Shear buckling analysis of functionally graded (FG) carbon nanotube reinforced skew plates with different boundary conditions

Abstract

In this paper, a four-nodded straight-sided geometric element is proposed for shear buckling problem of functionally graded material (FGM) composite and carbon nanotube (CNT) reinforced composite skew plate. By using the transformation rule, quadrilateral plate field is mapped into a square domain in the computational space using discrete singular convolution (DSC) method. Related governing equations of skew plate buckling and boundary conditions of the problem are transformed from the physical domain into a square computational domain by using the geometric transformation based singular convolution. The discretization process is achieved via the DSC method together with numerical differential and two-different regularized kernel such as regularized Shannon's delta (RSD) and Lagrange delta sequence (LDS) kernels. The accuracy of the present DSC results is first verified via exiting results in literature. Then, some parametric studies have been presented to show the effects of CNT volume fraction, CNT distribution pattern, geometry of skew plate and skew angle on the shear buckling responses of FG-CNTR composite skew plates with different boundary conditions. Some new results related to critical buckling of FGM and CNT reinforced composite skew plate have been presented which can serve as benchmark solutions for future investigations.