Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.

Implementation of Meshless FEM for Engineering Applications

Abstract: Meshless Finite Element Methods, namely element- free Galerkin and point-interpolation method were implemented and tested concerning their applicability to typical engineering problems like electrical fields and structural mechanics. A class-structure was developed which allows a consistent implementation of these methods together with classical FEM in a common framework. Strengths and weaknesses of the methods under investigation are discussed. As a result of this work joint usage of meshless methods together with classical Finite Elements are recommended. Keywords—Finite Elements, meshless, element-free Galerkin, point-interpolation.

Computational efficiency of meshfree methods with local-coordinates algorithm

Abstract: In this study, meshfree methods with uniform nodal distribution and local-coordinates shape functions are investigated. The proposed meshfree method can be used with various shape functions and is tested on a test patch with a Laplace governing equation and both essential and Neumann boundary conditions. It is shown to reduce the computational time dependency on the number of nodes by 36%. This reduction of dependency is significant as it reduces the computational time by several orders for analysis of problems requiring very fine nodal distribution. The meshfree method with uniform nodal distribution and local coordinates shape function reduces and converges to the perfectly uniform nodal distribution with finer nodal distributions. The technique is illustrated on a rectangular Kirchhoff-Love plate to show the practical use of the technique for allowing higher order shape function and finer nodal distribution to be used with multiple overlapping boundary conditions as well as on an electromagnetic problem to explain the uses of this technique on solving multiple similar problem cases with slight changes in geometry of boundary nodes. Overall, the present methodology provides a simple way to increase the computational efficiency of meshfree methods in range of an order while retaining many of its benefits.

Localized Meshless Methods With Radial Basis Functions For Eigenvalue Problems

Abstract: LOCALIZED MESHLESS METHODS WITH RADIAL BASIS FUNCTIONS FOR EIGENVALUE PROBLEMS

Comparison of different methods in computing electrostatic fields

Abstract: The paper aims at comparing two different methods for solving electrostatic field problems. These are: Finite element method and Finite difference method. The comparison of these two methods is performed on a practical design of an electric component and is based on: - mathematical model schematization, starting from the physical model. - automatic description of the mathematical model to the computer - computation times and memory requirements - computation precision in the solution of the example. These two methods have been implemented as different subroutines in the same main program, so that only the bulk of their computing methods is compared and the comparison does not depend on the computer and the programming language. The results show a general equivalence of the two methods, with some advantages to the Finite differences with respect to computation time and Finite elements with respect to precision.