Papers by Keyword: Meshless Method

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Authors: Francesco Gagliardi, I. Alfaro, Luigino Filice, E. Cueto
Abstract: The conventional tube extrusion process has been substituted by porthole die extrusion due to relevant advantages in terms of productivity and quality. However, the porthole die has a complex geometry to be effectively designed; consequently, several studies can be found out in the technical literature based on experimental and finite element analyses of the process. From this point of view, while the experimental investigations entail cost and time increasing, due to the die building complexity, finite element techniques present some drawbacks such as the difficulty to simulate material joining and the loss of accuracy due to the heavy mesh distortion and related remeshing. Therefore, the introduction of new numerical techniques for the analyses of this process could have positive effects. In this paper, the Natural Element Method (NEM) together to the alpha shapes and some extra numerical procedures are used in the simulation of tube extrusion, focusing the attention on the simulation of the welding line in a fully 3D analysis. The obtained results are compared with the finite element and experimental ones, measuring the accuracy of the proposed methodology.
Authors: Yong Ming Guo
Abstract: Point collocation methods have no mesh, no integration. While, the robustness of the point collocation methods is an issue especially when scattered and random points are used. To improve the robustness, some studies suggest that the positivity conditions can be important when using the point collocation methods. For boundary points, however, the positivity conditions cannot be satisfied, so that it is possible to get large numerical errors from the boundary points when using the point collocation methods. The author has proposed a point collocation method with a boundary layer of finite element. In this method, by introducing a boundary layer of finite element in boundary domain of workpiece, unsatisfactory issue of the positivity conditions of boundary points can be avoided, and the complicated boundary conditions can be easily imposed with the boundary layer of finite element. A forging process is analyzed by using the point collocation method with a boundary layer of finite element.
Authors: Jun Qiang Zhang
Abstract: The meshless finite volume method was employed to enforce the conservation of momentum in a local weak form. A novel hybrid meshless finite volume method (HMFVM) was proposed. The displacement and the stress were interpolated independently with a hybrid scheme in the process. To enforce the compatibility between stress and displacement, a smoothing stress was introduced via finite volume method. In this way, the HMFVM can avoid the appearance of derivatives of shape functions and improve the efficiency over the orthodox meshless finite volume method. Then, the HMFVM was applied to some Elasto-plastic problems, illustrating that it enjoys high precision and efficiency. As a result, the derivatives of shape function are avoid absolutely.
Authors: Xue Hai Wang, Ya Mei Liu, Qi Xun Lan
Abstract: The hybrid radial boundary node method is applied to solve the biharmonic problems. Based on modified variational principle, the variational formula of the biharmonic problems is established. The radial basis point interpolation is employed to approximate the boundary variables, while the domain variables are interpolated by a combination of the fundamental solution of the laplace equation and the biharmonic equation. Compared to the regular hybrid boundary node method, as the shape function has the delta function property, the boundary conditions of the original problem can be easily implemented, and the fictitious source points are not involved. Numerical examples show that this method is efficient for solving the biharmonic equation.
Authors: Yu Wang, Zhen Luo
Abstract: This paper proposes a meshless Galerkin level set method for structural shape and topology optimization of continua. To taking advantage of the implicit free boundary representation scheme, structural design boundary is represented through the introduction of a scalar level set function as its zero level set, to flexibly handle complex shape fidelity and topology changes by maintaining concise and smooth interface. Compactly supported radial basis functions (CSRBFs) are used to parameterize the level set function and also to construct the shape functions for mesh free function approximation. The meshless Galerkin global weak formulation is employed to implement the discretization of the state equations. This provides a pathway to simplify two numerical procedures involved in most conventional level set methods in propagating the discrete level set functions and in approximating the discrete equations, by unifying the two different stages at two sets of grids just in terms of one set of scattered nodes. The proposed level set method has the capability of describing the implicit moving boundaries without remeshing for discontinuities. The motion of the free boundary is just a question of advancing the discrete level set function by finding the design variables of the size optimization in time. One benchmark example is used to demonstrate the effectiveness of the proposed method. The numerical results showcase that this method has the ability to simplify numerical procedures and to avoid numerical difficulties happened in most conventional level set methods. It is straightforward to apply the present method to more advanced shape and topology optimization problems.
Authors: Supanut Kaewumpai, Suwon Tangmanee, Anirut Luadsong
Abstract: A meshless local Petrov-Galerkin method (MLPG) using Heaviside step function as a test function for solving the biharmonic equation with subjected to boundary of the second kind is presented in this paper. Nodal shape function is constructed by the radial point interpolation method (RPIM) which holds the Kroneckers delta property. Two-field variables local weak forms are used in order to decompose the biharmonic equation into a couple of Poisson equations as well as impose straightforward boundary of the second kind, and no special treatment techniques are required. Selected engineering numerical examples using conventional nodal arrangement as well as polynomial basis choices are considered to demonstrate the applicability, the easiness, and the accuracy of the proposed method. This robust method gives quite accurate numerical results, implementing by maximum relative error and root mean square relative error.
Authors: Ju Feng Wang, Feng Xin Sun
Abstract: This paper presents an improved interpolating moving least-squares (IIMLS) method, in which orthogonal functions system is used as the basis functions. In the IIMLS method, the final algebra equation system is not ill-conditioned, and can be solved without obtaining the inverse matrix. Hence, the computing speed and efficiency are improved. Then based on the IIMLS method, a meshless method is presented for the numerical solution of the regularized long wave (RLW) equation, which can be used to describe phenomena with weak nonlinearity and dispersion waves. And a numerical example is given to confirm the IMLS method.
Authors: Dang Qin Xue, Huan Ping Zhao, Jia Xi Zhang, Shu Lin Hou
Abstract: This paper formulates a radial basis function meshless method for the numerical simulation of the advection-diffusion problems. The spatial derivatives are approximated by RBF collocation technique whereas the temporal derivatives are discretized using the Crank-Nicholson method. Corresponding boundary conditions are enforced analytically at a discrete set of boundary nodes. The performances of the present method are demonstrated through their application to an advection-diffusion problem.
Authors: Jun Shan Li
Abstract: In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.
Authors: Feng Xin Sun, Ju Feng Wang
Abstract: Based on the MLS approximation, a meshless method for the numerical solution of the generalized Burger’s equation is presented in this paper. The nonlinear discrete scheme of the generalized equation is obtained, and is solved with the method of iteration. Compared with numerical methods based on mesh, the meshless method needs only the scattered nodes instead of meshing the domain of the problem. An example is given to demonstrate the accuracy of the proposed method. The numerical results agree well with the exact solutions.
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