STRUCTUAL ANALYSIS OF NEARLY INCOMPRESSIBLE MATERIALS USING MESH-FREE GALERKIN METHOD

초록

Mesh-free Galerkin method or element-free Galerkin method[1] discretizes a continuum by only a set of nodal points without fixed connectivity between nodes and many problems caused by bad mesh quality can be avoided by using mesh-free Galerkin method. Thus, mesh-free Galerkin method is expected to have advantages in dealing with large deformations. In this work, mesh-free Galerkin method is applied to structural analysis of large elastic deformations of hyper-elastic materials. Hyper-elastic materials such as rubbers are generally nearly incompressible, and this property causes some numerical difficulties such as volumetric locking which has been a significant concern in finite element method. Mesh-free Galerkin method also has locking problem. Dolbow et al.[2] and Huerta et al.[3] studied volumetric locking for linear elastic isotropic materials in the context of mesh-free Galerkin method with back-cell integration. According to [2] and [3], volumetric locking can be alleviated or suppressed by increasing dilation parameter or using selective reduced integration. However, in order to suppress locking by increasing dilation parameter, computing time increases too much. Selective reduced integration by Gauss quadrature rule on back-cell can suppress volumetric locking without significant increase in computing time but it cannot pass patch test. Therefore, in this research, the stabilized conforming nodal integration (SCNI) method proposed by Chen et al.[4] is used as integration method for mesh-free Galerkin method to analyze nearly incompressible materials. However, although original SCNI method can suppress volumetric locking, it can cause spurious modes or pressure oscillations. Thus, modified SCNI method [5] proposed to solve this problem is used in this work, but local volumetric locking near boundaries is observed by this method. By modifying integration domains for SCNI, this phenomenon can be removed and analysis of nearly incompressible