Study On Static Numerical Analysis Of Nonlinear Composite Pipelines In Place

There is significant numerical difference between the tensile modulus and thebending modulus in the cross-section of some special material nonlinear structuressuch as flexible pipes, umbilicals, and they are also strong nonlinear when thesestructures are under large deformations. Here a term “special material nonlinearity” ispresented for this. The purpose of this paper is to analyze the influence of the specialmaterial nonlinearity on the static spatial configuration of flexible pipelines.It is adopted that the inextensibility for the axial deformation is imposed onpotential energy functionals through the Lagrangian constraint condition, and then thetwo-node3D beam element has14dof. A proper generalized displacementinterpolation function is ditermined, and generalized element stress and strain arecreated, so geometric relationship matrix and constitutive relation matrix are deduced.Element incremental equilibrium equation and tangent stiffness matrix are formulated,and a static FEA numerical model is created. Transition matrix of element nodaldisplacements from the local element base frame to the global coordinate system isdeduced for excluding rigid displacement accurately from deformation. The methodsto calculate follower forces, non-following forces, and the internal force of elementsare presented. Based on these, a matlab program is developed and verified by twonumerical examples, and the reliability of the program on the calculation of staticconfiguration is demonstrated. Results are presented for the characterisitics of thespecial material nonlinearity on the static spatial configuration of such strucures:(1) If the tensile modulus has nonlinear changes with axial strain, there is nosignificant change on the overall shape but local form. Its effect on the configurationbecomes weaker with current velocity increasing.(2) If the bending modulus has nonlinear changes with curvature, there are somechanges on the overall shape and local form. Its effect on the configuration becomesstronger with current velocity increasing.(3) There are some changes on the overall shape and local form when the ratiobetween the tensile modulus and the bending modulus changes.