# A modified uncoupled lower-order theory for FG beams

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## Abstract

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.

## Keywords

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

### Acknowledgements

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

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