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Hygrothermal postbuckling analysis of smart multiscale piezoelectric composite shells

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Abstract

In this article, the hygrothermal postbuckling behaviour of multiscale doubly curved piezoelectric shells (MDCPS) has been evaluated through multiple scales perturbation method. The multiscale composite constituting of polymer/carbon nanotube/fiber and polymer/graphene platelet/fiber (PGF) in accordance with Halpin–Tsai model is considered for evaluation. The kinematics of the MDCPS is assumed to follow third order shear deformation theory (TSDT) and the non-linearity in the strain–displacement relation is adjudged through Von Karman relationship. Further, with the aid of Hamilton’s principle the governing equations of motion are derived. The present work studies the load–deflection curves for various distribution patterns such as U (uniform), X, A and O. In addition, the influence of various prominent parameters like applied voltage, magnetic potential, aspect and curvature ratio on the postbuckling characteristics of MDCPS is studied thoroughly.

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Correspondence to Farzad Ebrahimi.

Appendix

Appendix

Transformed shell principle coordinate can be expressed by:

$$ \begin{aligned} \overline{Q}_{11}^{n} &= Q_{11}^{n} \cos^{4} \theta + 2\left( {Q_{12}^{n} + 2Q_{66}^{n} } \right)\sin^{2} \theta \cos^{2} \theta + Q_{22}^{n} \sin^{4} \theta \\ \overline{Q}_{12}^{n} &= (Q_{11}^{n} + Q_{22}^{n} - 4Q_{66}^{n} )\sin^{2} \theta \cos^{2} \theta + Q_{12}^{n} \left( {\sin^{4} \theta + \cos^{4} \theta } \right) \\ \overline{Q}_{22}^{n}& = Q_{11}^{n} \sin^{4} \theta + 2\left( {Q_{12}^{n} + 2Q_{66}^{n} } \right)\sin^{2} \theta \cos^{2} \theta + Q_{22}^{n} \cos^{4} \theta \\ \overline{Q}_{66}^{n} &= \left( {Q_{11}^{n} + Q_{22}^{n} - 2Q_{12}^{n} - 2Q_{66}^{n} } \right)\sin^{2} \theta \cos^{2} \theta + Q_{66}^{n} \left( {\sin^{4} \theta + \cos^{4} \theta } \right) \\ \overline{Q}_{44}^{n} &= Q_{44}^{n} \cos^{2} \theta + Q_{55}^{n} \sin^{2} \theta \\ \overline{Q}_{55}^{n} &= Q_{55}^{n} \cos^{2} \theta + Q_{44}^{n} \sin^{2} \theta \\ \end{aligned} $$
(57)

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karimiasl, M., Ebrahimi, F. & Mahesh, V. Hygrothermal postbuckling analysis of smart multiscale piezoelectric composite shells. Eur. Phys. J. Plus 135, 242 (2020). https://doi.org/10.1140/epjp/s13360-020-00137-w

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