High Accuracy And Efficient Adaptive Analysis Based On Meshfree Point Interpolation Method

Numerical computation has been widely applied for scientific research and solving practical engineering problems in many fields,such as mechanical engineering,civil engineering,material,shipping,aerospace,hydraulic engineering and so on.Modern numerical computation is developing on high efficiency,high precision,low cost and high-powered.Traditional numerical techniques are not able to meet the requirements.Engineers always expect to obtain the ultimate goal for as high as possible calculation precision with the least amount of computational cost.A large number of research results show that the adaptive analysis is an effective way to improve the efficiency and precision of the numerical calculation.An adaptive numerical method is based on some intermediate results to automatically control the process of solving a partial differential equation.Finite element method(FEM)adaptive analysis has been developed for many years.Compare with the FEM,the new developed meshfree smoothed point interpolation method(S-PIM)has shown its advantages in numerical simulation,Therefore,adaptive analysis based on the S-PIM is a good topic worthy in-depth investigation.This thesis focus on constructing the adaptive analysis model based on the S-PIM with unstructured mesh,which includes taking full advantage of the triangle and tetrahedron's ability of discreting any complex model,successfully overcoming low precision problem of these types of elements,and providing a simple and effective error estimator based on the difference value of nodal fundamental physical variables.The error estimation,mesh subdivision and local critical values are studied systematically and deeply,which provides an effective way to solve problems such as the stress concentration,the singularity and crack.Meanwhile,this work also provides a second chance for the traditional triangular and tetrahedral elements.In this thesis,the research work mainly includes the following four parts:(1)The first part proposed the adaptive analysis procedure based on S-PIM,provided framework and flow chart.The novel error indicator which evaluates the maximum difference of strain energy values among nodes in each cell is proposed;a simple h-type local refinement scheme is adopted for triangle or tetrahedral cells;the local critical values based on refinement rate for two and three dimensional problems are defined,2D and 3D mesh automatic generators based on Delaunay technology were embedded in the adaptive procedure.(2)The basic principle of the node-based smoothed point interpolation method(NS-PIM)is described systematically and proposed the corresponding adaptive analysis procedure.Compared with the computation with uniform model,the present adaptive analysis can provide much better results in terms of precision and efficiency.The density distribution of adaptive mesh is consistent with the real error distribution,which verified the reliability of the proposed error indicator.A novel method was developed to calculate the local critical values based on cell area,which broke the limitation of artificial setting refinement rate,can obtain fully automatic adaptive analysis process without human intervention,and the performance is as good as adaptive analysis with refinement rate.Make full use of the unique property of the NS-PIM for providing upper bound strain energy as well as the lower bound property of FEM,the proposed adaptive analysis can effectively band the real strain energy of a model in a small range,which is supposed to have potential engineering practicality.(3)The third part proposed an efficient adaptive analysis process using the newly developed edge-based smoothed point interpolation method(ES-PIM)for both 2D and 3D elasticity problems.At first,the framework of adaptive analysis flow is provided,and two different error indicators are designed based on the node and edge.A new triangle refinement strategy is developed for adding nodes and two types of critical values are used.The ES-PIM programs coupled with 2D and 3D Delaunay mesh generator are developed.Consider the feasibility of the two kinds of error indicators,numerical results indicate that the error indicator based on node can identify high gradient area more accurately.The results show that the adaptive analyses of ES-PIM and FEM have higher precision and convergence than analysis with uniform mesh.The proposed adaptive process is simple,robust and efficient.Further study illustrates the full automatic adaptive analysis has much higher convergence rate than use refinement rate for 2D problems.(4)The forth part described the implementation of the adaptive analysis based on ES-PIM in acoustic problems.According to the characteristics of acoustic problems,a new error indicator has been designed considering the maximum values of velocity difference among the vertexes in each cell.Refinement strategy,local critical values and Delaunay mesh generator used in this part are similar to the counter part of adaptive ES-PIM on solid mechanics.The adaptive analysis is applied to 2D and 3D acoustic frequency response analysis,especially for automobile silencer and vehicle body problem of member warehouse.The results highlight the efficiency of adaptive analysis,which reduces computation consumption significantly.Then the adaptive analysis is conducted on model analysis for 2D problem,and the results have shown the validity and efficiency of the proposed error indicator.