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Meshfree methods
About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.
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01 Jan 2014
TL;DR: In this article, the authors focus on several special purpose elements and methods that are designed for specific circumstances, such as crack tip elements, infinite elements, finite strip elements and strip elements.
Abstract: This chapter focuses on several special purpose elements and methods that are especialy designed for specific circumstances. These elements are used for very specific purposes to either simplify meshing and calculation, or to obtain better accuracy, which usual elements cannot obtain. These include crack tip elements, infinite elements, finite strip elements and strip elements. In fracture mechanics, much interest for analysts is on the tip of the crack, as it is a singularity point where the stress field becomes mathematically infinite. When modeled with the conventional, polynomial-based finite elements (FEs) discussed in previous chapters, the FE approximations are usually quite bad unless a very dense mesh consisting of numerous small elements is modelled around the crack tip. Using elements with gradually increased artificial damping elements attached on the regular FE mesh is a very efficient way to model vibration problems with infinite boundaries. Another effective method of dealing with infinite domains is to use the finite element method (FEM) coupled with the boundary element method (BEM). The FEM is used in the interior portions of the problem domain where the problem is very complex, and the BEM is used for the exterior portion that can extend to infinity. The use of finite strip elements instead of the conventional FEs can be a very effective method for solving structural problems involving regular geometry and simple boundary conditions.
01 Jan 2006
TL;DR: This paper presents an experimental study of the meshless local Petrov-Galerkin methods, which are used to solve problems of computational mechanics with real-time requirements.
Abstract: Many numerical methods have been developed and used to solve problems of computational mechanics. Recently, one of the hottest topics in computational mechanics is the meshless or meshfree method. Some meshless methods have been proposed and achieved remarkable progress, such as the element-free Galerkin (EFG) method [1], the meshless local Petrov-Galerkin (MLPG) methods [2], and so on.
04 Sep 2002
TL;DR: In this article, the Corrected Smooth Particle Hydrodynamics (CSPH) method is used to simulate molten metal flow in high pressure die casting cavity, where the physical measurements of the flow are localised on a set of particles.
Abstract: This paper explains the numerical techniques required to model mould filling in high pressure die casting. Meshless methods can follow the behaviour of complex fluid flows making it an ideal numerical procedure for simulating the behaviour of molten metal inside the die cavities. In recent years, the advent of meshfree methods has led to the opening of new avenues in numerical computational techniques to follow the physical behaviour of fluid flow. As a result, particle based methods have emerged as a viable alternative for modelling in high pressure die casting. This paper discusses the numerical techniques used for the Corrected Smooth Particle Hydrodynamics (CSPH) method used to simulate molten metal flow in high pressure die casting cavity. CSPH is a Lagrangian based method implying the physical measurements of the flow are localised on a set of particles, which are free to move. This allows the simulation of complex free surfaces, including fragmentation. Finally, some numerical examples are given to demonstrate the validity of the method in high pressure die casting.
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TL;DR: In this paper, a strong meshless collocation technique was proposed to solve the Dirichlet problem for the Monge-Amp\`ere equation by using a polynomial trial space and collocation in the domain and on the boundary.
Abstract: This paper solves the two-dimensional Dirichlet problem for the Monge-Amp\`ere equation by a strong meshless collocation technique that uses a polynomial trial space and collocation in the domain and on the boundary. Convergence rates may be up to exponential, depending on the smoothness of the true solution, and this is demonstrated numerically and proven theoretically, applying a sufficiently fine collocation discretization. A much more thorough investigation of meshless methods for fully nonlinear problems is in preparation.