Notice of Retraction: Torsion of uniform bars using the improved Hybrid Boundary Node Method

Abstract

An improved Hybrid Boundary Node Method (Hybrid BNM) is developed for solving the torsion problem of uniform bars. The governing equation of the torsion problem is Poisson's equation. Based on the dual reciprocity method (DRM), the solution of problem is divided into complementary and particular solutions. The complementary solution is solved by the Hybrid BNM, and the DRM is employed to solve the particular one using radial basis functions (RBF). Hybrid BNM is a boundary type meshless method, which based on moving least squares (MLS) approximation. The method has many advantages, such as simple postprocess and high accuracy. However, shape functions for the classical MLS approximation lack the delta function property. Thus in this method, the boundary condition cannot be enforced easily and directly, and its computational cost is high for the inevitable transformation strategy of boundary condition. In the method we proposed, a regularized weight function is adopted, which leads to the MLS shape functions fulfilling the interpolation condition exactly, which enables a direct application of essential boundary conditions without additional numerical effort. Numerical results for the torsion of uniform bar are presented to demonstrate the efficiency and accuracy of the present method.