Research On Implicit Contact Nonlinear Algorithm And Design Of Finite Element Program

With the rapid development of electronic computer and finite element technology,CAE software plays an important role in the manufacturing indusustry by virtue of its high efficiency and low cost.The linear problem in the CAE software has been well solved,but the analysis of the contact problem,which is a highly nonlinear behavior,is still relatively complicated.Factors such as the unknownness of the contact pair,the change of the contact state with the change of the external load,and the frictional contact involving large deformations all cause strong nonlinear behavior in the solution process.For the implicit static contact problem,the correct solution of the contact stiffness and the method of an efficient contact search algorithm are the core points of solving the contact problem.In the nonlinear iteration process,the stable transmission of the contact force between the contact suface is always guaranteed,which is also the correct solution to the contact problem.It is also one of the most challenging tasks in the autonomous controllable CAE software.This paper mainly builds and develops the contact framework based on the implicit statics solver framework of the research group,and forms a set of contact finite element program based on Object-oriented programming technology for solving contact problems.The specific work content is as follows:(1)Based on the mechanical expression of nonlinear continuum mechanics,the basic theory of contact nonlinearity is introduced in detail,the finite element solution format of the node-to-surface contact model is deduced,and the expressions of contact stiffness and contact force vector are given explicitly,and developed a solid shell element based on the midplane nodes,combined with the basic theory of rigid body kinematics,the contact between shell elements and the coupling analysis of shell and solid are realized.Finally,the correctness of the algorithm is verified by the example of square beam torsion,ball pressing square,contact between rigid ball and shell and Taylor bar contact.(2)Based on the face-to-face contact discretization,combined with the contact stiness expression in the form of velocity and the tetrahedral element format,a three-dimensional contact domain system equation based on the nodal integral additional stable term is deduced,and a method based on tetrahedral element s to deal with the unstable term caused by nodal intergra tion of the contact domain is proposed,the time instability based on the nodal integral in the three-dimensional contact problem is successfully solved.The results show that the introduction of the sta ble term is helpful The ideal tangent stiffness matrix and internal force vector terms are obtained for the contact system,which successfully guarantees the stability of load transfer between the master and slave surfaces,and reduces the sensitivity to g rid deformation.Four classic examples of the classic Hertzian contact,the cube pressure angle model,the ironing model,and the quarter sphere model have proved the stability and correctness of the algorithm.(3)Based on the basic classes of implicit sta tics,a program framework for solving contact nonlinear analysis is develop ed,a number of abstract contact classes are created,and the design principles and basic classes of the contact program are introduced in detail.The algorithm and class classification module are defined as abstract classes,complete keyword input files are specified,and the run-time polymorphism mechanism is realized,which ensures the scalability and flexibility of the program.Finally,the contact program is used to simulate and analyze practical engineering problems.It can be seen from the calculation results that its solution accuracy and calculation efficiency are excellent.The extensibility and ease of use of the contact program in dealing with contact nonlinear studies lay s the foundation for subsequent functional expansion.