Formulation and Numerical Solution of the Stability Loss Problem of Elastic-Plastic Shells of Revolution with an Elastic Filler under Combined Axisymmetric and Torsional Loadings

A dynamic statement and a method for numerically solving the buckling problems of elastoplastic shells revolution with filler in axisymmetric non-axisymmetric shapes under quasi-static loading are presented within framework two approaches. In first approach, problem elastic-plastic deformation an elastic combined torsion is formulated two-dimensional (generalized axisymmetric) formulation based on hypotheses theory Timoshenko type Winkler foundation. The constitutive relations written cylindrical system Euler coordinates. For each shell element, local Lagrangian coordinate introduced. Kinematic recorded current state metric. distribution displacement velocity components over thickness strain rate tensors basis as sum momentless moment components, which, turn, symmetric asymmetric parts general basis. properties material taken into account flow nonlinear isotropic hardening. To take forms buckling, desired functions (both displacements forces, moments, contact pressure) expanded Fourier series circumferential direction. variational equations motion derived from equation dynamics. between deformable modeled conditions non-penetration along normal free slip tangent. dynamics nonaxisymmetric processes interconnected through physical plasticity. They large shape changes instantaneous stress-strain shell. At initial stage process, deflections small; therefore, obtained linearized respect to forms. initiate modes, solve defining equations, finite-difference explicit time integration scheme “cross” used. second approach continuum mechanics implemented three-dimensional setting. Both approaches make it possible simulate subcritical filler, determine ultimate (critical) loads wide range rates, taking geometric imperfections, study complex by tension, compression, torsion, internal external pressure. results numerical simulation compared experimental data steel ( R / h = 1.45) filler.