In this chapter a meshless method, based on the method of fundamental solutions (MFS) and radial basis functions (RBF), is developed to solve thin plate bending on an elastic foundation. In the presented algorithm, the analog equation method (AEM) is firstly used to convert the original governing equation to an equivalent thin plate bending equation without elastic foundations, which can be sol...

In this paper, the linearly conforming enriched radial basis point interpolation method is implemented for the elasto-plastic analysis of discontinuous medium. The linear conformability of the method is satisfied by the application of stabilized nodal integration and the enrichment of radial basis functions is achieved by the addition of linear polynomial terms. To implement the method for the ...

The Material Point Method (MPM) discrete solution procedure for computational solid mechanics is generalized using a variational form and a Petrov– Galerkin discretization scheme, resulting in a family of methods named the Generalized Interpolation Material Point (GIMP) methods. The generalization permits identification with aspects of other point or node based discrete solution techniques whic...

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...

The design of bone scaffold involves the analysis stress shielding, which can occur when Young’s modulus implant is higher than it replacing, leading to decay in surrounding tissue. It therefore very important that material adequately designed match properties tissue, allowing an appropriate load transfer. While some approaches exist literature exploring functional gradients density, there are ...

This paper proposes a novel meshless boundary method called the singular boundary method (SBM). This method is mathematically simple, easy-to-program, and truly meshless. Like the method of fundamental solutions (MFS), the SBM employs the singular fundamental solution of the governing equation of interest as the interpolation basis function. However, unlike the MFS, the source and collocation p...

K e y w o r d s R P I C M , Hermite-type interpolation, Meshfree, Partial differential equations. *Author to whom all correspondence should be addressed. Current address: Department of Mechanics, Zhejiang University, Hangzhou, P.R. China, 310027. 0898-1221/05/$ see front matter @ 2005 Elsevier Ltd. All rights reserved. Typeset by .AA/p%TEX doi:10.1016/j.camwa.2005.02.019 1426 x. Liu et al. 1. I...

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...