Papers by Keyword: Meshless Method

Abstract: We let the meshless method and the finite element method couple,so the meshless-finite element coupling method has the advantage. We based EFG - finite element coupling calculation principle and we drawn shape function of the coupling region, we obtained energy functional from weak variational equations and we find the numerical solution. EFGM-FE coupling method overcomes the simple use of meshless method to bring the boundary conditions and calculation intractable shortcomings of low efficiency. We found that this method is feasible and effective.

Abstract: Meshless method calculation accuracy is influenced by many factors, in which influence domain and node distribution are the most important. Due to the restrictions of the meshless methods themselves, their respective influence factors are different. In the paper, the advantages and disadvantages of the collocation method, the meshless method based on the local weak formulation and collocation (MWS), the meshless radial basis interpolation method based on global weak formulation (RPIM) and the weighted least squares meshless method (MWLS) are discussed by comparing the average error of nodes value in different influence domain radius. The results show that the accuracy of the MVS method is higher, but not stable; the radial basis interpolation method based on global weak formulation (RPIM) is a relatively stable method, but needs a large amount of calculation; better results can be obtained using the collocation with a small amount of the polynomial basis function added, simple and practicable.

Abstract: It is well known that traditional finite element (FEM) is an efficient method in solving engineering problems. However, when solving the acoustic problems in medium frequency, FEM suffers from the so-called pollution effect, which is directly related to the dispersion. In this paper, meshless method based on radial basis function (RBF) is introduced to solve the acoustic problem, which shows that the dispersion can be greatly reduced, thus it is very suitable for the solution of mid-frequency acoustic problem. In addition, an algorithm is presented to treat the boundary condition, which improves the performance of the meshless method.

Abstract: Meshless method or mesh free method has many advantages. So far, there are more than ten proposed meshless methods, each has their respective advantages and disadvantages. This paper will focus on the main several meshless methods, we will make a comparison and analysis of their respective adaptation range, at the same time, we will discuss the construction method of typical meshless approximation functions, and summarize the development of the meshless method, development trend and prospects.

Abstract: A meshless element-free Galerkin method (EFGM) which is applicable to arbitrary shapes but requires only nodal data is applied to two-dimensional steady-state ground-coupled heat transfer problems. The soil layer around underground constructions is modeled as a homogeneous medium and as a layered soil with two layers. The calculation precision of EFGM is validated by comparing EFGM results with those obtained by finite element method (FEM). EFGM reduce considerably the preparation of the model. EFGM is very appropriate for the ground-coupled heat transfer problems.

Abstract: With the compact support of radial point interpolation shape functions (RPIM), the stiffness matrix of system equation can be sparse, so its very suitable for meshless methods.This interpolation method have the Kronecker delta function property, so the essential boundary conditions can be enforced directly and accurately without any additional treatment. In this paper, the radial point interpolation shape function is used, calculate the shape function in different node distribution cases, analyse the compact support and Kronecker delta function,use penalty method to apply the essential boundary conditions. In this paper, the RPIM is applied to solving the deformation in one and two dimensional solids by different loads, the results demonstrated that the meshfree RPIM can effectively solve material mechanics problems.

Abstract: In order to investigate the calculation ability of meshless method and calculation precision for lift and drag force coefficient based on N-S equations with S-A turbulence model and Euler equations, numerical simulation of flow field around the DLR-F4 wing-body, supplied by the AIAA Drag Prediction Workshop, is employed using meshless method. Furthermore, the calculated results are compared with experiment results and Waller’s simulation results achieved by MGAERO software. It’s found that the present simulation results without consideration of fluid viscosity don’t agree well with Waller’s and experimental results. The present simulation results with consideration of fluid viscosity were found to be in good agreement with experimental results. These results indicate that meshless method coupled with S-A turbulence model could predict the natural flow characteristic around the DLR-F4 wing-body configuration well.

Abstract: In this paper, a forging problem is analyzed by using the overrange collocation method (ORCM), which is a new meshless method. By introducing some collocation points, which are located out of domain of the analyzed body, unsatisfactory issue of the positivity conditions of boundary points in collocation methods can be avoided. Because the overrange points are used only in interpolating calculation, no overconstrain occurs in partial differential equations on the solved problems.

Abstract: A meshless element-free Galerkin method (EFGM) which is applicable to arbitrary shapes but requires only nodal data is applied to two-dimensional steady-state ground-coupled heat transfer problems. The soil layer around underground constructions is modeled as a homogeneous medium and as a layered soil with two layers. Variational method is utilized to obtain the discrete equations. Moving least squares (MLS) approximants are used to construct the shape functions. Lagrange multiplier technique is employed to enforce the essential boundary conditions. The calculation precision of EFGM is validated by comparing EFGM results with those obtained by finite element method (FEM). EFGM reduce considerably the preparation of the model. EFGM is very appropriate for the ground-coupled heat transfer problems.

Abstract: The Smoothed Particle Hydrodynamics (SPH) method is a very important method to resolve hypervelocity problems and the basic theory of SPH method is introduced here. Then the three dimensional hypervelocity impact problems are simulated by using the model of chair. The results of SPH analysis show that (SPH) method is a numerical calculation method to resolve hypervelocity problems without mesh model but the particle model must be getting to calculate and the program code is less than other method. By analysis the results of the simulation is reasonable and very similar to the test result. It can be concluded that the advantages of SPH demonstrated make it a good and an ideal method to simulate the impact problem and other problems.