Application Research Of The High Order Finite Element Method In Analysis Of Three Dimensional Concrete Gravity Dam

In recent years,with the development of computer technology,the finite element method has developed rapidly.As a kind of very important numerical calculation method,it has been used widely in various engineering fields.The finite element method has obtained many important results for analysis and computation of many practical engineering problems related to the national economy and people's livelihood,which has made important contributions for national prosperity and the social and economic development.In the fields of engineering research,the finite element method has been used in housing construction.bridge and tunnel,aircraft manufacturing,port engineering,biology and so on,it has played a major role in these fields and has achieved significant economic benefits.Many scholars at home and abroad have done a lot of research in the design and calculation of hydraulic structures by using the traditional finite element method(h-version finite element method),and have achieved fruitful results.But as the limitation of the h-version finite element method,it can not obtaincompletely satisfactory results in solving the problems of design and calculation of hydraulic structures.In the past more than 20 years,the finite element method has made a lot ofimportant progresses in the mathematical theory and algorithm,convergence and error estimation of p and h-pversion finite element method have been rigorously proved.some domestic and foreign scholars have applied successfully two and three dimensional p-version finite element method intothe analysis of hydraulic building,and obtained some important results,but for the applications of the threedimensional h-pversion finite element method in analysis of hydraulic structures,only a few results are obtained.This paper will explore the applications of the three dimensionalh-pversion finite element method in analysis of hydraulic structures,and obtain the better numerical calculation results than the results by using h-version and p-version finite element method.Based on the mathematical theory of p-version and h-p version finite element method,this paper uses Stress Check finite element computational software developed by the ESRD(Engineering Software Research&Development,Inc)as the numerical calculation tool,analyzes numerically the model problems inthe hydraulic structures by using thehigh order finite element method.This paper chooses the threedimensional concrete gravity dam as a model of computation and analysis,studies its stress and displacement under basic load combination,and discuss detailedly how to apply the p-version and h-p versionfinite element method intodesign and calculation of hydraulic structures.We also analyzes and compares the calculation results with the results obtained by ANSYS,which is based on the h-version finite element method.Results show that the application of boththe p-version and h-p version finite element method in calculation and analysis of hydraulic structuresis effective and feasible.Compared with the h-version finite element method,the p-version and h-p version finite element method have less number of grids,higher convergence rate,higher accuracy and smaller error.The p-version and h-p version finite element method have unique advantages in the design and calculation of hydraulic structures.Finally,we obtain the following conclusions by making the static analysis of three dimensional concrete gravity dam with h-version and p-version and h-p version finite element method:1)Compared with the h-version finite element method,the high order finite element method(p-version and h-p version finite element method)can obtainthe better numerical computation results by increasing the order of interpolation functionand refining meshes simultaneously,at the same time,the results of energy norm error estimation show that the convergence rate of the h-p version finite element methodis faster.With the increasing of the order of interpolation function and refining meshes simultaneously,the convergence rate of the finite element solution increases rapidly.2)It is proved that the application of the p-version and h-p versionfinite element method in the static analysis of three dimensional concrete gravity dam is effective and feasible by the comparison and analysis of the numerical simulation results.We obtain the higher precision and less error resultsby improving the order of interpolation function and refining finite element mesh simultaneously(i.e,applying the h-p version finite element method into the static analysis of 3D concrete gravity dam)when the number of grid is far less than the number of grid of the h-version finite element method.3)In this paper,the detailed implementation process in the practical application of the high order finite element method is discussed,the results of numerical simulation show that the application of high order finite element method in hydraulic structure is promising.Further,we can also consider the application of the high order finite element method in research of the dynamic response in 3D concrete gravity dam.