A numerical model to analyse the impact between piping and gapped restraints

Problems involving gapped restraints or more generally unilateral restraints are found in many situations. In the nuclear engineering for example, gapped restraints are utilized in pipelines specially those called high energy pipelines, as a mean to protect against postulated ruptures and consequently from the pipe-whip phenomenon. Also inside heat exchangers, tubes transversally cross support plates which have small holes with nominal diameters a little bigger than those of the tubes. The impact of a beam against a rigid support has been previously analysed by Galeao, Guerreiro and Loula (1984) in a related paper. The algorithm proposed there combines the Newmark's method with an impact model which simulates the impulsive force as a rectangular pulse. It was shown there that no numerical instability occurs as it is the case when one try to simulate the rigid gapped support as a spring with high stiffness. In the present work an iterative scheme will be used in order to generalize that algorithm to allow for the consideration of many gapped restraints. Instead of using the whole matrix of the system this iterative scheme deals with a reduced matrix of the order of the number of unilateral restraints, reducing considerably computation time. (orig./GL)