A METHOD FOR CALCULATING RESIDUAL AND TRANSVERSE STRESS EFFECTS IN FLEXIBLE PIPE PRESSURE SPIRALS

摘要

The present paper addresses a method for calculating residual and transverse stress effects in flexible pipe pressure spirals. The motivation for the work is related to the fact that these effects are important to include when performing fatigue assessment of flexible pipes and the industry need for effective tools for handling such problems. The development was based on a twofold strategy using 2D curved beam theory to describe the alternating contact and out of plane stress effects, whereas a boundary element formulation was applied to calculate the in plane stress effects. For the 2D curved beam formulation, a plane strip along the pressure spiral is considered, thus including a number of bodies representing each winding of the spiral. The problem is formulated in terms of finite elements applying the Principle of Virtual Displacements. Each body interacts with the other bodies by contact elements formulated by a simple penalty formulation. The contact elements operate in the local surface coordinate system and include eccentricity, surface stiffness and friction effects. The loading model includes the following effects: 1. Contact pressure from other layers 2. Global curvature from bending 3. Internal pressure The equilibrium equations are solved by a Newton-Raphson iterative scheme and the results obtained in terms of transverse contact forces are used as a boundary condition when calculating the transverse in plane stresses. The transverse stresses are calculated using boundary element analysis based on a symmetric Galerkin approximation. Compared to the more usual collocation method, Galerkin is more accurate, and it provides a more convenient mathematicalumerical formulation of the hypersingular integration. The linear element approximation initially employed in this work is presently being replaced by a new code which uses quadratic interpolation. The most important advantage of this more advanced code is the ability to do crack propagation simulations using a highly accurate improved singular crack tip element. The above equations have been implemented into a computer code termed BOUNDARY that communicates with the already developed program modules BFLEX (Saevik et. al., 1998), for stress analysis of the tensile armour and PFLEX (Saevik, 1999), for longitudinal stress analysis of the pressure spirals. The results in terms of contributions to the stress tensors from each module are stored on a common data base for each load case, enabling fatigue analysis post processing assessing all metallic layers in a flexible pipe. The paper includes description of the theory as well as a test example of the developed computer code.