Application Of Homotopy Analysis Method In Structural Analysis Of Submarine Pipelines

There are many problems to be solved in the structure analysis of submarine pipeline,such as the buckling problem of corroded submarine pipeline,the vibration problem of submarine pipeline conveying fluid system and the vibration problem of spanning submarine pipeline.The solution of the above problems is of great significance to the stable and safe operation of submarine pipelines.Homotopy analysis method is a kind of approximate analytic method which has been widely used and has excellent effect in many fields,such as fluid mechanics and heat transfer.In this thesis,the homotopy analysis method is applied to the analysis of submarine pipeline structure,and the validity and accuracy of the homotopy analysis method in the structure analysis of submarine pipeline are illustrated by solving the problems of corrosion of submarine pipeline buckling,vibration of submarine pipeline conveying fluid system and vibration of spanning submarine pipeline in the structure analysis of submarine pipeline,which reveals its application prospect and has certain theoretical research significance.In this thesis,the above three problems are discussed in depth,which has some practical value in engineering.In this thesis,the buckling pressure and buckling mode of submarine pipeline with complex corrosion shape are solved by homotopy analysis method,and the results are in good agreement with the results of finite element method,which shows the validity and accuracy of homotopy analysis method in solving this problem.Tthe buckling pressure of corroded submarine pipeline under different working conditions is solved by using homotopy analysis method,and the parametric analysis shows that the critical buckling pressure of corroded submarine pipeline decreases with the increase of corrosion depth and corrosion width.The influence of corrosion depth on the critical buckling pressure of pipeline is greater than that of corrosion width.Under the same circumstances,the buckling pressure of parabolic corrosion pipeline is greater than that of elliptical corrosive pipeline.Based on the critical buckling pressure data,this thesis presents a calculation method of critical buckling pressure of submarine pipelines with different corrosive shapes based on neural network,in order to facilitate the application of engineering practice.In this thesis,the vibration problem of the basic submarine pipeline conveying fluid system is solved by homotopy analysis method,and the results are compared with the existing literatures to illustrate the validity and accuracy of the homotopy analysis method to solve this problem.The vibration frequency of basic submarine pipeline conveying fluid system under different working conditions is obtained by using homotopy analysis method,and the critical velocity of submarine pipeline conveying fluid under different boundary conditions is obtained based on frequency.The cantilever submarine pipeline conveying fluid system is discussed,and the following conclusions are obtained: The critical velocity increases with the increase of the fluid mass ratio.The critical fluid mass ratio increases with the increase of the velocity on the whole,but decreases under some small range velocity.The vibration problem of the submarine pipeline conveying fluid system under thermal load is solved by using homotopy analysis method,and the critical velocity of the heat load pipeline system under different temperature difference is obtained,and it is found that the critical velocity of the submarine pipeline conveying fluid system under thermal load decreases with the increase of temperature difference.In this thesis,the relationship between homotopy analysis method and variational iteration method is illustrated by an example based on the basic submarine pipeline conveying fluid system,and an identity about polynomial function integral is found.In this thesis,the control differential equation of spanning submarine pipeline is deduced based on Euler-Bernoulli beam theory,and the vibration frequency of pipeline is obtained by using homotopy analysis method to solve the control differential equation.Comparing the results with the existing literature,it is found that it is effective and accurate to solve the problem by using homotopy analysis method.The vibration frequency of spanning submarine pipeline under different working conditions is calculated by homotopy analysis method,and it is found that the inclined angle of pipeline has little effect on the frequency of spanning submarine pipeline when the spanning length is small.When the spanning length is large,the inclined angle of pipeline has a great influence on the frequency of the spanning submarine pipeline.The frequency of each order of the pipeline increases with the increase of the inclined angle and the depth of the pipeline,and decreases with the increase of the internal pressure and spanning length of the pipeline.Among the four influencing factors,the pipe length has the greatest influence on the frequency of the pipeline,the pipe depth and the pipe internal pressure have the same influence,and the inclined angle has the least influence frequency.