Relationship between Bending Solutions of FGM Timoshenko Beams and those of Homogenous Euler-Bernoulli Beams

Abstract:

Relationship between bending solutions of functionally graded Timoshenko beams (FGMTB) and those of homogenous Euler-Bernoulli beams (HEBB) were studied in this presentation. The deflection and the rotational angle of FGMTB are expressed in terms of the deflection of the corresponding HEBB with the same geometry, loadings and end constraints. Consequently, solutions of bending of the FGMTB are simplified as the calculation of the transition coefficients which can be easily determined by the variation law of the gradient of the material properties and the geometry of the beams because the solutions of corresponding HEBB are well known. As examples, solutions for the FGM Timoshenko beams under S-S, C-C, C-F and C-S end constraints and subjected to arbitrary transverse loadings were presented. These analytical solutions can be as benchmarks in the further investigations of behaviors of FGM beams.

• Periodical: Applied Mechanics and Materials (Volumes 166-169)
• Pages: 2831-2836
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.166-169.2831
• Online since: May 2012
• Authors: Shi Rong Li, Ze Qing Wan, Peng Zhang
• Keywords: Analytical Solution, Bending, Functionally Graded Material (FGM), Timoshenko Beam

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