Archive of Applied Mechanics

, Volume 89, Issue 4, pp 755–768 | Cite as

A modified uncoupled lower-order theory for FG beams

  • Y. L. Pei
  • P. S. Geng
  • L. X. LiEmail author


Though the higher-order beam theory is variationally consistent, the lower-order beam theory has more definite engineering significance in practical applications. This paper begins with the modified uncoupled higher-order theory of functionally graded (FG) beams. After evaluating the three rigidity coefficients, contribution of the two higher-order generalized stresses to the virtual work is ignored and therefore a modified uncoupled lower-order theory is established for FG beams, including the basic equations and the shear correction factor, so that the lower-order beam theory is theoretically correlated with the high-order beam theory. The cases of pure shearing, pure bending and pure tension are solved, compared and discussed for a FG beam. The analytical solutions validate the accuracy and applicability of the present uncoupled lower-order theory.


FG beam Rigidity coefficients The principle of virtual work Uncoupled higher-order beam theory Uncoupled lower-order beam theory 



This work was supported by the National Natural Science Foundations of China (Grant Nos. 11672221, 11272245, 11321062).


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Key Laboratory of Environment and Control for Flight Vehicle, School of Aerospace EngineeringXi’an Jiaotong UniversityXi’anChina

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