the variational techniques of Ritz's, the methods of padding loads, variable parameters of rigidity, series loadings. The idealized outcomes actuate mining and substantiation of a new method for the solution of physically non-linear problems of a plate theory, mining of the effective scheme of a linearization of an equilibrium equation, obtaining of analytical expressions for parameters of rigidity permitting maximum precisely to allow at elasto-plastic calculation for a kind of the law of strengthening. The influencing on stres s-strained state of boundary conditions and geometrical features of laminas is parsed. The practical value of activity consists in creation of a complex of computer programs permitting to automize of their calculation of laminas and fast to overhaul numerical experiment at originating of necessity of the count of change geometry, edge conditions, law of strengthening, kind of loading. The intrusion and usage of an offered method, software obtained numerical outcomes for designing and analysis of parameters of actual thin-wall designs is planned. The obtained solutions can be utilised for approbation of other methods of the elasto-plastic analysis. Areas of possible application - engineering, building, aircraft manufacturing.