Analysis Of Particle Reinforced Composites Based On Quadtree-hybrid Stress Element Method

Compared with traditional homogeneous materials,particle-reinforced composite materials have irreplaceable advantages,so they are widely used in aerospace,defense and military,automobile and ship fields.However,the addition of the reinforcing phase will inevitably bring some negative effects while improving the mechanical properties,such as reducing the fracture and fatigue properties of the material.These negative effects are often related to the shape,size and distribution of the microstructure of the inclusions.Taking into account the complexity and randomness of the microstructure of inclusions,the macroscopic equivalent performance is an important indicator for evaluating the performance of particle-reinforced composites.Based on the hybrid stress element method,combined with quadtree mesh and polygon-quadtree mesh,a new numerical calculation model is proposed in this paper.Its advantages are: The hybrid stress element overcomes the difficulty in constructing the displacement shape function of the irregular polygon element,and the assumed high-order stress field can obtain higher accuracy with a sparse grid;There are only 6 types of the basic elements of the quadtree grid,and the relevant calculation parameters of these basic elements can be calculated in advance.In the actual calculation,it is only necessary to read and call directly according to the element type,which greatly improves the calculation efficiency.This method is used to analyze the influence of inclusion parameters on the macroscopic equivalent modulus of the material.The specific work mainly includes:(1)The FORTRAN program for quadtree meshing is written.It can generate pure quadtree mesh model and polygon-quadtree hybrid mesh model of particle-reinforced composite material with random inclusions.(2)On the basis of the existing calculation program,the calculation program of hybrid stress element based on quadtree mesh is modified and completed.The stiffness matrix,H matrix and G matrix of the basic element are pre-calculated.In actual calculation,it is directly called according to the element type,which saves the calculation time of the element stiffness matrix of all quadtree elements.And compared with the finite element software MARC to verify the effectiveness and efficiency.(3)The influence of the number of element nodes,the degree of mesh refinement and whether polygon elements are used on the calculation accuracy is analyzed.(4)Considering the randomness of the microstructure,the homogenization method and the Monte Carlo method are used to analyze the influence of the volume ratio,number,and aspect ratio of the inclusions on the equivalent elastic modulus of the particle-reinforced composite material.