An Application Of Symplectic Method In The Local Buckling Of Submarine Pipelines

With the rapid development of China's offshore oil and gas industry,submarine pipeline transportation engineering has entered an important period of vigorous development.As an important part of the process of exploitation and transportation of offshore oil and gas resources,subsea pipeline has become a major demand of our country to ensure its safe operation.Because of the complex marine environment and the high temperature and high pressure characteristics of the material transported in the pipeline,the load on the local pipeline section is not uniform.When the non-uniform load exceeds a certain critical value,the local buckling deformation of submarine pipelines will occur,and eventually lead to pipeline failure,resulting in huge economic losses and environmental pollution.Aiming at the buckling failure of submarine pipelines under local axial compression,the symplectic method under Hamiltonian system is used to analyze and simulate the pre-buckling and post-buckling problems.The main research contents include:(1)The theoretical analysis model of local buckling of long cylindrical shells is established.The model takes the elastic cylindrical shell as the research object,and the local axial compression is the main load mode.The main purpose of the model is to analyze the critical load of the pre-buckling of the shell.By introducing a set of primitive and dual variables,and according to the variational principle,the Hamiltonian canonical equations and their corresponding boundary conditions and compatibility conditions are established,so that the basic problems are equivalently oriented from the Lagrangian system to the Hamiltonian system.In Hamiltonian system,the forward buckling problem can be reduced to symplectic eigenvalues and symplectic eigenvalues.According to the bifurcation conditions and algebraic equations,the critical load and the corresponding buckling modes can be determined,and the variation law of the critical load and buckling modes with the key factors such as the length of the loading area,the thickness and radius of the shell can be obtained.The results show that the zero eigenvalue problem expresses the axisymmetric buckling mode,and the non-zero eigenvalue problem gives the non-axisymmetric buckling mode.In addition,local loads can cause "bamboo" buckling modes(n(28)0),bending buckling modes(n(28)1)and crushing buckling modes(n(28)2)of infinite cylindrical shells.The research methods and results can provide a basis for the analysis of buckling failure of submarine pipelines.(2)The generalized Hamiltonian system for the nonlinear post-buckling problem of pipelines is established,and the governing equations of the post-buckling problem expressed by the original variables and their dual variables are obtained.Therefore,the system is closely related to the Hamiltonian system of the forward buckling problem.By using the symplectic eigenvalues and symplectic eigenvalues of Hamiltonian systems,the continuity conditions caused by local loads are transformed into the problems of non-homogeneous generalized Hamiltonian systems.With the help of eigensolutions,symplectic conjugate orthogonal normalization,symplectic eigensolution expansion and quasi-linearization methods in Hamiltonian system,the problem of solving post-buckling problem can be reduced to the problem of solving linear ordinary coefficient differential equations,and the analytic expression of the problem can be obtained by recursive relations.Then a semi-analytical method and a numerical method for post-buckling problems are proposed.This method is used to analyze the post-buckling behavior and development process of pipelines,including the role and transformation of axisymmetric and non-axisymmetric buckling modes in the post-buckling development process.At the same time,the buckling modes and evolution process which play a dominant role in the process of buckling expansion are given.The results show that the evolution modes of bending buckling and crushing buckling of submarine pipelines under local axial loads are very important to the failure of submarine pipelines.In this paper,the symplectic method is used to combine the local pre-buckling and postbuckling of submarine pipelines,and a set of effective analytical and numerical methods for studying the buckling failure of submarine pipelines are presented.