Solving Non-linear Elasticity Problems by a WLS High Order Continuation

In this paper, a high order mesh-free continuation for nonlinear elasticity problems is presented. This proposal consists to introduce the Weighted Least Squares (WLS) in a High Order Continuation (HOC). The WLS has been employed to create shape functions using a local support domain. The HOC permits to transform the nonlinear problems in a succession of linear problems of the same tangent matrix. A strong formulation of the problem is adopted to avoid the numerical integration and mesh generation. In this work, a numerical study has been conducted in nonlinear elasticity problems in order to study the behaviour and stability of the proposed approach. Several examples are investigated numerically in order to demonstrate the robustness and efficiency of the proposed approach. This proposed approach has shown its efficiency in management of complex geometries and irregular nodal distributions with respect to other approaches.