Some recent improvements in meshfree methods for incompressible finite elasticity boundary value problems with contact

Two major difficulties are encountered in the meshfree solution of incompressible boundary value problems. The first is due to the employment of higher-order quadrature rules that leads to an over-constrained discrete system in incompressible problems. The second is associated with the treatment of essential boundary conditions and contact conditions owing to the loss of Kronecker delta properties in the meshfree shape functions. This paper discusses some recent enhancements in meshfree methods for incompressible boundary value problems, carries out numerical convergence analysis, and compares accuracy and efficiency improvement of these methods. Presented methods are a pressure projection method to remedy the over-constrained discrete system, and a mixed transformation method and a boundary singular kernel method for imposition of essential boundary conditions and contact constraints. Several linear and nonlinear problems were analyzed to demonstrate the effectiveness of the new approaches.