Error Accuracy Analysis And Optimization Of The Voronoi Element Finite Element Method With Inclusions

Particle reinforced composite is a new type of composite material.The common reinforcement methods of our composite materials are: fiber reinforced and particle reinforced.Particle reinforced composite materials are used to improve the mechanical properties of composite materials,improve the fracture,wear resistance,hardness and other properties.High hardness,corrosion-resistant and friction resistant particle materials are added to the materials.Compared with traditional materials,their material strength is better Because of its superior mechanical properties,it is widely used in many important fields such as architecture,national defense and military.As an effective numerical simulation analysis method,the finite element method is widely used in many disciplines and practical engineering problems because of its high accuracy and flexibility.However,in the practical engineering application,there must be some errors between the numerical solution and the analytical solution of the actual model when using the finite element method to establish the numerical model for analysis,including the possible errors between the theoretical model and the calculation model,the errors generated when using the numerical method to approximate the simulation,the errors caused by the unreasonable mesh division,and the elements and clamps under different models How to improve the accuracy and reduce the error of numerical simulation results is the problem discussed in this paper.In this paper,through the establishment of the numerical analysis model of the particle reinforced composite,the numerical simulation of the particle reinforced composite is carried out,and the Voronoi element method and the general finite element method Marc software are used for comparative analysis,so as to obtain the influence of the Voronoi element method of the particle reinforced composite on the overall stress field under different conditions.For the same calculation model,the common finite element method needs to divide thousands of elements,which needs to be meshed many times to reflect the internal situation of the microstructure,which will bring a lot of computation and workload,while the Voronoi element method only needs a few elements for meshing to reflect the internal situation of the material,and Voronoi mesh can not only reflect the internal situation of the material Each inclusionis a Voronoi element,which fully embodies the advantages of the Voronoi hybrid element method in numerical simulation and analysis of composite materials,such as fewer elements and high precision.A relatively complex problem can be simulated with fewer nodes.Using Voronoi hybrid element method to establish different numerical calculation models,analyze and discuss the factors that affect the accuracy of numerical simulation results in different situations.By using common finite element method and Voronoi element method to carry out numerical simulation analysis on different examples,it can be concluded that for the stress nephogram on the designated path of the same numerical calculation model,Voronoi element method and common finite element method are used to obtain the stress The variation range of stress values in the stress nephogram is basically the same,which proves that the numerical simulation results of Voronoi hybrid element method have better accuracy and effectiveness.In this paper,the error accuracy analysis and optimization of numerical simulation results of Voronoi element with inclusions are studied.1.The first mock exam of three different element types is compared by using VCFEM method and general finite element MARC method.The numerical results of the same model in different stress components on the specified path are basically the same.The stress field of the whole stress field is basically consistent with the stress direction.It proves that the Voronoi element finite element method is used to analyze the multilateral Voronoi without inclusions.Shape element,Voronoi element with inclusions and mixed Voronoi element have good reliability and effectiveness.2.Based on the basic theory of Voronoi element finite element method,this paper analyzes and discusses the shape,size and quantity of inclusions,the random distribution of inclusion space,the offset distance between the edge of inclusions and the center line,the angle between the element boundary and the vertical center line,the staggered distance of inclusions between elements,and the difference of element grid division.The FORTRAN calculation program has been compiled by Voronoi element method In this paper,the numerical simulation results of the whole stress field of the particle reinforced composite under different conditions are discussed,and the influencing factors of the error accuracy of the numerical simulation results of the Voronoi element with inclusions are analyzed.3.By constructing the G interpolation matrix of the higher order interpolationfunction the first mock exam is written to compiling the Voronoi matrix finite element method,and the Fortran program and the number of unit edge nodes are optimized.The different Voronoi element calculation models are established.The results of the numerical simulation before and after optimization of the same path in different directions of the same model are compared and the Voronoi and the optimization of each example are given.The results show that the more the number of nodes on the edge of the element,the larger the long axis and the short axis of the inclusion,and the closer the edge of the inclusion is to the boundary of the element,the more obvious the optimization effect of the numerical simulation results is.It is verified that the increase of the number of nodes on the edge of the element and the improvement of the Voronoi element method numerical simulation results by the FORTRAN program The error accuracy of the fruit has certain feasibility and validity.