tailieunhanh - On the elastoplastic stability problem of the thin round cylindrical shells subjected to complex loading processes with the various kinematic boundary conditions

In this paper, the elastoplastic stability of cylindrical shells simultaneously subjected to compression force along the generatrix and external pressure has been presented. Two types of considered kinematic boundary conditions are simply supported and clamped at the butt-ends. The expressions for determining the critical forces by using the Bubnov-Galerkin method [3] have been established. The sufficient condition of extremum for a long cylindrical shell also is considered. Some results of numerical calculation have been also given and discussed. | Vietnam Journal of Mechanics, VAST, Vol. 26, 2004, No. 1 (11 - 22) ON THE ELASTOPLASTIC STABILITY PROBLEM OF THE THIN ROUND CYLINDRICAL SHELLS SUBJECTED TO COMPLEX LOADING PROCESSES WITH THE VARIOUS KINEMATIC BOUNDARY CONDITIONS D AO VAN D UNG Hanoi National University ABSTRACT . In this paper, the elastoplastic stability of cylindrical shells simultaneously subjected to compression force along the generatrix and external pressure has been presented. Two types of considered kinematic boundary conditions are simply supported and clamped at the butt-ends. The expressions for determining the critical forces by using the Bubnov-Galerkin method [3] have been established. The sufficient condition of extremum for a long cylindrical shell also is considered. Some results of numerical calculation have been also given and discussed. 1 Stability problem Let's consider a thin round cylindrical shell of length L, radius R and thickness h. We choose a orthogonal coordinate system Ox 1 x2x3 so that the axis Ox1 belonging to t he . middle surface and lying along the generatrix of the shell, x2 = R(h with 81-the angle of circular arc and X3 in the direction of the normal to the middle surface. Assume t hat a material of shell is incompressible and shell is subjected to the compression force p(t) along the generatrix and external pressure q1(t) which depend arbitrarily on a loading parameter t. One of t he main aims of the stability problem is to find t he moment t* when the instability of the structure happens and respectively the critical loads p* = p(t *), qi = q1 (t*). Suppose t hat the unloading does not happen in the structure. We use t he criterion of bifurcation of equilibrium state to investigate the proposed problem. An investigation of the elastoplastic stability problem is always made two parts: prebuckling process and post-buckling process . Pre-buckling process Suppose t hat at any moment t there exists a membrane plane stress state in the .