A Refined Simple First-Order Shear Deformation Theory for Static Bending and Free Vibration Analysis of Advanced Composite Plates

Abstract

A refined simple first-order shear deformation theory is developed to investigate the static bending and free vibration of advanced composite plates such as functionally graded plates. By introducing the new distribution shape function, the transverse shear strain and shear stress have a parabolic distribution across the thickness of the plates, and they equal zero at the surfaces of the plates. Hence, the new refined theory needs no shear correction factor. The Navier solution is applied to investigate the static bending and free vibration of simply supported advanced composite plates. The proposed theory shows an improvement in calculating the deflections and frequencies of advanced composite plates. The formulation and transformation of the present theory are as simple as the simple first-order shear deformation. The comparisons of deflection, axial stresses, transverse shear stresses, and frequencies of the plates obtained by the proposed theory with published results of different theories are carried out to show the efficiency and accuracy of the new theory. In addition, some discussions on the influence of various parameters such as the power-law index, the slenderness ratio, and the aspect ratio are carried out, which are useful for the design and testing of advanced composite structures.

Formulation of a New Mixed Four-Node Quadrilateral Element for Static Bending Analysis of Variable Thickness Functionally Graded Material Plates

“…Table 11. It is obvious that the numerical results of the plates using the proposed element agree very well with those of CPT [26], the results of Nguyen et al [18] using a refined simple FSDT, the solutions of Zenkour [26] using GSDT, and the 3D exact solutions [26]. In comparison with 3D solutions, the presented numerical results are minor difference.…”

“…at is the reason why numerous researchers focus on investigating the dynamic as well as static behaviors of the FGM structures, for example, beams [5][6][7][8][9][10], plates [11][12][13][14][15][16][17][18], shells [19][20][21], and other structures [22,23]. Many plate theories have been established and/or applied to investigate these structures, for example, classical plate theory (CPT), first-order shear deformation (FSDT), higherorder shear deformation theory (HSDT), and quasi-3D shear deformation theory.…”

Role of Transverse Shear Modulus in the Performance of Corrugated Materials

“…It may be classified as one of the FOSD method and serve as an alternative to the FOSD approach presented by Hernandez-Perez et al in their 2014 study [ 24 ]. Another example of FOSD was presented by Nguyen et al in 2019 [ 27 ] for advanced composite plates such as functionally graded plates, where no shear correction factor was used. In the literature, also the alternatives to FOSD may be found, for instance in the work of Anish et al [ 28 ], the so-called improved shear deformation theory was presented, in which a cubic variation of the thickness coordinate in the displacement field is employed.…”

The Role of Buckling in the Estimation of Compressive Strength of Corrugated Cardboard Boxes

“…If we also want to consider the transverse shear stiffness [ 34 , 35 ], and , in order to obtain a more precise prediction, the formula for the critical load should take the following form [ 32 ]: where: …”