Study On Efficient Meshless Method For Mechanical Analysis Of Orthotropic Materials

As a commonly used material in engineering,boron / epoxy composite materials are widely used in many industries such as aerospace,civil engineering,engineering machinery,automobile manufacturing,large ships,etc.The direction shows different mechanical properties,so the theory of orthogonal anisotropy is often used as the basis of its numerical simulation.The orthotropic materials represented by boron / epoxy are applied to many high-precision industrial equipment,and the corresponding structural strength calculation results are related to the safe operation of the entire structure.Therefore,for orthotropic materials The study of numerical calculation methods is particularly important.Different from isotropic materials,the elastic coefficient matrix of orthogonal anisotropic materials contains more independent elastic constants,which leads to more complicated distribution of stress field and displacement field of the structure,which brings certain difficulties to numerical calculation..The higher-order meshless method can more accurately reflect the stress field,but when too many integration points are used,the calculation efficiency will be low.In this paper,the second-order uniform meshless method is applied to orthotropic materials.While the calculation accuracy is guaranteed,the calculation efficiency is higher than the general meshless method.This paper is dedicated to the research and establishment of an efficient and high-precision element-free Galerkin method for the mechanical analysis of orthotropic materials.The main work is as follows:(1)In this paper,the process of establishing the meshless normal shape function by the moving least squares approximate function is deduced in detail,and the algorithm flow of the corresponding node shape function is established;the elastic constitutive relationship of orthotropic materials is derived,The corresponding Galerkin weak form is established,and the meshless method is used for spatial dispersion,and the final discrete equation is obtained.(2)Since the shape function of the meshless method is a rational number,this leads to that the commonly used integration methods such as Gaussian integration and Hammer integration cannot accurately integrate the weak form.In this paper,QC3 integration method based on triangle background grid is established.(3)In this paper,FORTRAN language is used to compile relevant programs for the mechanical analysis of orthotropic materials,including standard Gaussian integration,linear finite element and the consistent integration method proposed in this paper.(4)In the last chapter of this paper,the meshless program written is verified by the numerical example of the fragmentation test 2.The numerical results show that the second-order uniform three-point integration method greatly reduces the number of integration points required,while still ensuring the high accuracy and high convergence of the high-order meshless method,thus significantly improving the analysis of the meshless method.The computational efficiency of cross-anisotropic materials also shows that the meshless method has broad prospects when analyzing orthotropic materials.