Static analysis of transversely or axially functionally graded tapered beams

Abstract

This paper presents the analytical solutions for the static analysis of the transversely or axially functionally graded beams with tapered cross-section. The elastic modulus of the beam varies continuously in the thickness or axial direction according to the power form. The closed form solution for the transversely functionally graded tapered beams is accomplished from the governing equation based on the Euler–Bernoulli beam theory and the principle of virtual work. The power series methodology is introduced to solve the governing equation for the axially functionally graded beam by transforming the governing equation into the series form. For comparison, the finite element model is utilised to obtain the approximate solution for both transversely or axially functionally graded tapered beam. Numerical examples are performed to validate the present study with the literature and the finite element solution.

Keywords:

• Functionally graded tapered beam
• Closed form solution
• Power series method

Acknowledgement

The support of the research reported here by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0019373 & 2012R1A2A1A01007405) is gratefully acknowledged.