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Temperature stress analysis for bi-modulus beam placed on Winkler foundation

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Abstract

The materials with different moduli in tension and compression are called bi-modulus materials. Graphene is such a kind of materials with the highest strength and the thinnest thickness. In this paper, the mechanical response of the bi-modulus beam subjected to the temperature effect and placed on the Winkler foundation is studied. The differential equations about the neutral axis position and undetermined parameters of the normal strain of the bi-modulus foundation beam are established. Then, the analytical expressions of the normal stress, bending moment, and displacement of the foundation beam are derived. Simultaneously, a calculation procedure based on the finite element method (FEM) is developed to obtain the temperature stress of the bi-modulus structures. It is shown that the obtained bi-modulus solutions can recover the classical modulus solution, and the results obtained by the analytical expressions, the present FEM procedure, and the traditional FEM software are consistent, which verifies the accuracy and reliability of the present analytical model and procedure. Finally, the difference between the bi-modulus results and the classical same modulus results is discussed, and several reasonable suggestions for calculating and optimizing the certain bi-modulus member in practical engineering are presented.

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Authors and Affiliations

  1. Department of Civil Engineering, Shanghai University, Shanghai, 200072, China

    Jinling Gao & Wenjuan Yao

  2. Shanghai Open Steel Structure Co., Ltd., Shanghai, 200127, China

    Jiankang Liu

Authors
  1. Jinling Gao
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  2. Wenjuan Yao
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  3. Jiankang Liu
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Corresponding author

Correspondence to Wenjuan Yao.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11072143 and 11272200)

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Gao, J., Yao, W. & Liu, J. Temperature stress analysis for bi-modulus beam placed on Winkler foundation. Appl. Math. Mech.-Engl. Ed. 38, 921–934 (2017). https://doi.org/10.1007/s10483-017-2216-6

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  • DOI: https://doi.org/10.1007/s10483-017-2216-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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