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Steel and Composite Structures
  Volume 35, Number 2, April25 2020, pages 249-260

Vibrational characteristic of FG porous conical shells using Donnell\'s shell theory
Kai Yan, Yao Zhang, Hao Cai and Vahid Tahouneh

    The main purpose of this research work is to investigate the free vibration of conical shell structures reinforced by graphene platelets (GPLs) and the elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. To this end, a shell model is developed based on Donnell\'s theory. To solve the problem, the analytical Galerkin method is employed together with beam mode shapes as weighting functions. Due to importance of boundary conditions upon mechanical behavior of nanostructures, the analysis is carried out for different boundary conditions. The effects of boundary conditions, semi vertex angle, porosity distribution and graphene platelets on the response of conical shell structures are explored. The correctness of the obtained results is checked via comparing with existing data in the literature and good agreement is eventuated. The effectiveness and the accuracy of the present approach have been demonstrated and it is shown that the Donnell\'s shell theory is efficient, robust and accurate in terms of nanocomposite problems.
Key Words
    Donnell\'s shell theory; porosity; Halpin-Tsai micromechanics model; conical structures; graphene platelets (GPLs)
Kai Yan, Yao Zhang and Hao Cai: Key Lab of Building structural Retrofitting and Underground Space Engineering of the Ministry of Education,
Shandong Jianzhu University, Jinan, Shandong 251010, China
Vahid Tahouneh: Young Researchers and Elite Club, Islamshahr Branch, Islamic Azad University, Islamshahr, Iran

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