Dual reciprocity hybrid radial boundary node method for the analysis of Kirchhoff plates

A meshless method of dual reciprocity hybrid radial boundary node method (DHRBNM) for the analysis of arbitrary Kirchhoff plates is presented, which combines the advantageous properties of meshless method, radial point interpolation method (RPIM) and BEM. The solution in present method comprises two parts, i.e., the complementary solution and the particular solution. The complementary solution is solved by hybrid radial boundary node method (HRBNM), in which a three-field interpolation scheme is employed, and the boundary variables are approximated by RPIM, which is applied instead of moving least square (MLS) and obtains the Kronecker’s delta property where the traditional HBNM does not satisfy. The internal variables are interpolated by two groups of symmetric fundamental solutions. Based on those, a hybrid displacement variational principle for Kirchhoff plates is developed, and a meshless method of HRBNM for solving biharmonic problems is obtained, by which the complementary solution can be solved.In order to solve the particular solution, a basic form of particular solution of Kirchhoff plates is developed, by which the particular solutions for all kinds of Kirchhoff plates can be interpolated. Combined with HRBNM and dual reciprocity method (DRM), a meshless method of DHRBNM is proposed for an arbitrary Kirchhoff plate. Numerical examples are given to illustrate that the present method is a simple, efficient, accurate and attractive one, and can be further extended into some practical problems.