• Structural Engineering and Mechanics
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• 제72권5호
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• pp.653-673
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• 2019

This work investigates a novel quasi-3D hyperbolic shear deformation theory is presented to discuss the buckling of new type of sandwich plates. This theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements through the thickness. The enhancement of this formulation is due to the use of only five unknowns by including undetermined integral terms, contrary to other theories where we find six or more unknowns. It does not require shear correction factors and transverse shear stresses vary parabolically across the thickness. A new type of FGM sandwich plates, namely, both FGM face sheets and FGM hard core are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Analytical solutions are obtained for a simply supported plate. The accuracy of the present theory is verified by comparing the obtained results with quasi-3D solutions and those predicted by higher-order shear deformation theories. The comparison studies show that the obtained results are not only more accurate than those obtained by higher-order shear deformation theories, but also comparable with those predicted by quasi-3D theories with a greater number of unknowns.

• Steel and Composite Structures
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• 제27권5호
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• pp.599-611
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• 2018

In this article a four unknown quasi-3D shear deformation theory for the bending analysis of functionally graded (FG) plates is developed. The advantage of this theory is that, in addition to introducing the thickness stretching impact (${\varepsilon}_z{\neq}0$), the displacement field is modeled with only four variables, which is even less than the first order shear deformation theory (FSDT). The principle of virtual work is utilized to determine the governing equations. The obtained numerical results from the proposed theory are compared with the CPT, FSDT, and other quasi-3D HSDTs.

• Advances in nano research
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• 제11권6호
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• pp.621-640
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• 2021

Effect of thickness stretching on mechanical behavior of functionally graded (FG) carbon nanotubes reinforced composite (CNTRC) laminated nanoplates resting on elastic foundation is analyzed in this paper using a novel quasi 3D higher-order shear deformation theory. The key feature of this theoretical formulation is that, in addition to considering the thickness stretching effect, the number of unknowns of the displacement field is reduced to four, and which is more than five in the other models. Single-walled carbon nanotubes (SWCNTs) are the reinforced elements and are distributed with four power-law functions which are, uniform distribution, V-distribution, O-distribution and X-distribution. To cover various boundary conditions, an analytical solution is developed based on Galerkin method to solve the governing equilibrium equations by considering the nonlocal strain gradient theory. A modified two-dimensional variable Winkler elastic foundation is proposed in this study for the first time. A parametric study is executed to determine the influence of the reinforcement patterns, power-law index, nonlocal parameter, length scale parameter, thickness and aspect ratios, elastic foundation, thermal environments, and various boundary conditions on stresses, displacements, buckling loads and frequencies of the CNTRC laminated nanoplate.

• Smart Structures and Systems
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• 제22권3호
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• pp.303-314
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• 2018

An original quasi-3D hyperbolic shear deformation theory for simply supported functionally graded plates is proposed in this work. The theory considers both shear deformation and thickness-stretching influences by a hyperbolic distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower surfaces of the plate without using any shear correction coefficient. By expressing the shear parts of the in-plane displacements with the integral term, the number of unknowns and equations of motion of the proposed theory is reduced to four as against five in the first shear deformation theory (FSDT) and common quasi-3D theories. Equations of motion are obtained from the Hamilton principle. Analytical solutions for dynamic problems are determined for simply supported plates. Numerical results are presented to check the accuracy of the proposed theory.

• Steel and Composite Structures
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• 제22권5호
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• pp.975-999
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• 2016

This work investigates a thermomechanical bending analysis of functionally graded sandwich plates by proposing a novel quasi-3D type higher order shear deformation theory (HSDT). The mathematical model introduces only 5 variables as the first order shear deformation theory (FSDT). Unlike the conventional HSDT, the present one presents a novel displacement field which includes undetermined integral variables. The mechanical properties of functionally graded layers of the plate are supposed to change in the thickness direction according to a power law distribution. The core layer is still homogeneous and made of an isotropic ceramic material. The governing equations for the thermomechanical bending investigation are obtained through the principle of virtual work and solved via Navier-type method. Interesting results are determined and compared with quasi-3D and 2D HSDTs. The influences of functionally graded material (FGM) layer thickness, power law index, layer thickness ratio, thickness ratio and aspect ratio on the deflections and stresses of functionally graded sandwich plates are discussed.

• Advances in nano research
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• 제12권2호
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• pp.117-137
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• 2022

Effect of thickness stretching on free vibration, bending and buckling behavior of carbon nanotubes reinforced composite (CNTRC) laminated nanoplates rested on new variable elastic foundation is investigated in this paper using a developed four-unknown quasi-3D higher-order shear deformation theory (HSDT). The key feature of this theoretical formulation is that, in addition to considering the thickness stretching effect, the number of unknowns of the displacement field is reduced to four, and which is more than five in the other models. Two new forms of CNTs reinforcement distribution are proposed and analyzed based on cosine functions. By considering the higher-order nonlocal strain gradient theory, microstructure and length scale influences are included. Variational method is developed to derive the governing equation and Galerkin method is employed to derive an analytical solution of governing equilibrium equations. Two-dimensional variable Winkler elastic foundation is suggested in this study for the first time. A parametric study is executed to determine the impact of the reinforcement patterns, nonlocal parameter, length scale parameter, side-t-thickness ratio and aspect ratio, elastic foundation and various boundary conditions on bending, buckling and free vibration responses of the CNTRC plate.

• Structural Engineering and Mechanics
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• 제85권6호
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• pp.765-780
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• 2023

In this work, a novel combined logarithmic, secant and tangential 2D and quasi-3D refined higher order shear deformation theory is proposed to examine the buckling analysis of simply supported uniform functionally graded plates under uniaxial and biaxial loading. The proposed formulations contain a reduced number of variables compared to others similar solutions. The combined function employed in this study ensures automatically the zero-transverse shear stresses at the free surfaces of the structure. Various models of the material distributions are considered (linear, quadratic, cubic inverse quadratic and power-law). The differentials stability equations are derived via virtual work principle with including the stretching effect. The Navier's approach is applied to solve the governing equations which satisfying the boundary conditions. Several comparative and parametric studies are performed to illustrates the validity and efficacity of the proposed model and the various factors influencing the critical buckling load of thick FG plate.

• Geomechanics and Engineering
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• 제34권3호
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• pp.233-250
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• 2023

This paper investigates the flexural analysis of isotropic, transversely isotropic, and laminated composite plates using a new higher-order normal and shear deformation theory. In the present theory, only five unknown functions are involved compared to six or more unknowns used in the other similar theories. The developed theory does not need a shear correction factor. It can satisfy the zero traction boundary conditions on the top and the bottom surfaces of the plate as well as account for sufficient distribution of the transverse shear strains. The thickness stretching effect is considered in the computation. A simply supported was considered on all edges of the plate. The plate is subjected to uniform and sinusoidal distributed load in the static analysis. Laminated composite, isotropic, and transversely isotropic plates are considered. The governing equations are obtained utilizing the virtual work principle. The differential equations are solved via Navier's procedure. The results obtained from the developed theory are compared with other higher-order theories considered in the previous studies and 3D elasticity solutions. The results showed that the proposed theory accurately and effectively predicts the bidirectional bending responses of laminated composite plates. Several parametric studies are presented to illustrate the various parameters influencing the static response of the laminated composite plates.

• Structural Engineering and Mechanics
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• 제74권1호
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• pp.105-119
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• 2020

In this work, a novel higher-order shear deformation theory (HSDT) for static and free vibration analysis of functionally graded (FG) plates is proposed. Unlike the conventional HSDTs, the proposed theory has a novel displacement field which includes undetermined integral terms and contains fewer unknowns. Equations of motion are obtained by using Hamilton's principle. Analytical solutions for the bending and dynamic investigation are determined for simply supported FG plates. The computed results are compared with 3D and quasi-3D solutions and those provided by other plate theories. Numerical results demonstrate that the proposed HSDT can achieve the same accuracy of the conventional HSDTs which have more number of variables.

• Geomechanics and Engineering
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• 제14권6호
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• pp.519-532
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• 2018

In this work, two dimensional (2D) and quasi three-dimensional (quasi-3D) HSDTs are proposed for bending and free vibration investigation of functionally graded (FG) plates using hyperbolic shape function. Unlike the existing HSDT, the proposed theories have a novel displacement field which include undetermined integral terms and contains fewer unknowns. The material properties of the plate is inhomogeneous and are considered to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori-Tanaka model, in terms of the volume fractions of the constituents. The governing equations which consider the effects of both transverse shear and thickness stretching are determined through the Hamilton's principle. The closed form solutions are deduced by employing Navier method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. In-plane stress components have been determined by the constitutive equations of composite plates. The transverse stress components have been determined by integrating the 3D stress equilibrium equations in the thickness direction of the FG plate. The accuracy of the present formulation is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature.