We consider adaptive meshless discretisation of the Dirichlet problem for Poisson equation based on numerical differentiation stencils obtained with the help of radial basis functions. New meshless stencil selection and adaptive refinement algorithms are proposed in 2D. Numerical experiments show that the accuracy of the solution is comparable with, and often better than that achieved by the me...

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously nonhomogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for ...

In this paper, the meshless integral method based on the regularized boundary integral equation [1] has been extended to analyze the large deformation of elastoplastic materials. The updated Lagrangian governing integral equation is obtained from the weak form of elastoplasticity based on Green-Naghdi’s theory over a local sub-domain, and the moving least-squares approximation is used for meshl...

A meshless local Petrov-Galerkin (MLPG) method is applied to solve problems of Reissner-Mindlin shells under thermal loading. Both stationary and thermal shock loads are analyzed here. Functionally graded materials with a continuous variation of properties in the shell thickness direction are considered here. A weak formulation for the set of governing equations in the Reissner-Mindlin theory i...

This paper presents a meshless point collocation method for three-dimensional crack propagation. The meshless point collocation method is based on direct discretization of strong-form governing equations to achieve a truly meshless scheme that does not require mesh structures or a numerical integration procedure. These characteristics of the point collocation method enable the direction of an a...

The aim of the present paper is the development of an efficient numerical algorithm for the solution of magnetohydrodynamics flow problems for regular and irregular geometries subject to Dirichlet, Neumann and Robin boundary conditions. Toward this, the meshless point collocation method (MPCM) is used for MHD flow problems in channels with fully insulating or partially insulating and partially ...

During the past few years, the idea of using meshless methods for numerical solution of partial differential equations (PDEs) has received much attention throughout the scientific community, and remarkable progress has been achieved on meshless methods. The meshless local Petrov–Galerkin (MLPG) method is one of the ‘‘truly meshless’’ methods since it does not require any background integration ...

a meshless approach, collocation discrete least square (cdls) method, is extended in this paper, for solvingelasticity problems. in the present cdls method, the problem domain is discretized by distributed field nodes. the fieldnodes are used to construct the trial functions. the moving least-squares interpolant is employed to construct the trialfunctions. some collocation points that are indep...

We develop a meshless method for simulating soft organ deformation. The method is motivated by simple, automatic model creation for real-time simulation. Our method is meshless in the sense that deformation is calculated at nodes that are not part of an element mesh. Node placement is almost arbitrary. Fully geometrically nonlinear total Lagrangian formulation is used. Geometric integration is ...

The large deformation analysis is one of major challenges in numerical modelling and simulation of metal forming. Although the finite element method (FEM) is a well-established method for modeling nonlinear problems, it often encounters difficulties for large deformation analyses due to the mesh distortion issues. Because no mesh is used, the meshless methods show very good potential for the la...