Meshfree methods

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

Limit analysis of plates and slabs using a meshless equilibrium formulation

Abstract: A meshless Element-Free Galerkin (EFG) equilibrium formulation is proposed to compute the limit loads which can be sustained by plates and slabs. In the formulation pure moment fields are approximated using a moving least-squares technique, which means that the resulting fields are smooth over the entire problem domain. There is therefore no need to enforce continuity conditions at interfaces within the problem domain, which would be a key part of a comparable finite element formulation. The collocation method is used to enforce the strong form of the equilibrium equations and a stabilized conforming nodal integration scheme is introduced to eliminate numerical instability problems. The combination of the collocation method and the smoothing technique means that equilibrium only needs to be enforced at the nodes, and stable and accurate solutions can be obtained with minimal computational effort. The von Mises and Nielsen yield criteria which are used in the analysis of plates and slabs, respectively, are enforced by introducing second-order cone constraints, ensuring that the resulting optimization problem can be solved using efficient interior-point solvers. Finally, the efficacy of the procedure is demonstrated by applying it to various benchmark plate and slab problems.

Some meshless methods for electromagnetic field computations

Abstract: A presentation of some meshless methods of approximation is proposed These numerical methods are very attractive since they have good convergence rates for the unknown function and its derivatives This behaviour is observed on several numerical examples A meshless Galerkin method is developed Application to the post-treatment and the computation of electromagnetic fields is reviewed

An Introduction to Moving Least Squares Meshfree Methods

Abstract: We deal here with some fundamental aspects of a category of meshfree methods based on Moving Least Squares (MLS) approximation and interpolation. These include EFG, RKPM and Diffuse Elements. In this introductory text, we discuss different formulations of the MLS from the point of view of numerical precision and stability. We talk about the issues of both “diffuse” and “full” derivation and we give proof of convergence of both approaches. We propose different algorithms for the computation of MLS based shape functions and we give their explicit forms in 1D, 2D and 3D. The topics of weight functions, the interpolation property with or without singular weights, the domain decomposition and the numerical integration are also discussed. We formulate the integration constraint, necessary for a method to satisfy the linear patch test. Finally, we develop a custom integration scheme, which satisfies this integration constraint.

High pressure die casting simulation using a Lagrangian particle method

Abstract: Mould filling simulation in high pressure die casting has been an attractive area of research for many years. Several numerical methodologies have been attempted in the past to study the flow behaviour of the molten metal into the die cavities. However, many of these methods require a stationary mesh or grid which limits their ability in simulating highly dynamic and transient flows encountered in high pressure die casting processes. In recent years, the advent of meshfree methods have expanded the capabilities of numerical techniques. Hence, these methods have emerged as an attractive alternative for modelling mould filling simulation in pressure die casting processes. In the present work, a Lagrangian particle method called corrected smooth particle hydrodynamics (CSPH) is used to simulate fluid flow in the high pressure die casting cavity. This paper mainly focuses on deriving the fundamental governing equations based on a variational formulation and presents a number of mould filling examples to demonstrate the capabilities of the CSPH numerical model.