On the use of Radial Point Interpolation Method (RPIM) in a high order continuation for the resolution of the geometrically nonlinear elasticity problems

In this work, we propose a new high order algorithm based on the coupling of Radial Point Interpolation Method (RPIM) and a high order continuation to solve the geometrically nonlinear elasticity problems under a strong formulation. The high order continuation has an adaptive step length which is very efficient and performed especially for solving the nonlinear problems. The specificity of RPIM is the exact implementation of boundary conditions because its shape functions have the Kronecker delta function property as in the conventional Finite Element Method (FEM). Therefore, it has proven that the RPIM shape functions have not only possess all advantages of the enforcing boundary conditions, but also can accurately reflect the properties of stresses distribution. This algorithm allows obtaining the solution with a less expensive CPU time to that of incremental iterative methods. A numerical comparison between the proposed algorithm and the others of literature is illustrated on some examples of geometrically nonlinear elasticity problems.