A stable, meshfree, nodal integration method for nearly incompressible solids

An improved nodal integration method for nearly incompressible materials is proposed. Although nodal integration methods can avoid displacement type locking with nearly incompressible materials, they often encounter pressure oscillations. A mixed approach to nodal integration is exploited to avoid the oscillation. The method is applied to nodal integration using meshless shape functions and appears to work well in simple two dimensional benchmark tests. The method currently relies on a structured discretization but generalizations are proposed as the basis for future work.