![]() In this work, the proposed approach has been referred to it as HOC-WLS. Thanks to the development of the main variables into Taylor series, non-linear elastic problem is transformed into a succession of linear differential equations with the same tangent operator followed of a continuation technique is used to obtain the whole solution. This approach combines a high order continuation and the Weighted Least Squared (WLS) as a discretization method. ![]() In this paper, a new numerical approach is proposed. Other authors used a high order continuation using Radial Point Interpolation method under a strong formulation. Recently several authors developed a high order continuation using the Moving Least Squares approximation as a discretization method under a strong formulation to solve various non linear problems. have presented a technique based on the application of a variant of the Lagrange extrapolation through the computation of weights capable of detecting regions with discontinuities. presented an approach termed generically the ‘Finite Point Method’ based on a Weighted Least Square Interpolation of point data and point collocation for evaluating the approximation integrals. took advantage of the concepts of weighted least squares surface estimation and implicit surface definition to more precisely define the region of integration for solid mechanic’s simulations that are performed within a PIC framework. The Weighted Least Squares (WLS) approximation is wildly used in data fitting. This category don’t need a background mesh and the numerical integration. The second category of mesh-free methods is based on strong formulation. The first one concerns the mesh-free methods based on weak formulation that still require a background mesh like the Diffuse Element Method (DEM), Element Free Galerking (EFG) and Point Interpolation Method (PIM) etc. ![]() Nevertheless, not all mesh-free methods have this advantage. These methods provide the possibility to avoid mesh generation and connectivity between the nodes which require a considerable computation time. In the recent years, many authors have shown the interest in developing mesh-free methods to overcome some difficulties. ![]()
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