Three Dimensional Elastic Frictional Contact System Modeling And Optimization Of Penalty Function Method Based On The Boundary Element Method

Boundary element method is a new and efficient numerical method,which is based on the finite element.It absorbs and integrates the advantages of the finite element method,and continues to improve and innovate.Also,it has the advantages of high precision,high dimension reduction and complex simulation of boundary shape.In terms of the problem of boundary integral equation in friction contact system contains multiple basic unknown quantities(such as the unknown displacement and unknown boundary surface forces),the boundary element method can assemble system coefficient matrix better,and satisfy the contact conditions.Therefore,the boundary element method is very flexible to deal with such nonlinear problems.In this paper,the penalty function method for three dimensional elastic friction contact system was studied according to the principle of minimum potential energy based on the boundary element method.The mathematical programming model of penalty factor was established.The existence and uniqueness of the solution and the optimality conditions were discussed.Also,the influence of penalty factor selection on system solution was analyzed.This paper was organized as follows:Firstly,the research background,the present research status at home and abroad was proposed.At the same time,the source and significance of the research,as well as the main ideas and content were presented.Meanwhile,the basic theory of boundary element method and the knowledge of mathematical programming knowledge were constructed.Secondly,the penalty factor mathematical model was established from the perspective of the principle of minimum potential energy,which was based on the boundary element method.In addition,the non penetration constraint as a penalty term was added into elastic contact system,thus the complex engineering problem converted into a mathematical problem.It deeply provided a new way to solve the nonlinear problems such as frictional contact problems.Then,the boundary element method in the formation of the characteristics of large spare matrix was studied by using the optimization theory,and the final formation of the equivalent form of matrix equations was obtained.The existence and uniqueness of the solution was strictly proved and the optimality conditions were given.Finally,the GMRES(m)algorithm was used to solve the model.According to a numerical example,the change trend and the influence of the penalty factor on the system were analyzed.Meanwhile,the theoretical analysis and numerical calculation showed that the penalty factor optimization model was very effective for solving the system,which could greatly reduce the computation time and the amount of calculation.