Boundary Moving Least Square method for numerical evaluation of two-dimensional elastic membrane and plate dynamics problems

摘要

This paper discusses the Boundary Moving Least Square (BMLS) method for numerical implementation of various 2-D elasticity membrane and plate dynamics problems. The proposed technique is an amalgamation of boundary collocation meshless method and Moving Least Square (MLS) method. BMLS employs discrete boundary nodes in the axial direction to generate tensor product nodes in the entire solution domain, thereby simplifying complex multi-dimensional functions into manageable one-dimensional functions, as well as improving the overall computational and programming efficiency. Several numerical experiments were carried out and the result of BMLS was compared with that of Finite Element Method (FEM), which revealed that the BMLS numerical results are smoother and more continuous compared to the FEM, and exhibit distinctive characteristics of regularity and stability. BMLS is a practical numerical method with good prospects for solving membrane and plate dynamics problems.