Exact Elasticity Solution for the Density Functionally Gradient Beam by Using Airy Stress Function

Abstract:

In this paper the problem of a density-functionally gradient beam subjected to uniform load is studied. Airy stress function methodology is used to obtain a set of analytical solutions for simply supported and clamped beams subjected to uniform load. A stress function in the form of polynomial is proposed and determined. The treatment for fixed-end boundary conditions is the same as that presented by Timoshenko and Goodier (1970). By this method all of the analytical plane-stress solutions can be obtained for a uniformly loaded isotropic beam with rectangular cross section under different types of classical boundary conditions.

• Periodical: Applied Mechanics and Materials (Volumes 110-116)
• Pages: 4669-4676
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.110-116.4669
• Online since: October 2011
• Authors: Alireza R. Daneshmehr, Saeed Momeni, Mahdi Reza Akhloumadi
• Keywords: Beam, FGM, Stress Function

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