Eigenvalue Buckling Analysis Of Hydraulic Plane Steel Gate Based On P-version Finite Element Method

The mathematical theory foundation of the p-version finite element method has been established completely,and its error estimation and convergence have also been obtained and proved,which provides a solid foundation for the application of the p-version finite element method in engineering practice.There have been a few studies on the application of the p-version finite element method in various engineering practice fields,but few studies consider the application of the p-version finite element method for the problem of structural stability analysis.The traditional h-version finite element method is usually used for stability checking,such as eigenvalue buckling analysis,but the convergence rate of the h-version finite element method for eigenvalue buckling analysis is relatively slower.The p-version finite element method improves the computational accuracy of the numerical solution by means of ascending order spectrum,and at the same time,the exponential convergence rate is obtained.Therefore,the p-version finite element method can deal with the eigenvalue buckling problem more effectively.In this paper,the application of the p-version finite element method in the eigenvalue buckling analysis of hydraulic plane steel gate is studied.Firstly,the linear system under corresponding load and constraint conditions is solved,and then the generalized eigenvalue problem is transformed into the standard eigenvalue problem.Then,the eigenvalue problem is solved by Lanczos iteration.The p-version finite element method can obtain the higher precision stress field when solving the linear problem.Moreover,when the number of elements is fixed,the numerical solution converges rapidly with the increasing of the order p of the interpolation polynomial.The number of grids can be reduced as much as possible,which reduces the computational load for solving the subsequent eigenvalue problems.In addition,the p-version finite element method only requires coarser mesh and less preprocessing when calculating stress and strain.In practical engineering,eigenvalue buckling analysis is usually used to calculate and analyze large scale linear equations,and the coefficient matrix of the linear equations is usually larger and sparser.Lanczos iterative method can handle the calculation of sparse matrix well,and has a good application effect on large engineering structure problems.In this paper,the eigenvalue buckling analysis and calculation of thin plates,thin plates with long circular holes and stiffened plates are carried out to verify the effectiveness of p-version finite element method and the accuracy of numerical results when calculating eigenvalue buckling problems.Then,the p-version finite element method is used to conduct eigenvalue buckling analysis of hydraulic plane steel gate in actual engineering,verify the overall stability of steel gate,and study the buckling instability of steel gate under what circumstances,which provides a certain basis for the engineering design,installation,construction and operation and maintenance management in future projects.The results show that the p-version finite element method has the advantages of less preprocessing,less mesh division,higher computational accuracy and faster convergence rate in the eigenvalue buckling analysis.Moreover,the number of meshes can be greatly reduced by adapting to the surface boundary without subdividing the mesh.The numerical solution with exponential convergence rate can be obtained by increasing the order of the interpolation polynomial,which has a good research prospect and application value.