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An integral shear and normal deformation theory for bending analysis of functionally graded sandwich curved beams

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Abstract

An efficient integral higher-order shear and normal deformation theory (IHSNDT) is developed based on a unified and enriched kinematic model to investigate the static bending phenomenon of functionally graded (FG) sandwich curved beams under uniform mechanical loads. The essential feature and most prominent aspect of this theory is that it explains the hyperbolic cosine distribution of transverse shear stress through the thickness of a beam with stretching effect and satisfies the stress-free boundary conditions on the upper and lower surfaces without needing any shear correction factor. The material properties of FG skins are presumed to vary continuously through the thickness direction according to power-law distribution and that the core is made of a homogeneous material. The governing equations and the associated boundary conditions have been established analytically within the framework of the principle of virtual work and then they are solved via Navier’s technique. To verify the correctness of the proposed beam formulation, the non-dimensional results of displacements and stresses obtained for simply supported FG sandwich curved beams are compared with the available solutions in the literature for various power-law index, skin-core-skin thickness and length-to-thickness ratios. The importance of the present study is that it contributes to some new results on the static behavior of FG sandwich curved beams due to its advantages as a fundamental structural element compared to straight ones, which can serve as a reference for future research.

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Authors and Affiliations

  1. Department of Civil Engineering, University of Tiaret, BP 78 Zaaroura, 14000, Tiaret, Algeria

    Kada Draiche

  2. Civil Engineering Department, Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Sidi Bel Abbès, Algeria

    Kada Draiche & Abdelouahed Tounsi

  3. Laboratoire de Modélisation Et Simulation Multi-Échelle, Université de Sidi Bel Abbes, Sidi Bel Abbès, Algeria

    Abdelmoumen Anis Bousahla

  4. YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea

    Abdelouahed Tounsi

  5. Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, Dhahran, Eastern Province, 31261, Saudi Arabia

    Abdelouahed Tounsi

  6. Department of Mathematics, Govt. College University Faisalabad, Faisalabad, 38000, Pakistan

    Muzamal Hussain

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  1. Kada Draiche
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  2. Abdelmoumen Anis Bousahla
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  3. Abdelouahed Tounsi
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  4. Muzamal Hussain
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Draiche, K., Bousahla, A.A., Tounsi, A. et al. An integral shear and normal deformation theory for bending analysis of functionally graded sandwich curved beams. Arch Appl Mech 91, 4669–4691 (2021). https://doi.org/10.1007/s00419-021-02005-0

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