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Bending analysis of different material distributions of functionally graded beam

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Abstract

Most analyses of functional graded materials (FGM) focusing on power law distribution, which presents stress concentration at the interface when material properties change rapidly. The objective of the current paper is to develop two symmetric and anti-symmetric functions and compare their effects on the static deflection and bending stresses with classical power-law distribution. The proposed distributions are a symmetric power-law and a sigmoid function which is anti-symmetric. To homogenized micromechanical properties of FGM, the effective material properties are derived on the basis of Voigt model. Kinematic relation of Euler–Bernoulli beam is assumed and virtual work is proposed to derive the equilibrium equations. A finite element model is proposed to form stiffness matrix and force vector and then solve the problem numerically. Proposed model has been validated. Numerical results presents the effect of power exponent, and elasticity ratios on a static deflection and stresses of FG beams. The most significant finding is that, the symmetric power function is more reliable and can considerably reduce the stress than the other two functions. However, the sigmoid function distribution represents the highest stress.

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Acknowledgements

This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant No. (135-759-D1435). The authors, therefore, acknowledge with thanks DSR technical and financial support.

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  1. Department of Mechanical Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, 21589, Saudi Arabia

    S. M. Aldousari

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Aldousari, S.M. Bending analysis of different material distributions of functionally graded beam. Appl. Phys. A 123, 296 (2017). https://doi.org/10.1007/s00339-017-0854-0

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