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RETRACTED ARTICLE: Nonlinear buckling mode transition analysis of axial–thermal–electrical-loaded FG piezoelectric nanopanels incorporating nonlocal and couple stress tensors

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Abstract

Piezoelectric nanostructures are one of the essential components in the design of electromechanical systems and devices at nanoscale. In the present exploration, a size-dependent panel model accommodating the both softening and stiffening features is introduced for nonlinear stability characteristics of functionally graded (FG) piezoelectric cylindrical nanopanels under combinations of axial mechanical load with external electric actuation and temperature change. In accordance with this objective, an efficient numerical strategy based upon the moving Kriging meshfree (MKM) technique is employed within the framework of the nonlocal couple stress (NCS) continuum elasticity. The established NCS-based numerical model has the capability to incorporate the buckling mode transition phenomenon as well as satisfying the function property of Kronecker delta via imposing essential boundary conditions with no use of predefined mesh and directly at the associated nodes. The NCS-based nonlinear equilibrium curves are traced including the modal transition corresponding to various parameter investigations of FG piezoelectric nanopanels. It is deduced that the nonlocal stress tensor leads to increase the difference between the minimum postbuckling loads associated with the first and second buckling modes, while the couple stress tensor causes to reduce it. It is also demonstrated that by changing the sign of electric actuation from negative to positive, the softening character of nonlocality as well as the strengthening character associated with the couple stress size dependency become a bit more significant. Furthermore, the roles of both unconventional stress tensors are more prominent in the value of the second bifurcation point in comparison with the first one.

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Acknowledgements

This work was financially supported by 111 Project (Grant No. D21021); Municipal Science and Technology Planning Project of Guangzhou (Grant No. 20212200004); Technology Planning Project of Guangdong Province (No. 2020A1414010399).

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Authors and Affiliations

  1. Wind and Vibration Engineering Research Center, Guangzhou University, Guangzhou, 510006, China

    Rui Rao & Zijie Ye

  2. College of Urban and Rural Construction, Zhongkai University of Agriculture and Engineering, Guangzhou, 510225, China

    Zhicheng Yang

  3. School of Science and Technology, The University of Georgia, 0171, Tbilisi, Georgia

    Saeid Sahmani

  4. Department of Mechanical Engineering, Eastern Mediterranean University, Famagusta, North Cyprus via Mersin 10, Turkey

    Babak Safaei

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  1. Rui Rao
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Correspondence to Zhicheng Yang or Saeid Sahmani.

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Rao, R., Ye, Z., Yang, Z. et al. RETRACTED ARTICLE: Nonlinear buckling mode transition analysis of axial–thermal–electrical-loaded FG piezoelectric nanopanels incorporating nonlocal and couple stress tensors. Archiv.Civ.Mech.Eng 22, 125 (2022). https://doi.org/10.1007/s43452-022-00437-1

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