ANALYSIS OF THE CONSERVATIVE SMOOTHING EFFECT ON THE ACCURACY OF DYNAMIC ELASTIC-PLASTIC SPHERICAL SHELLS BUCKLING NUMERICAL SIMULATION

Large changes of a lead spherical shell enclosed in an aluminum spacesuit under the action of an overload pulse are considered. The defining system of equations is formulated in Lagrange variables in a two-dimensional (axisymmetric) formulation. Strain and stress rates are determined in the local coordinate system. Kinematic relations are recorded in the metric of the current state. The relations of the flow theory with isotropic hardening are used as state equations. The contact interaction of the shell and the spacesuit is modeled by non-penetration conditions taking into account friction. The numerical solution of the problem under given boundary and initial conditions is based on the finite element method moment scheme and the explicit time integration “cross” type scheme. 4-node isoparametric finite elements with bilinear form functions are used to discretize the defining system of equations for spatial variables. To suppress the numerical solution high-frequency oscillations, the procedure of nodal displacements rates conservative smoothing is used. As shown by the results of numerical research spherical shell in the process of intensive dynamic loading undergoes large deformation and rotation angles as a rigid whole. The calculation results reliability is confirmed by a good correspondence to the experimental data. The influence of conservative smoothing procedure and moment components of deformations and stresses on the solution accuracy is analyzed. It is shown that without conservative smoothing procedure using, the shape of the spherical shell buckling obtained in the calculation does not correspond to the experimental data. Neglect of the moment components of strains and stresses leads to the development of instability of the “hourglass” type.