We use the first-order shear deformation theory and a meshless method based on radial basis functions in a pseudospectral framework for predicting the free vibration behavior of thick orthotropic, monoclinic and hexagonal plates. The shape parameter is obtained by an optimization procedure. The three translational and two rotational degrees of freedom of a point of the laminate are independentl...

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...