tailieunhanh - Solving method for stability problem of elastoplastic cylindrical shells with compressible material subjected to complex loading processes

The system of stability equations of elasto plastic cylindrical shell made of compressible material was established in work [3] In the present paper, we study the solution of the problems and methods for determining the critical load. The obtained results describe the influence of the compressibility of material on the stability of the shell. When a material is incompressible, these results to the previous well-known ones (see [1, 2, 4, ~). | Vietnam J ourna l of Mechanics, NCST of Vol. 23, 2001, No 2 (69 - 86) SOLVING METHOD FOR STABILITY PROBLEM OF ELASTOPLASTIC CYLINDRICAL SHELLS WITH COMPRESSIBLE MATERIAL SUBJECTED TO COMPLEX LOADING PROCESSES DAO VAN D UNG Vietnam National University, Hanoi A BSTRACT. T he system of stability equations of elasto plastic cylindrical shell made of compressible material was established in work [3] . In the present paper, we study the solution of the problems and methods for determining the critical load. The obtained results describe the influence of the compressibility of material on the stability of the shell. When a material is incompressible, these results to the previous well-known ones (see [1, 2, 4, ~). . 1. Stability problem Let's consider a cylindrical shell of length L, radius R and thickness h. We choose X1 lying along the generatrix of t he shell, X2 = Rei with el - the angle of circular arc and z in the direction of the normal to the middle surface. Assume t hat a material is compressible. We consider the shell being acted upon by the external forces p 11 , p 12 , p 22 which depend arbitrarily on a loading parameter t . One of the main aims of the stability problem is to find the moment t* when the instability of structure happens and respectively the critical loads , p:j = Pii (t*). Suppose that the unloading does not happen in the structure. We use the criterion of bifurcation of equilibrium state to study the proposed problem. An analysis of the elastoplastic stability problem is always m ade in two parts: pre-buckling process and post-buckling process. 1 .1 . Pre- buckling proce ss Suppose that at any moment t there exists a membrane plane stress state in the shell ' - 9K' p(t) -dt = - or s = '(s) () U, The coefficients in () and () are of the form ai = 1 4C 3' + 4NC + 9KC' 1 3 2' + 9K , C= 1 N 4¢' !32 = {34 = 0, 3N +¢' 9K + () The relation () becomes i () ,2 N'lf; 2(aif3 4 + a3{3 2 + et5)((3if34 +