Elasto-plastic analysis of thick cylinders subjected to internal electro-magnetic loading

A study of elasto-plastic deformation of circular cylindrical shells subjected to internal electromagnetic forces is presented in this paper. The five governing equations in terms of resultant forces and resultant moments with respect to basic displacement vector components u, v and w are used. Theoretical formulations, based on the first-order shear deformation theory (FSDT), take into consideration transverse shear deformation and rotary inertia. The deformation theory of plasticity is employed for constitutive equations. The cylinders are composed of an elastic-plastic material with the von Mises yield criteria and non-linear plastic behaviour. Galerkin method is employed to convert the partial differential equations (PDEs) to ordinary differential equations (ODEs). The Newmark family of methods is used to numerically time integration of system of coupled second order ODEs. In order to prove the validity of the presented method and the solving process, the results obtained with the present analysis are compared with a set of available data. Good agreement observed between the results of the two approaches. Certainly, the aim of this paper is to create a more reliable and precise mathematical model of hollow-cylinders to avoid performing several experiments.