Post-buckling Characteristics Of The Uspended Tubular Strings In Vertical Wells With Finite Element Method

The post-buckling behavior of the suspended tubular strings in wellbore is complicated due to the constraints of transverse deformation,which is of great significance to the post-buckling study of tubular string.In this paper,the assumption of buckling deflection curve of tubing in conventional theoretical method is discarded.The tubular strings are discretized beam elements.We establish a geometric and contact double nonlinear finite element model of suspended tubular string in vertical wells.In order to solve the problems of convergence difficulty and algorithm instability during static buckling analysis,the dynamic relaxation method for static buckling analysis of suspended tubular string in the wellbore is proposed.In the calculation of the sinusoidal buckling of suspended tubular strings is transforming to helical buckling,it is found that with the increase of axial compression load,the lateral buckling of the suspended strings suddenly becomes spiral shape with two contact points.The dimensionless critical load of the sinusoidal buckling to the helical buckling transition is 4.41 without the tensile section.With the tensile section,the dimensionless critical load decreases to 3.81.To measure the pitch of helical buckling,we introduce two methods.The first method is to use the spiral angle between the bottom and top contact points to measure the pitch,and the second method is to use the spiral angle of the continuous contact section to measure the pitch.The dimensionless critical loads of the two methods are 7.52 and 8.34 when the two ends are hinged,and 8.30 and 8.98 when the two ends are fixed without the tensile section.With the tensile section,the critical load decreases with the increase of length and tends to be stable.The quasi-static method is used to numerical simulation of the whole buckling transition process during unloading and loading of the compression load.We find that the tubular deformation evolves from continue-line contact to bottom-top-point,continuous-point,spatial two-point,spatial one-point,planar one-point contact,and finally back to vertical configuration during unloading.This deformation sequence is reversed during loading.During the transition from planar one-point contact to spatial two-point contact deformation,the buckling shape and related physical quantities change abruptly.During unloading and loading,the dimensionless critical loads of the first three buckling deformations are basically the same.For the buckling deformations with spatial two-point and planar one-point contact,and for spatial one-point contact deformation,the critical loads of loading are about 5% and 50% larger than that of unloading,respectively.For the spatial one-point contact deformation with dimensionless length greater than 40 and other buckling deformations with dimensionless length greater than 20,the critical loads obtained in the buckling process remain almost unchanged.This paper calculates the post-buckling characteristics of suspended tubular strings,including various post-buckling configurations and critical loads,as well as mechanical parameters such as shear,bending moment and contact force,which can provide a scientific basis for the analysis of post-buckling deformation and stress state of suspended tubular strings.