Nonlinear dynamic analysis of piping system using the PSEUDO force method

The nonlinearities induced by piping constraints are taken into account as generalized pseudo forces on the right-hand side of the governing hydamic equilibrium equations. Then an existing linear elastic finite element piping code, IPIPE, was modified to permit application of the procedure. This option was inserted such that the analyses could be performed using either the direct integration method or via a modal superposition method, the Newmark-Beta integration procedure being employed in both methods. The modified code was proof tested against several problems taken from the literature or developed with the nonlinear dynamics code OSCIL. The problems included a simple pipe loop, cantilever beam, and lumped mass system subjected to pulsed and periodic forcing functions. The problems were selected to gage the overall accuracy of the method and to insure that it properly predicted the jump phenomena accociated with nonlinear systems. Implementation of the method was found to be straightforward with the simplest iteration procedure for the psuedo force vector sufficing. The results predicted with the method agreed in all important aspects with existing solutions as well as those generated with other methods. As with linear analyses, the modal superposition solution mode was found to be the most efficient, however, exhibiting slightly greater inaccuracies