An Iterative Method for Solving Static Piping Analysis Including Friction Between Pipes and Support

Abstract

We present an iterative method to solve static piping analysis including Coulomb friction between pipes and supports. It is known that the most stable method to find the solution of this problem is to look for the correct stiffness to add in the plane orthogonal to the direction of the restraints for the resulting forces to be of correct intensity. The naivest way to pick the stiffnesses at each step is to choose the ones that would give the correct forces intensities if the displacements were correct. It is very effective in term of precision, but sometimes slow in term of execution. The penalty comes from the fact that the stiffness matrix is different at each iteration and thus that it must be factorized again. In this article we propose a way to increase the speed of convergence: selecting a subset of supports among the ones where convergence is the worst, and introducing sub-iterations focusing only on those supports can reduce the number of main iterations. Those sub-iterations can be calculated at a much lesser cost than the main ones by using the generalized Sherman-Morrison formula. This algorithm was successfully implemented into the piping analysis software PIPESTRESS version 3.9.1 developed by DST Computer Services SA (the version number is temporary, the release date is Q3/Q4 of 2018).