Hierarchical interpolation function in 2d plate analysis

Abstract

The HFEM method, as an interpolation of the finite element method (FEM), allows us to set up a molecular grid system in an orderly and customizable way on complex object surfaces to produce accurate results. Finite element method is an approximate numerical method for solving problems described by partial differential equations on the bounded domain of any shape and boundary condition with which the precise solution of the equation system cannot be obtained algebraically. Hierarchical Finite element method (HFEM) is a special case of the Rayleigh-Ritz method [1-2] and the biggest difference between FEM and HFEM is the interpolation function. Although HFEM has much in common with the classical Rayleigh-Ritz methods, the results of approximation functions in HFEM method is greater flexibility and improved convergence rates as well as greater accuracy. Research in these areas not only solves modern problems technical requirements, but also demonstrates the use of advanced theories to overcome the limitations of the fundamental mechanics of materials