A Mechanical-Based Solution for Axially Functionally Graded Tapered Euler-Bernoulli Beams

Abstract

In this article, structural analysis of axially functionally graded tapered beams is studied from a mechanical point of view using a finite element method. Introducing the concept of basic displacement functions (BDFs), it is shown that exact shape functions could be explicitly obtained in terms of BDFs via application of basic principles of structural mechanics. BDFs are obtained using the unit-dummy-load method. Carrying out static analysis, it is verified that exact results are provided by applying one or a few elements. The competency of the present element in stability and free vibration analyses is verified through several numerical examples.