The displacement boundary conditions for Reddy higher-order shear cantilever beam theory

Abstract

The paper presents the analytical results aimed at studying the deformations of cantilever beams based on Reddy higher-order shear theory. Five different displacement boundary conditions are investigated. The first two conditions are conventional simplified displacement boundary conditions, and the third one is determined by the least squares method. Besides, two new simplified boundary conditions are given by considering the definition of the fixed end of cantilever beams. Compared with the solutions by the finite element method, results by the two new boundary conditions are found to be much better than those by the conventional ones, especially for deep beams. The new boundary conditions which are first presented are not as good as the condition determined by the least squares method, but they are simple and easy to be coded by engineers.