Study On Contact Algorithms For Polygonal Hybrid Stress Element Method

In the case of small element,it is difficult to obtain accurate stress field and stress concentration by existing non-uniform models.An optimization algorithm for the theory of PHSEM(Polygonal Hybrid Stress Element Method)is proposed by using direct restriction method.The advantages of PHSEM in the construction of stress function and the division of integral region make it more suitable for complex model boundary and material boundary and easier to divide grids.The complete code is accomplished according to the above achievement.The results show that the method can obtain the macroscopic nonlinear mechanical response,accurate stress field and obvious stress concentration phenomenon in powder compaction process,which provides useful means for solving the complex optimization problem.The main work of this paper is as follows.1.The development of contact problem calculation at home and abroad is analyzed.The contact theory,such as traditional Lagrange multiplier method,penalty function method and improved method,is introduced in detail.The shortcomings in calculation efficiency,accuracy and contact simulation effect are pointed out.2.Based on the modified complementary energy function of hybrid stress element proposed by Pian T.H.H,and assuming that the stress field and displacement field satisfy the equilibrium condition.The PHSEM(Polygonal Hybrid Stress Element Method)is developed.The displacement interpolation is only processed on the boundary of the element to achieve the compatibility and continuity of the displacement boundary conditions,so that the increase of the number of edges of the element will not make the construction of the interpolation function more difficult,and can adapt to the complex material and model boundary and freely divide the mesh.The element is applied to Contact analysis field.3.According to the characteristics of polygonal hybrid stress element and a series of contact criteria in complex contact process,a complete set of contact analysis algorithm is established,and a calculation program is compiled accordingly.The problems and difficulties encountered in the process of programming and execution are discussed,and the corresponding solutions are summarized and implemented.4.An efficient discontinuous contact analysis model based on polygonal hybrid stress element is established.In view of the number of elements,nodes,calculation efficiency,calculation accuracy,stress distribution and the capture of stress concentration phenomenon,the results of PHSEM and FEM are compared and analyzed.The results show that they are in accordance with the objective law,and the results obtained by PHSEM are effective and correct.The accuracy of contact analysis and the efficiency of contact search of the PHSEM are qualitatively analyzed.It is proved that PHSEM has the advantages of flexible mesh generation and can use fewer elements to obtain higher-order stress fields and stress concentration phenomena.5.The process of powder compaction is simulated and the polygon hybrid stress element programming model is applied.It greatly reduces the number of cells and nodes,improves the computational efficiency,and can be verified and adjusted in the calculation process.