Meshless Algorithm Research And Its Application In Stress Analysis For Flame Tube Structure

Flame tube should not only bear the mixed gases of high temperature,and to accept the cooling air from mixing hole,therefore its uneven heating;It’s easy to have a crack,block,burning and burning through failure.This will affect the operation of the engine and reduce engine life.In order to ensure the cooling effect,a large number of gas film cooling holes are needed to be arranged on the flame tube wall.The stress analysis of the mixing hole and the hole edge of the flame tube is the basis of the creep buckling analysis and the creep fatigue life prediction.In the previous study,using the finite element method for stress analysis of the flame tube,mostly ignored the existence of holes,or only consider the larger mixing holes,this makes the calculated stress error on the side of hole is very big,affecting the crack initiation analysis and life prediction.One possible solution is to divide the fine grid in the hole,but it also leads to a large number of grids which are needed to calculate the finite element strength of the flame tube.At the same time,in order to ensure the quality of the grid,it will spend a lot of time on the grid.Therefore,it is necessary to use special analytical techniques such as meshless method.In this paper,the principle and application scope of meshless method are analyzed and made a literature review.Around the element free Glerkin method(EFG),the theoretical analysis and numerical simulation are carried out to calculate the strength of the flame tube structure using the meshless method:Firstly,by comparing the meshless method with the finite element method,the common characteristics and differences between the meshless method and the finite element method are found.Then,the wave front method is introduced into the meshless method.Research findings: 1.When the meshless method is used,the number of nonzero elements in the coefficient matrix is more than that of the finite element method,even dealing with a medium scale model,it requires a large amount of storage space and a longer computation time;2.The meshless method and the finite element method are adopted for different impact node schemes;3.As the finite element method,if all the sub stiffness matrices associated with a node are assembled into the overall stiffness matrix,the node can be eliminated in meshless method,this meets the application conditions of the wave front method.Based on these comparisons,the wave front method in finite element method is modified and applied to the element free Galerkin method.The corresponding calculation program is written,and the linear elastic problem is taken as an example.Numerical examples show that the element free Galerkin method with the wave front method compared to the general meshless method has the following two advantages: 1.It can reduce the demand of data storage;2.The number of floating point operations to calculate the linear equations of n is O(N3)when calculated by other direct method,the number is O(n)by wave front method,which greatly improves the computation speed.Secondly,this paper analyzes the advantages and disadvantages of applying the essential boundary conditions in the element free Galerkin method,and proposes an improved EFG-RPIM coupling method.It is found that the common method of applying the essential boundary condition has its own advantages,but at the same time,there are obvious shortcomings.There is not a unified solution for different problems.At present,coupling the radial point interpolation method(RPIM)and the element free Glerkin method to impose essential boundary conditions is a promising solution.The RPIM method has the disadvantages of large amount of calculation,if only using the RPIM method in the region where the boundary conditions are required to be applied,and the meshless Galerkin method in other regions,we can combine the advantages of the two methods to establish a coupled meshless method.The EFG-RPIM coupling method has been proved to be slightly lower than the element free Galerkin method but higher than the RPIM method in terms of computational accuracy and computational efficiency.Through the research,we find that the method can be improved,and it is pointed out that the EFG-RPIM coupling method has a large error in the coupling boundary.In order to improve the error at the coupling boundary,this paper presents an improved scheme of EFG-RPIM transition,which has a simple principle and is easy to program.At the same time,the numerical examples show that the new scheme has good accuracy.Third,the application of hybrid stress method in the meshless method is studied.Based on energy functional,this paper deduced the hybrid stress meshless solving equation.Based on the equilibrium equation and the potential function,the two stress shape function matrices in Descartes coordinate system and polar coordinate system are obtained.The stress analysis of the structure with holes is presented in this paper.It is found that the calculation of the stress shape function matrix for the structure with holes can make the calculation accuracy of hybrid stress meshless method higher than that of the original meshless method.Finally,based on the above three improved schemes,this paper presents a meshless method for the stress calculation of the flame tube.The object of this study is a three-dimensional aero-engine flame tube of float structure.The finite element method,the meshless method and the hybrid stress meshless are used.The linear equations are solved by the wave front method,and the essential boundary conditions are applied by the EFG-RPIM coupling method.Through the comparison of the calculated results,it is found that the hybrid stress meshless method can reduce the number of the influence nodes in the calculation of displacement shape function,and at the same time,the calculation accuracy of meshless method is not lower than the original meshless method.Aero engine flame tube has a complex structure lead to difficult to calculate,the element free Galerkin method was partly improved and applied to the strength analysis of aero-engine flame tube of float structure,the examples show that the method is effective,broaden the calculation method for the calculation of flame tube structure.