The regular hybrid boundary node method in the bending analysis of thin plate structures subjected to a concentrated load

Abstract

This paper proposes a computational procedure based on the regular hybrid boundary node method (RHBNM) for solving the thin plate subjected to a concentrated load. The solution is decomposed into the particular solution arising from the concentrated load and the complementary solution for the homogeneous equation . In the solution procedure, the particular solution is first obtained by the fundamental solution. For the latter, we employ the RHBNM to solve. The RHBNM is a promising boundary type meshless method based on a modified variational principle and the moving least squares (MLS) approximation, and exploits the meshless attributes of the MLS and the reduced dimensionality advantages of the boundary element method (BEM). In this paper, a modified variational functional of the thin plate is developed, in which the independent variables are the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain. The MLS method is employed to approximate the boundary variables whereas the domain variables are interpolated by a linear combination of fundamental solutions of both the biharmonic equation and Laplace's equation . Some numerical tests illustrate the validity and efficiency of the present method. ► The meshless RHBNM is extended to thin plate subjected to a concentrated load. ► Particular solution arising from concentrated load is obtained by fundamental solution. ► The complementary solution for the homogeneous equation is obtained by the RHBNM. ► A modified variational is developed to derive the system of equations. ► The numerical tests show that the accuracy and convergence rate are very high.