An IRBFN cartesian grid method based on displacement-stress formulation for 2D elasticity problems

Abstract

Traditional finite element methods (FEM) and boundary element methods (BEM) have been based on weak-form formulations. Recently, weak-form meshless (meshfree) methods are being developed as an alternative approach. Weak-form methods have the following advantages. a) They have good stability and reasonable accuracy for many problems. b) The traction (derivative or Neumann) boundary conditions can be naturally and conveniently incorporated into the same weak-form equation. However, elements have to be used for the integration of a weak form over the global problem domain and the numerical integration is still computationally expensive for these weak-form methods. On the other hand, collocation methods are based on strong-form governing equations and have been found to possess the following attractive advantages. a) There is no need for numerical integration of the governing equations. b) The implementation is simple. However, the strong-form approach is less stable due to the pointwise nature of error minimisation. Furthermore, strong-form methods such as finite difference and pseudo spectral methods are restricted to regular domains.