# Equilibrium-Based Finite Element Analysis of the Reissner–Mindlin Plate Bending Problem

## TL;DR

This paper introduces a stress-based finite element method for solving plate bending problems using specific elements and boundary conditions.

## Contribution

The novelty lies in applying specific finite elements to the stress function for Reissner–Mindlin plates with a focus on boundary conditions.

## Key findings

- The study uses Bogner–Fox–Schmit and Hsieh–Clough–Tocher elements for stress approximation.
- Displacement-based elements with 12 and 22 degrees of freedom are used for comparison.
- The 2D boundary condition variant is analyzed for its impact on numerical results.

## Abstract

A stress-based finite element approach to the Reissner–Mindlin plate bending problem is proposed. The rectangular Bogner–Fox–Schmit and triangular Hsieh–Clough–Tocher elements are applied to approximate the Southwell stress function describing the statically admissible stress field in a plate. To have some reference for the numerical results and estimate errors of the approximate solutions, two displacement-based elements with 12 and 22 degrees of freedom are also utilised. The variant of boundary conditions—known in the literature as 2D or hard BC—is analysed in the present study.