A hybrid T-Trefftz polygonal finite element for linear elasticity

TL;DR

This paper introduces a hybrid T-Trefftz polygonal finite element method for linear elasticity, combining homogeneous solutions with boundary displacement fields to achieve high accuracy in numerical simulations.

Contribution

It develops a novel hybrid formulation using T-complete sets and boundary displacement fields for polygonal finite elements in linear elasticity.

Findings

High accuracy results in benchmark problems

Effective enforcement of displacement continuity

Optimal T-complete function selection

Abstract

In this paper, we construct hybrid T-Trefftz polygonal finite elements. The displacement field within the polygon is repre- sented by the homogeneous solution to the governing differential equation, also called as the T-complete set. On the boundary of the polygon, a conforming displacement field is independently defined to enforce continuity of the displacements across the element boundary. An optimal number of T-complete functions are chosen based on the number of nodes of the polygon and degrees of freedom per node. The stiffness matrix is computed by the hybrid formulation with auxiliary displacement frame. Results from the numerical studies presented for a few benchmark problems in the context of linear elasticity shows that the proposed method yield highly accurate results.