Discretization and time integration techniques for transient nonlinear dynamics of fast reactor subassemblies

The model theory discussed in this paper considers how properties like time-varying mass distribution and a hexagonal cross section flattening together with the strongly stiffening pin-bundle, and energy dispersion and dissipation due to axial fluid expulsion and growth of plastic zones as well as distributed pressure forces and inertia terms affect the elastoplastic bending of a single subassembly, which is treated as a Timoshenko beam. The discretization distinguishes two modes of motion: flattening (crushing) and bending. The amplification factor between them is determined as a byproduct of the iterations necessary to assure force consistency and displacement compatibility. For simplicity it assumed that plastic zones behave like a membrane during bending of the beam. These kinematics are applied to three different spatial discretizations treating either the nodes or the intervals defined along the beam axis as objects for the equations of bending motion: i) micro-rigid lumped masses (MRLM); (ii) finite elements with lumped masses (FELM); (iii) finite elements with consistent masses (FECM). The cross-section flattening is geometrically and physically non-linear. It causes the moments of inertia of the symmetric beam section and the fluid masses contained within the intervals (elements) to decay with time. The combination of these effects make the discrete models highly nonlinear and dissipative. The accuracy, efficiency and stability of appropriate time-integrators (Newmark β, Houbolt, Taylor-series) is remarkably influenced by typical model properties like the size of mesh, element and system or the type and order of shape functions or stress resultant interpolation. The Courant number helps to demonstrate the interrelationship between space and time discretization