In this paper the other performance of this method is presented. and the convergence of the method is proven theoretically in .the general case of a harderung body which obeys the elastoplastic process theory. The more complicated 3D problem of bodies of revolution subjected to non-axially symmetric load is investigated. | . Vietnam Journal of Mechanics, NOST of Vietnam Vol. 22, , No 3 (133 - 148) MODIFIED ELASTIC SOLUTION METHOD IN SOLVING ELASTOPLASTIC PROBLEMS OF STRUCTURE COMPONENTS SUBJECTED TO COMPLEX LOADING DAO HUY BICH Vietnam National University, Hanoi SUMMARY. Modified elastic solution method in the elastoplastic process theory has been proposed by the author [2] and was applied in solving some 2D and 3D elastoplastic problems of structure compo~ents subjected to complex loading. The method makes use of an algorithm in which a step is made in the loading process and iterations are carried out on this step. The performance of the method was fulfilled and the convergence of the method was considered numerically. In this paper the other performance of this method is presented. and the convergence of the method is proven theoretically in .t he general case of a harderung body which obeys the elastoplastic process theory. The more complicated 3D problem of bodies of revolution subjected to non-axially symmetric load is investigated. 1. Boundary value problem of the elastoplas~ic process theory and modified elastic solution method The formulation of the boundary value problem of the elastoplastic process theory and analysis of the existence and uniqueness theorems have been carried out in [3, 4]. Let Ki(x, t) and Fi(x, t) be external volume and surface .forces that act on the body and let 'Pi(x, t) be displacement on the body's surface. It is necessary to find displacements ui(x,t), strain tensor C"ij(x,t) and stress tensor O'ij (x,t) , where t - the loading parameter, that satisfy the following equations 00' " iJ aXj C"i . 1 = + pKi = 1, ! (Bui + Buj) ' Bxi Bxi . 2 . skeeke Sii =~ Aeij+(P-A) Sii' 3 au2 a= 3K e. =KO, x E 0, () E 0, () xEO , () x E 0, () X 2 133 and the boundary conditions u tJ· ·nJ· -- .L'i, .,;., 0 -:- 0 US, Su U Su = ()' () S, Sun Su. = 0, t E [O, Tj, where A= Uu. s + ( 3 G- Uu.)·(1-cos0 1 )ar, . s .
