Numerical study of the shape parameter dependence of the local radial point interpolation method in linear elasticity

• The LRPIM is derived from the local weak form of the equilibrium equations for solving a thin elastic plate.
• The method LRPIM is used the trial and test functions in the weak form.
• Convergence of the LRPIM depends on number of parameters derived from local weak form and sub-domains.
• The effect of distributions nodes number by varying nature of material and the RBF-TPS.
• The calculated results are compared with the analytical solution of the deflection.

The method LRPIM is a Meshless method with properties of simple implementation of the essential boundary conditions and less costly than the moving least squares (MLS) methods. This method is proposed to overcome the singularity associated to polynomial basis by using radial basis functions. In this paper, we will present a study of a 2D problem of an elastic homogenous rectangular plate by using the method LRPIM. Our numerical investigations will concern the influence of different shape parameters on the domain of convergence,accuracy and using the radial basis function of the thin plate spline. It also will presents a comparison between numerical results for different materials and the convergence domain by precising maximum and minimum values as a function of distribution nodes number. The analytical solution of the deflection confirms the numerical results. The essential points in the method are:
• The LRPIM is derived from the local weak form of the equilibrium equations for solving a thin elastic plate.
• The convergence of the LRPIM method depends on number of parameters derived from local weak form and sub-domains.
• The effect of distributions nodes number by varying nature of material and the radial basis function (TPS).