An improved natural stabilized nodal integration for locking-related materials in meshfree methods

An improved naturally stabilized nodal integration (NSNI) is presented for resolving displacement locking concerned with highly orthotropic and nearly incompressible materials in the linear setting. It is recognized that the original NSNI is susceptible to the locking when dealing with these types of materials. The proposed method utilizes spectral decomposition to split the elasticity matrix into stiff and nonstiff parts. The terms associated with the stiff modes in the bilinear form are sampled by nodal integration (NI) without stabilization, whereas the other terms are integrated with NSNI. This approach leads to a unified implementation to handle locking in both types of materials. The performance and convergence of the proposed formulation are verified through several two- and three-dimensional numerical examples, illustrating the advantages of the presented method over its standard counterpart.