Method for Hydrodynamic Coupling of Concentric Cylindrical Shells and Beams
Dynamic analyses of pressurized water reactor vessels, core support structures, and internals require accurate representation of dynamic coupling due to fluid in annuli between concentric cylindrical shells. In practice, the structure is frequently modeled using beam elements with Fritz’s hydrodynamic mass matrix as is implemented using the FLUID38 element. In advanced reactor designs, it is desirable to have a comprehensive analysis model that includes shell modes while remaining sufficiently simple for long nonlinear transient dynamic analyses. The aim of this paper is to describe a straightforward method that can be used to represent hydrodynamic mass effects in models of concentric cylindrical vessels constructed of shell elements. In the method, shell displacement and hydrodynamic inertial forces are expressed as Fourier series. The Fourier series are entered into ANSYS using linear constraint equations that relate displacements of each shell node to displacements at supplementary sets of “Fourier nodes”. Hydrodynamic mass is then entered using STIF27 elements connecting Fourier nodes associated with corresponding nodes on inner and outer shells. The method allows the Fritz beam mode mass to be entered separately from mass matrices representative of each shell mode. The method also applies when either the inner or outer shell or both may be represented as a beam. Examples of the method are presented with a discussion of techniques for evaluating mass matrices for shell modes based on theory and experimental data. Application of the method is demonstrated for irregular meshes and variable-thickness or folded-plate structures of near cylindrical form. Examples also demonstrate that the method is enhanced by its compatibility with using superelements (MATRIX50) to represent more complex shell structures.