Splitting the pipeline model
The rather complex pipeline model, built from circular cylinder shells and toroid shells into a spatial structure, is made accessible for calculation through splitting of the 3D model into two independent models, being:
•a "beam" model, consisting of the pipeline axis with the stiffness properties of the pipe cross-section. At the location of the bends (toroids) the reduction of the bending stiffness of the cross-section, as a result of ovalisation, is taken into account. The counteracting effect of the internal pressure on this stiffness reduction is considered as well. The beam model is loaded by the internal or external overpressure, temperature variations that mainly cause longitudinal deformations, with or without deadweight of the pipeline (and its contents) and soil deformations that mainly cause lateral deformations of the pipeline. Wave and current loads at offshore pipelines may be present as well. Point load patterns may act in overall directions or they may be attached to the local pipeline orientation. At bends longitudinal deformations are transformed into lateral deformations and vice versa. Determination of displacement behaviour and internal forces in the pipeline is done by means of a finite element based method of calculation in which the pipe and soil properties are treated in an integrated way. From the internal forces in the pipeline, stresses in the pipe cross-sections are calculated. At the bends the influence of the ovalisation of the cross-section on the stress distribution over the circumference is considered. This ovalisation causes higher order pipe bending stresses that are known as stress intensification. The counteracting effect of the internal pressure is introduced in the calculation method. Optionally the limited bend angle stiffness and related stressing can be taken into account. The pipeline material can be specified as isotropic, even elasto-plastic, mainly for ductile materials or as anisotropic mainly for brittle composite materials, like glass fibre reinforced plastic pipes. Geometric non-linearity (large displacements or "stress stiffening") may be accounted for optionally too.
•a "ring" model, consisting of the pipe cross-section with the stiffness properties of the pipe wall. The "rerounding" effect of the internal pressure on the deformation behaviour of the cross-section is taken into account. The ring model primarily is loaded by the internal pressure. On the cross-section the local soil reaction, resulting from the displacement of the cross-section as a whole, causes deformation of the cross-section. In a similar way the overburden weight and temporary top loads cause deformation of the cross-section. Calculation of the stresses over the circumference of the cross-section is done by means of a differential equation that is solved through Fourier-series. Calculation of stresses in the pipe material is carried out in 48 points equidistantly distributed over the cross-section circumference at the inner as well at the outer wall face. In case of elasto-plastic material behaviour the mid wall point is included. Successive ring ovalisations may be "redistributed" to account for the longitudinal integration.
PipelineModel, last changed: 2/5/2020