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Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method

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Abstract

This paper presents the free vibration and buckling analyses of functionally graded carbon nanotube-reinforced (FG-CNTR) laminated non-rectangular plates, i.e., quadrilateral and skew plates, using a four-nodded straight-sided transformation method. At first, the related equations of motion and buckling of quadrilateral plate have been given, and then, these equations are transformed from the irregular physical domain into a square computational domain using the geometric transformation formulation via discrete singular convolution (DSC). The discretization of these equations is obtained via two-different regularized kernel, i.e., regularized Shannon’s delta (RSD) and Lagrange-delta sequence (LDS) kernels in conjunctions with the discrete singular convolution numerical integration. Convergence and accuracy of the present DSC transformation are verified via existing literature results for different cases. Detailed numerical solutions are performed, and obtained parametric results are presented to show the effects of carbon nanotube (CNT) volume fraction, CNT distribution pattern, geometry of skew and quadrilateral plate, lamination layup, skew and corner angle, thickness-to-length ratio on the vibration, and buckling analyses of FG-CNTR-laminated composite non-rectangular plates with different boundary conditions. Some detailed results related to critical buckling and frequency of FG-CNTR non-rectangular plates have been reported which can serve as benchmark solutions for future investigations.

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Acknowledgements

This work was supported by the Research Center for Interneural Computing of China Medical University of Taiwan. Ömer Civalek would like to thank the committee member of Research Center for Interneural Computing of China Medical University of Taiwan for their help via solution of differential equations.

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  1. China Medical University, Taichung, Taiwan

    Ömer Civalek

  2. Department of Civil Engineering, Suleyman Demirel University, 32260, Isparta, Turkey

    Mehmet Avcar

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ÖC: conceptualization, modeling and software, methodology, validation, ınvestigation, formal analysis, writing -original draft, and supervision. MA: software, writing, editing, resources, visualization, formal analysis, and computational analysis.

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Civalek, Ö., Avcar, M. Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method. Engineering with Computers 38 (Suppl 1), 489–521 (2022). https://doi.org/10.1007/s00366-020-01168-8

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