Large axisymmetrical elasto-plastic deformations of circular plates in shape forming processes (Q2759475)

Axisymmetrical problem of forming elastic shells of revolution by plastic deformation of plane circular rough workplaces under uniformly distributed normal pressure is considered. Equilibrium equations for deformed geometry and nonlinear geometrical relations are used. It is assumed that at all points of structure simple loading is realized the Kirchhoff-Love hypotheses and the deformation plasticity theory are applicable. The complete system of geometrically and physically nonlinear governing equations is written. Algorithm of numerical solution of the problem is described. Linearization of physical nonlinearity is done by the method of variable parameters of elasticity. Geometrical nonlinearity is linearized by the Newton-Kantorovich technique. A numerical example is considered, plots of stress resultants, couples and shape of deformed surface are presented.