Development of hybrid boundary node method in two-dimensional elasticity

Abstract

As a truly meshless method, the Hybrid Boundary Node Method (HBNM) does not require a ‘boundary element mesh’, either for the purpose of interpolation of the solution variables or for the integration of ‘energy’. It has been applied to solve the potential problems. This paper presents a further development of the HBNM to the 2D elastic problems. In this paper, the hybrid displacement variational formulations have been coupled with the Moving Least Squares (MLS) approximation. The rigid body movement method is employed to solve the hyper-singular integrations. The ‘boundary layer effect’, which is the main drawback of the original HBNM, has been circumvented by an adaptive integration scheme. In the present method, the source points of the fundamental solution are arranged directly on the boundary. Thus, the uncertain scale factor taken in the Regular Hybrid Boundary Node Method (RHBNM) can be avoided. The parameters that influence the performance of this method are studied through several numerical examples and the known analytical solutions. The treatment of singularity and further integration has been given by a series of effective approaches. The computation results obtained by the present method are shown that good convergence and high accuracy with a small node number are achievable.