THE EFFECT OF APPROXIMATING DEFORMATION CURVES ON CRITICAL LOAD VALUES OF LATERAL BENDING OF A CYLINDRICAL SHELL

Abstract

A 3D geometrically and physically nonlinear problem of elastoplastic deformation and loss of stability of a steel cylindrical shell with loose filling loaded in lateral bending is considered. The problem is formulated in a dynamic form, using Lagrange variables (a current Lagrange formulation of the problem). Deformation of the shell is described in terms of mechanics of elastic-viscoplastic media without using the hypotheses of the theory of thin-walled structures. The equation of motion is derived from the power balance of virtual work kinematic relation are defined in the metrics of the current state. Elastoplastic deformation is described using the theory of flow with isotropic hardening. The effect of the filling is modeled with an analytical function depending on spatial variables and time. Loss of stability of the shell is determined using the parameter protraction method, the parameter used being time. The problem is numerically analyzed using the moment scheme of the FEM and the cross-type explicit time integration scheme. The ends of the cylindrical shell rest on rigid supports. To reach the ultimate state, the shell, in addition to its weight and the weight of the filling, is loaded with an additional lateral force. It is shown that the analytical results do not differ considerably from the experimental data if a bilinear approximation without accounting for critical values of stresses and strains is used, as, to analyze stability of an elastoplastic shell, the tangential module of hardening of the material has to be correctly prescribed.

Keywords: cylindrical shell, filling, stability, plastic strains, finite element method.