Meshfree methods

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

Analysis of laminated composite plates using element-free galerkin method

Abstract: The desire to use materials with high strength/weight or stiffness/weight ratio is increased the importance of composite materials nowadays. Due to this, much attention has been devoted to the numerical analysis of composite plates. The performance of well-known numerical methods, Finite Element Method (FEM) and Boundary Element Method (BEM), are based on the quality mesh structures. Meshfree methods are free from the meshes and the drawbacks of mesh-based interpolation techniques. Because of its high convergence rate, Element-Free Galerkin Method (EFGM) is one of the most widely used meshfree method in solid body mechanics and it is a promising candidate for the analysis of composite materials. In this study; deflection analysis of laminated composite plates are studied using EFGM. Several laminated composite plate problems are solved using EFGM and the displacement results of EFGM solutions are compared with the results of exact and FEM solutions at the critical points.

Applications of Meshfree Method based on Reproducing Kernel Particle Method

Abstract: From 60's, conventional finite element method has been developed and showed its superiority in structural mechanics. But, the finite element analysis of metal forming processes often breaks down due to severe mesh distortion at large deformation. In recent years, a new family of computational methods has emerged. The so-called meshfree or meshless methods have been investigated and used by many researchers for treating a large variety of engineering problems. The main feature of these methods is that the domain of the problem is represented by a set of nodes, and a finite element mesh is unnecessary. That is, the concept of meshfree methods is that only nodal point data are used for modelling and solving. This computational methods reduces time-consuming model generation and refinement effort, and it provides a higher rate of convergence than that of the conventional finite element methods. The displacement shape functions are constructed using the reproducing kernel approximation that satisfies consistency conditions. In this research, a meshfree method approach based on the reproducing kernel particle method (RKPM) is applied to metal forming analysis. Numerical examples are analyzed to verify the performance of the meshfree method for metal forming analysis.

Meshless Virtual Cloth

Abstract: A systematic description of a novel physically-based virtual cloth simulation method using meshless models is carried out in this paper. This method is based upon continuum mechanics and discretized without explicit connections between nodes. The mechanical behavior of this cloth model is consistent and is independent of the resolution. Kirchhoff-Love (KL) thin shell theory is used as the basis of the cloth model. Approaches to the parametrization and boundary sewing problems are presented to suit with meshless models. Furthermore, a co-rotational method is proposed in order to take care of large deformation problems. As for the collision solution, a new shape-function-based collision detection method is developed for meshless parameterized surfaces. The experimental results show that our cloth simulation model based upon meshless methods can produce natural and realistic results.

Propagator based meshless methods for a class of continuum problems

Abstract: This paper presents a generalization to elastodynamics of the path integral or propagator formulation of elastostatics 1 , which yields a very convenient framework for meshless computational implementations. Equilibrium equations are here recovered as a particular case setting velocities to zero. It is shown that boundary conditions can be imposed in a more consistent and natural way through a suitable prolongation of the displacement field outside the domain. This procedure allows to use a broader class of approximating schemes than theboundary propagators'. Two different discretization techniques are used: simple polynomial fitting and Moving Least Squares interpolants. First, both techniques are used to solve some equilibrium problems (stress concentration and fracture) in order to compare their performance and study convergence rates. Finally, the problem of eigenvalue and eigenvector extraction from the dynamic equations is addressed, where some peculiarities of the formulation are revealed.

A Matlab software for approximate solution of 2D elliptic problems by means of the meshless Monte Carlo random walk method

Abstract: This paper is devoted to the development of an innovative Matlab software, dedicated to the numerical analysis of two-dimensional elliptic problems, by means of the probabilistic approach. This approach combines features of the Monte Carlo random walk method with discretization and approximation techniques, typical for meshless methods. It allows for determination of an approximate solution of elliptic equations at the specified point (or group of points), without a necessity to generate large system of equations for the entire problem domain. While the procedure is simple and fast, the final solution may suffer from both stochastic and discretization errors. The attached Matlab software is based on several original author’s concepts. It permits the use of arbitrarily irregular clouds of nodes, non-homogeneous right-hand side functions, mixed type of boundary conditions as well as variable material coefficients (of anisotropic materials). The paper is illustrated with results of analysis of selected elliptic problems, obtained by means of this software.