In this paper, static and free vibrations behaviors of the orthotropic functionally graded material (FGM) plates resting on the two-parameter elastic foundation are analyzed by the a mesh-free method based on the first order shear deformation plate theory (FSDT). The mesh-free method is based on moving least squares (MLS) shape functions and essential boundary conditions are imposed by transfer...

Point sets from range scanners are noisy and do not contain additional data such as normals, which makes it difficult to create a mesh for rendering. We use the moving least-squares (MLS) approximation to get normals and differential information, and approximate the surface near each point by an MLS surface. From this we obtain a splat of a new octagonal shape which approximates the local curva...

It is a common procedure for scattered data approximation to use local polynomial fitting in the least-squares sense. An important instance is the Moving Least-Squares where the corresponding weights of the data site vary smoothly, resulting in a smooth approximation. In this paper we build upon the techniques presented by Wendland and present a somewhat simpler error analysis of the MLS approx...

In this work we present a high-accurate discretization to solve the compressible Navier-Stokes equations using an Arbitrary Lagrangian-Eulerian meshless method (SPH-MLS), which can be seen as general formulation that includes some well-known meshfree methods particular case. The is based on use of Moving Least Squares (MLS) approximants weight functions Galerkin and accurate discretize convecti...

Sharp features in manufactured and designed objects require particular attention when reconstructing surfaces from unorganized scan point sets using moving least squares (MLS) fitting. It’s an inherent property of MLS fitting that sharp features are smoothed out. Instead of searching for appropriate new fitting functions our approach computes a modified local point neighborhood so that a standa...

We propose a new family of barycentric coordinates that have closed-forms for arbitrary 2D polygons. These coordinates are easy to compute and have linear precision even for open polygons. Not only do these coordinates have linear precision, but we can create coordinates that reproduce polynomials of a set degree m as long as degree m polynomials are specified along the boundary of the polygon....

In this paper, one of the simplest and most regular members of the family of the Meshless Local Petrov-Galerkin (MLPG) methods; namely MLPG5, is applied to analyze the thick-walled isotropic laminated cylinders under elasto-static pressure. A novel simple technique is proposed to eliminate a very important difficulty of the meshless methods to deal with material discontinuities regarding to the...

A truly Meshless Local Petrov-Galerkin (MLPG) method is developed for solving 3D elasto-static problems. Using the general MLPG concept, this method is derived through the local weak forms of the equilibrium equations, by using a test function, namely, the Heaviside step function. The Moving Least Squares (MLS) are chosen to construct the shape functions. The penalty approach is used to impose ...

A mesh-free method based on moving least squares approximation (MLS)  and weak form of governing equations including two dimensional equations of motion and Maxwell’s equation is used to analyze the free vibration of functionally graded piezoelectric material (FGPM) beams. Material properties in beam are determined using a power law distribution. Essential boundary conditions are imposed by the...

An alternative to radial basis function interpolation and approximation is the so-called moving least squares method. As we will see below, in this method the approximation Pf to f is obtained by solving many (small) linear systems, instead of via solution of a single – but large – linear system as we did in the previous chapters. To make a connection with the previous chapters we start with th...