Shear forces and twisting moments in plates using Mindlin elements

Abstract

Finite elements based on Mindlin plate theory are used to study the distribution of shear forces and twisting moments on the boundaries of plates with various support conditons and thickness‐to‐span ratios. Differences between results obtained using Mindlin and Kirchhoff plate theories are highlighted. Potential difficulties in the interpretation of results obtained from finite element analysis are discussed and appropriate shear force sampling procedures are reviewed. The present work is a pilot study for a larger project with the basic aim of providing engineers with an unambiguous method for obtaining stress resultants in Mindlin plate analysis. Some examples are presented which illustrate the excellent results which may be obtained with judicious mesh division even in regions with steep gradients of the stress resultants near plate corners. These examples also demonstrate some of the difficulties facing engineers who have to try to interpret finite element results for plates.