A volume-averaged nodal projection method for the Reissner-Mindlin plate model

TL;DR

This paper presents a new meshfree Galerkin method for Reissner-Mindlin plates that avoids shear-locking and uses volume-averaged nodal projection with maximum-entropy approximations, demonstrating high accuracy across various thicknesses.

Contribution

It introduces a shear-locking free, meshfree Galerkin approach based on primitive variables and volume-averaged nodal projection for Reissner-Mindlin plates.

Findings

Accurate results for a wide range of plate thicknesses.

Method effectively avoids shear-locking.

Demonstrated stability with bubble-like enrichment.

Abstract

We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and is devoid of shear-locking. The proposed approach uses linear maximum-entropy approximations and is built variationally on a two-field potential energy functional wherein the shear strain, written in terms of the primitive variables, is computed via a volume-averaged nodal projection operator that is constructed from the Kirchhoff constraint of the three-field mixed weak form. The stability of the method is rendered by adding bubble-like enrichment to the rotation degrees of freedom. Some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses.