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 incompre ssible boundary value problems. The first is due to the employment of highe r-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 K ronecker delta properties in the meshfree shape functions. This paper discu sses some recent enhancements in meshfree methods for incompressible bounda ry value problems, carries out numerical convergence analysis, and compares accuracy and efficiency improvement of these methods. Presented methods ar e a pressure projection method to remedy the over-constrained discrete syst em, and a mixed transformation method and a boundary singular kernel method for imposition of essential boundary conditions and contact constraints. S everal linear and nonlinear problems were analyzed to demonstrate the effec tiveness of the new approaches.