Research On Local Mesh Refinement And Application Of 3D Numerical Manifold Method

Numerical manifold method(NMM)is a very powerful and accurate numerical method for geotechnical engineering.It has something in common with finite element method(FEM)and is better than it.In this study,three-dimensional numerical manifold method programming mainly uses three-dimensional hexahedral mesh for automatic sub model calculation,in which the non-refinement module uses unified cuboid mathematical mesh as a whole,the encryption module adds ladder mathematical mesh for local encryption layout,and then generates three-dimensional numerical manifold cover system,including three-dimensional mathematical cover,three-dimensional physical cover and three-dimensional numerical manifold cover Generation of popular units.The weight function,covering displacement function,constraints and loads in the three-dimensional numerical manifold method are studied,and the two-dimensional numerical manifold is pushed to three-dimensional.It is the pursuit of numerical manifold method and even mathematical analysis method to improve the calculation accuracy in geotechnical engineering analysis.Mesh refinement is one of the methods to improve the accuracy in numerical manifold method,and global refinement will seriously lead to low calculation efficiency.Therefore,it is necessary to study the local refinement of covering system grid in numerical manifold method,and put forward one to four levels of local mesh refinement of numerical manifold method.According to the actual situation to choose the mesh refinement level to calculate and analyze.Then,for the refinement scheme design algorithm,the mathematical cover,physical cover and manifold element are updated on the original designed numerical manifold cover system for numerical calculation.Finally,based on the algorithm of coverage system generation,C++ object-oriented programming technology is used to develop the program.The numerical simulation is carried out by two numerical examples of the finite rectangular plate with the central edge crack and the finite plate with the bilateral crack under the uniaxial tension.The error between the crack strength factor and the analytical solution is obtained by using the designed numerical manifold calculation program,and the contour in the direction of the model after the first to the fourth level local mathematical grid refinement is drawn by TECPLOT software.The results of the examples show that in the first level refinement to the fourth level refinement,the calculation accuracy of the fourth level refinement is the highest,and the calculation error is the smallest,which also conforms to the law that the finer the refinement,the higher the accuracy of the calculation results,so it is concluded that the local refinement scheme is effective.The research on the local refinement algorithm of numerical manifold method is improved.