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Evaluation of refined theories for multilayered shells via Axiomatic/Asymptotic method

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Abstract

This paper is devoted to refined shell theories for the analysis of isotropic and laminated shells. Refined theories are built by assuming higher expansion order for the displacement field in the shell thickness directions. The implementation of these theories is made according to the Carrera unified formulation (CUF) which makes it possible to obtain shell governing equations in terms of fundamental nuclei whose form is independent of the chosen theory shell. Equivalent single layer and layer wise schemes are used. The axiomatic/ asymptotic technique is employed to evaluate the effectiveness of each displacement variable in the adopted displacement expansion. The error introduced by each term deactivation is evaluated with respect to a reference solution and according to a given error criterion; if the error computed does not exceed an a priori defined threshold the term is considered as not relevant and discarded. In this way it is possible to construct reduced models for each stress/displacement component. Attention has been restricted to closed form Navier type solutions and simply supported orthotropic shells are considered in the numerical investigation. Analysis of the displacement variables relevance is performed considering the influence of the kind of material and of the geometry, specifically isotropic and laminated materials and thick and thin shells. “Best”′ reduced models are proposed and related distributions are discussed.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Daoud S. Mashat, E. Carrera, Ashraf M. Zenkour & Sadah A. Al Khateeb

  2. Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Italy

    E. Carrera & A. Lamberti

  3. Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh, 33516, Egypt

    Ashraf M. Zenkour

Authors
  1. Daoud S. Mashat
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  2. E. Carrera
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  3. Ashraf M. Zenkour
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  4. Sadah A. Al Khateeb
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  5. A. Lamberti
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Corresponding author

Correspondence to E. Carrera.

Additional information

Recommended by Associate Editor Jun-Sik Kim

Erasmo Carrera received his Ph.D. in Aerospace Engineering in 1991. He is Professor of Aerospace Structures and Aeroelasticity. His main research topics are composite materials, finite elements, beams, plates and shells, postbuckling and stability by FEM, smart structures, thermal stress, aeroelasticity, multibody dynamics, inflatable structures, rotor-dynamics and design and analysis of non-classical lifting systems. He has introduced the Carrera Unified Formulation as a tool to develop second generation Theory of Structures.

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Mashat, D.S., Carrera, E., Zenkour, A.M. et al. Evaluation of refined theories for multilayered shells via Axiomatic/Asymptotic method. J Mech Sci Technol 28, 4663–4672 (2014). https://doi.org/10.1007/s12206-014-1033-2

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  • DOI: https://doi.org/10.1007/s12206-014-1033-2

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