An implicit three-dimensional finite-element formulation for long-duration structural analysis of piping systems

This paper describes an implicit three-dimensional finite-element formulation for the structural analysis of reactor piping systems. The numerical algorithm considers hoop, flexural, axial, and torsion modes of the piping structures. It is unconditionally stable and can be used for calculation of piping response under static or long duration dynamic loads. The method uses a predictor-corrector, successive iterative scheme which satisfies the equilibrium equations. A set of stiffness equations representing the discretized equations of motion are derived to predict the displacement increments. The calculated displacement increments are then used to correct the element nodal forces. The algorithm is fairly general, and is capable of treating large displacements and elastic-plastic materials with thermal and strain-rate effects. The implicit-time integration scheme described herein has been incorporated into the three-dimensional piping code SHAPS. Two sample problems are presented to illustrate the analysis. The first problem deals with a dynamic analysis of a pipe-elbow loop. The second problem studies the piping response to seismic excitation. The results are discussed in detail.