Infinitesimal deformations of a homogeneous and isotropic thick elastic plate have been analyzed by using a meshless local Petrov– Galerkin (MLPG) method and a higher-order shear and normal deformable plate theory (HONSDPT). Radial basis functions (RBF) are employed for constructing trial solutions, while a spline function is used as the weight function over a local subdomain. The present metho...

A meshless approximation and local integral equation (LIE) formulation are proposed for elastodynamic analysis of a hollow cylinder made of quasicrystal materials with decagonal quasicrystal properties. The cylinder is assumed to be under shock loading. Therefore, the general transient elastodynamic problem is considered for coupled phonon and phason displacements and stresses. The equations of...

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 ...

This paper advocates a method for real-time physical deformation and arbitrary cutting simulation of heterogeneous objects with multi-material distribution, whose originality centers on the tight coupling of domain-specific finite element method (FEM) 1 and material-distance-aware meshless approach in a CUDA-centric parallel simulation framework. We employ hierarchical hexahedron serving as bas...

An algorithm for use with several meshless schemes is presented based on a local extremum diminishing property. The scheme is applied to the Euler equations in two dimensions. The algorithm is suitable for use with many meshless schemes, three of which are detailed here. First, a method based on Taylor series expansion and least squares is highlighted. Next, a similar least squares method is us...

The Meshless Local Petrov-Galerkin (MLPG) mixed collocation method is proposed in this paper, for solving elasticity problems. In the present MLPG approach, the mixed scheme is applied to interpolate the displacements and stresses independently, as in the MLPG finite volume method. To improve the efficiency, the local weak form is established at the nodal points, for the stresses, by using the ...

Numerical solutions obtained by the Meshless Local Petrov-Galerkin (MLPG) method are presented for two dimensional steady-state heat conduction problems. The MLPG method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. The penalty method is adopted to efficiently enforce the essential boundary co...

in this paper, an adaptive meshless method of line is applied to distribute the nodes in the spatial domain. in many cases in meshless methods, it is also necessary for the chosen nodes to have certain smoothness properties. the set of nodes is also required to satisfy certain constraints. in this paper, one of these constraints is investigated. the aim of this manuscript is the implementation ...

Meshless methods have been extensively popularized in literature in recent years, due to their flexibility in solving boundary value problems. The meshless local Petrov-Galerkin(MLPG) method for solving the bending problem of the thin plate is presented and discussed in the present paper. The method uses the moving least-squares approximation to interpolate the solution variables, and employs a...

A comparison between weak form meshless local Petrov-Galerkin method (MLPG) and strong form meshless diffuse approximate method (DAM) is performed for the diffusion equation in two dimensions. The shape functions are in both methods obtained by moving least squares (MLS) approximation with the polynomial weight function of the fourth order on the local support domain with 13 closest nodes. The ...