Viscoplastic analysis of shells of revolution under axisymmetric loads

Using a general geometrically linear theory of inelastic shells by Kollmann and Mukherjee a hybrid strain finite-element model is formulated. It is then specialized for an axisymmetrically loaded conical geometry as originally used by Zienkiewicz and co-workers for elastic problems. A summary of Hart's inelastic constitutive model is then given. The following section is devoted to the strategy of the numerical solution and to time integration. The finite-element model is solved for fixed times where the rates of the displacements, strains and stresses are obtained. Using Euler's implicit time integration scheme for reasons of numerical stability the integrated quantities can be computed. However, the implicit Euler rule leads to a highly non-linear algebraic problem, which is solved by iteration using an algorithm developed by Cordts and Kollmann. Finally, a numerical example is presented. A pressure vessel is considered and the results are demonstrated. Using this example the applicability of the inelastic finite-element model on the real technical problems is demonstrated. (orig.)