A two-phase DLSM model is proposed to model transverse isotropic materials, in which the layer structure of the anisotropic materials is explicitly represented. Equations are derived to obtain elastic parameters of the two phase model from the elastic modules in parallel to the bedding planes and that in normal direction of the bedding planes. Then, the mechanical properties of the two-phase DL...

Development of a new meshless technique is described that presents certain advantages over conventional meshless schemes due to unique weights that force alignment of the derivative approximation. The method is completelymeshless, yet retains the low storage and simple fluxdistribution technique that are characteristic of finite volumemethods. The newmethod is based on thewell-knownTaylor serie...

In this paper, we explore the effect of numerical integration on the meshless method used to approximate the solution of an elliptic partial differential equation with non-constant coefficients with Neumann boundary conditions. We considered meshless methods with shape functions that reproduce polynomials of degree k ≥ 1. We have obtained an estimate for the energy norm of the error in the appr...

In this paper, the two-dimensional Stokes problem is analyzed by the modified collocation Trefftz method (MCTM) and the Laplacian decomposition. The coupled Stokes equations are converted to three Laplace equations by utilizing the Laplacian decomposition and then the boundary-type meshless MCTM is adopted to solve the resultant Laplace equations. The MCTM, free from mesh and numerical quadratu...

In this study, a cellular automaton (CA) is developed o combine the advantages of finite element method (FEM) and meshless method to analyze two-dimensional elastic problems. By the CA, a two-dimensional domain is discretized into a grid of nodes which are distributed randomly in the domain. For convenience, the nodes are classified into the FEM group and the meshless group. In the FEM zone tha...

The Natural Element Method (NEM) is a meshless Galerkin method which has shown promise in the area of computational mechanics. In earlier applications of NEM [1–3], natural neighbor (Sibson) coordinates [4] were used to construct the trial and test functions. Recently, Belikov and co-workers [5] proposed a new interpolation scheme (non-Sibsonian interpolation) based on natural neighbors. In thi...

in this paper, we propose a new numerical method for solution of urysohn two dimensional mixed volterra-fredholm integral equations of the second kind on a non-rectangular domain. the method approximates the solution by the discrete collocation method based on inverse multiquadric radialbasis functions (rbfs) constructed on a set of disordered data. the method is a meshless method, because it i...

In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of E. Kansa’s well-known unsymmetric meshless collocation method. For a numerical implementation of the convergent variation, a previously proposed greedy technique is coupled with linear optimization. This algorithm allows a fully adaptive on-the-fly data-dependent m...

A meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n, and the condition that the shape functions depend only on the node positions. Furthermore, the method proposed also shares several of the advantages of the Finite Element Method such as: (a) the simplicity of the shape functi...

In this paper, we articulate a meshless computational paradigm for the effective modeling, accurate physical simulation, and real-time animation of point-sampled solid objects. Both the interior and the boundary geometry of our volumetric object representation only consist of points, further extending the powerful and popular method of point-sampled surfaces to the volumetric setting. We build ...