Dual reciprocity hybrid boundary node method for 2-D elasticity with body force

Abstract

A boundary-type meshless method named dual reciprocity hybrid boundary node method (DRHBNM) is presented. It can be applied to solve elasticity problems with body force, centrifugal load, or other similar problems. In this method, the solution comprises two parts, i.e., the general solution and the particular solution. The general solution is solved by the hybrid boundary node method (HBNM), and the particular one is obtained by the dual reciprocity method (DRM). This method extends the Kelvin fundamental solution for static elastic problems without body force to non-homogeneous problems with body or inertial forces. A modified variational formulation is applied to form the discrete equations of HBNM. The moving least squares (MLS) are employed to approximate the boundary variables, while the domain variables are interpolated by the classical fundamental solution. The particular solution for the body force is obtained by DRM, and the integration in the domain is interpolated by the radial basis function. The proposed method retains the characteristics of the meshless method. At the same time, it employs the fundamental solution as in the boundary element method (BEM). Therefore, this method has the advantages of both meshless method and BEM. It does not require a ‘boundary element mesh’, either for the purpose of interpolation of the solution variables, or for the integration of the ‘energy’. The points in the domain are used only to interpolate particular solutions by the radial basis function and it is not necessary for the integration and approximation of the solution variables. Finally, the boundary solution variables are interpolated by the independent smooth segment boundary. As special treatments for corners are not required, it can obtain accurate boundary tractions for non-smooth boundaries. Numerical examples of 2-D elasticity problems with body force are used to demonstrate the versatility of the method and its fast convergence. The computational results for unknown variables are accurate. Also, the variable parameters have little influence on the results and can be changed in wide ranges. It is shown that the present method is effective and can be widely applied to practical problems.