Journal
ENGINEERING WITH COMPUTERS
Volume 38, Issue SUPPL 1, Pages 489-521Publisher
SPRINGER
DOI: 10.1007/s00366-020-01168-8
Keywords
Geometric transformation; Discrete singular convolution; Carbon nanotube reinforced; Four-nodded element; Quadrilateral plates
Funding
- Research Center for Interneural Computing of China Medical University of Taiwan
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This paper presents a study of the free vibration and buckling analyses of functionally graded carbon nanotube-reinforced (FG-CNTR) laminated non-rectangular plates using a four-nodded straight-sided transformation method. The geometric transformation formulation via discrete singular convolution (DSC) is used to transform the equations of motion and buckling from the irregular physical domain into a square computational domain. The numerical solutions show the effects of various parameters on the vibration and buckling analyses of the FG-CNTR-laminated composite non-rectangular plates.
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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