Displacement based finite element formulations over polygons: a comparison between Laplace interpolants, strain smoothing and scaled boundary polygon formulation

TL;DR

This paper compares three displacement-based finite element methods over polygons, analyzing their accuracy, convergence, and extension to higher-order polygons in linear elasticity and fracture mechanics.

Contribution

It provides a comparative study of Laplace interpolant FEM, smoothed FEM, and scaled boundary polygon formulation, including their numerical integration techniques and potential for higher-order polygons.

Findings

Laplace interpolant FEM shows high accuracy in benchmark tests.

Smoothed FEM demonstrates improved convergence properties.

Scaled boundary polygon formulation is extendable to higher-order polygons.

Abstract

Three different displacement based finite element formulations over arbitrary polygons are studied in this paper. The formulations considered are: the conventional polygonal finite element method (FEM) with Laplace interpolants, the cell-based smoothed polygonal FEM with simple averaging technique and the scaled boundary polygon formulation. For the purpose of numerical integration, we employ the sub-traingulation for the polygonal FEM and classical Gaussian quadrature for the smoothed FEM and for the scaled boundary polygon formulation. The accuracy and the convergence properties of these formulations are studied with a few benchmark problems in the context of linear elasticity and the linear elastic fracture mechanics. The extension of scaled boundary polygon to higher order polygons is also discussed.