Meshfree methods

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

Meshless local petrov-galerkin method for elasto-static analysis of thick-walled isotropic laminated cylinders

Abstract: In this paper, one of the simplest and most regular members of the family of the Meshless Local Petrov-Galerkin (MLPG) methods; namely MLPG5, is applied to analyze the thick-walled isotropic laminated cylinders under elasto-static pressure. A novel simple technique is proposed to eliminate a very important difficulty of the meshless methods to deal with material discontinuities regarding to the high continuity of their shape functions. The Moving Least Squares (MLS) approximation is used for constructing the trial functions, and a simple Heaviside step function is chosen for the test function. The direct interpolation method is employed to impose the essential boundary conditions. Acceptable agreements with the analytical solutions and finite element method results are obtained specially at the material discontinuity boundaries, which suggest its application in other classes of problems.

Natural Neighbour Strategies for the Simulation of Laser Surface Coating Processes

Abstract: In this paper two different formulations for the numerical simulation of laser surface coating processes are presented and analysed. Both are based on the use of natural neighbour interpolation, but one employs a Galerkin approach and takes temperature as the primary variable while the second one is based on the use of finite differences and enthalpy as primary variable. The main practical difference is thus the description of the interphase of the melted zone during the process. While in the first method the interphase is described by a set of nodes that evolve in time, in the second one it is located somewhere between a string of nodes. Both formulations are described and compared, showing their potential benefits for the simulation of the before mentioned process.

Isogeometric analysis and patchwise reproducing polynomial particle method for plates

Abstract: Isogeometric analysis (IGA) is a framework bridging the gap between Computer Aided Design (CAD) and Finite Element Analysis (FEA). So it drastically reduces the error in the representation of the computational domain and the re-meshing by the use of \exact" CAD geometry directed at the coarsest level of discretization. This is achieved by using B-splines or Non-Uniform Rational B-Splines (NURBS). In order to handle the singularities arising in the PDEs, we construct a novel NURBS geometrical mapping that generates singular functions resembling the singularities. Also, we consider how to use the proposed mapping method in IGA of elliptic problems and elasticity containing singularities without changing the design mapping. For this end, the mapping method is used to enrich NURBS basis functions around a neighborhood of corner singularity so that they can capture the singular behavior of the solutions to be approximated. For a crack singularity, we cut out a singular zone including the crack tip by using Partition of Unity (PU) functions and paste back the image of the parameter space corresponding to the singular mapping proposed. Finally, Reproducing Polynomial Particle Method (RPPM) is one of meshless methods that use meshes minimally or do not use meshes at all. The RPPM is employed for free vibration and buckling of the rst order shear deformation model, called the Reissner-Mindlin plate, and for analysis of boundary layer of the Reissner-Mindlin plate. Also, we demonstrate that our method is more eective than other existing methods in dealing with Reissner-Mindlin plates with various material properties and boundary conditions.

A coupled finite element-meshfree smoothed point interpolation method for nonlinear analysis

Abstract: In this paper, coupling between the finite element method (FEM) and the smoothed point interpolation methods (SPIM) is employed in the study of inelastic problems where the meshfree methods presents attractive characteristics. These studies are based on a strategy whose inelastic region is previously discretised by a SPIM method, while the rest of domain is represented by FEM. Linear and nonlinear numerical simulations are presented, and the results of simulations are compared, when possible, to analytical solutions and experimental results in order to demonstrate the main features of the proposed coupling.