• Structural Engineering and Mechanics
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• 제55권5호
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• pp.1001-1014
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• 2015

Bending analysis of functionally graded (FG) nano-plates is investigated in the present work based on a new sinusoidal shear deformation theory. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. The material properties of nano-plate are assumed to vary according to power law distribution of the volume fraction of the constituents. The size effects are considered based on Eringen's nonlocal theory. Governing equations are derived using energy method and Hamilton's principle. The closed-form solutions of simply supported nano-plates are obtained and the results are compared with those of first-order shear deformation theory and higher-order shear deformation theory. The effects of different parameters such as nano-plate length and thickness, elastic foundation, orientation of foundation orthtotropy direction and nonlocal parameters are shown in dimensionless displacement of system. It can be found that with increasing nonlocal parameter, the dimensionless displacement of nano-plate increases.

• Structural Engineering and Mechanics
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• 제84권6호
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• pp.707-722
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• 2022

In this study, a new refined hyperbolic shear deformation theory (RHSDT) is developed using an equivalent single-layer shell displacement model for the static bending and free vibration response of cross-ply laminated composite spherical shells. It is based on a new kinematic in which the transverse displacement is approximated as a sum of the bending and shear components, leading to a reduction of the number of unknown functions and governing equations. The proposed theory uses the hyperbolic shape function to account for an appropriate distribution of the transverse shear strains through the thickness and satisfies the boundary conditions on the shell surfaces without requiring any shear correction factors. The shell governing equations for this study are derived in terms of displacement from Hamilton's principle and solved via a Navier-type analytical procedure. The validity and high accuracy of the present theory are ascertained by comparing the obtained numerical results of displacements, stresses, and natural frequencies with their counterparts generated by some higher-order shear deformation theories. Further, a parametric study examines in detail the effect of both geometrical parameters (i.e., side-to-thickness ratio and curvature-radius-to-side ratio), on the bending and free vibration response of simply supported laminated spherical shells, which can be very useful for many modern engineering applications and their optimization design.

• Steel and Composite Structures
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• 제18권1호
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• pp.91-120
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• 2015

A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates is presented in this paper. It contains only four unknowns, accounts for a hyperbolic distribution of transverse shear stress and satisfies the traction free boundary conditions. Equations of motion are derived from Hamilton's principle. The Navier-type and finite element solutions are derived for plate with simply-supported and various boundary conditions, respectively. Numerical examples are presented for functionally graded sandwich plates with homogeneous hardcore and softcore to verify the validity of the developed theory. It is observed that the present theory with four unknowns predicts the response accurately and efficiently.

• Steel and Composite Structures
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• 제26권2호
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• pp.125-137
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• 2018

In this work, the bending and free vibration analysis of multilayered plates and shells is presented by utilizing a new higher order shear deformation theory (HSDT). The proposed involves only four unknowns, which is even less than the first shear deformation theory (FSDT) and without requiring the shear correction coefficient. Unlike the conventional HSDTs, the present one presents a novel displacement field which incorporates undetermined integral variables. The equations of motion are derived by using the Hamilton's principle. These equations are then solved via Navier-type, closed form solutions. Bending and vibration results are found for cylindrical and spherical shells and plates for simply supported boundary conditions. Bending and vibration problems are treated as individual cases. Panels are subjected to sinusoidal, distributed and point loads. Results are presented for thick to thin as well as shallow and deep shells. The computed results are compared with the exact 3D elasticity theory and with several other conventional HSDTs. The proposed HSDT is found to be precise compared to other several existing ones for investigating the static and dynamic response of isotropic and multilayered composite shell and plate structures.

• Steel and Composite Structures
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• 제24권5호
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• pp.569-578
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• 2017

In this research work, a simple and accurate hyperbolic plate theory for the buckling analysis of functionally graded sandwich plates is presented. The main interest of this theory is that, in addition to incorporating the thickness stretching effect (${\varepsilon}_z{\not=}0$), the displacement field is composed only of 5 unknowns as the first order shear deformation theory (FSDT), instead of 6 like in the well-known "higher order shear and normal deformation theories". Thus, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Governing equations are obtained by employing the principle of minimum total potential energy. Comparison studies are performed to verify the validity of present results. A numerical investigation has been conducted considering and neglecting the thickness stretching effects on the buckling of sandwich plates with functionally graded skins. It can be concluded that the present theory is not only accurate but also simple in predicting the buckling response of sandwich plates with functionally graded skins.

• Structural Engineering and Mechanics
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• 제60권4호
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• pp.547-565
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• 2016

In this work a new 3-unknown non-polynomial shear deformation theory for the buckling and vibration analyses of functionally graded material (FGM) sandwich plates is presented. The present theory accounts for non-linear in plane displacement and constant transverse displacement through the plate thickness, complies with plate surface boundary conditions, and in this manner a shear correction factor is not required. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only 3 unknowns as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT). The plate properties are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton's principle. Analytical solutions of natural frequency and critical buckling load for functionally graded sandwich plates are obtained using the Navier solution. The results obtained for plate with various thickness ratios using the present non-polynomial plate theory are not only substantially more accurate than those obtained using the classical plate theory, but are almost comparable to those obtained using higher order theories with more number of unknown functions.

• Steel and Composite Structures
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• 제23권3호
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• pp.339-350
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• 2017

In this paper, various nonlocal higher-order shear deformation beam theories that consider the size dependent effects in Functionally Graded Material (FGM) beam are examined. The presented theories fulfill the zero traction boundary conditions on the top and bottom surface of the beam and a shear correction factor is not required. Hamilton's principle is used to derive equation of motion as well as related boundary condition. The Navier solution is applied to solve the simply supported boundary conditions and exact formulas are proposed for the bending and static buckling. A parametric study is also included to investigate the effect of gradient index, length scale parameter and length-to-thickness ratio (aspect ratio) on the bending and the static buckling characteristics of FG nanobeams.

• Geomechanics and Engineering
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• 제16권2호
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• pp.141-150
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• 2018

In this current work a quasi 3D "trigonometric shear deformation theory" is proposed and discussed for the dynamic of thick orthotropic plates. Contrary to the classical "higher order shear deformation theories" (HSDT) and the "first shear deformation theory" (FSDT), the constructed theory utilizes a new displacement field which includes "undetermined integral terms" and presents only three "variables". In this model the axial displacement utilizes sinusoidal mathematical function in terms of z coordinate to introduce the shear strain impact. The cosine mathematical function in terms of z coordinate is employed in vertical displacement to introduce the impact of transverse "normal deformation". The motion equations of the model are found via the concept of virtual work. Numerical results found for frequency of "flexural mode", mode of shear and mode of thickness stretch impact of dynamic of simply supported "orthotropic" structures are compared and verified with those of other HSDTs and method of elasticity wherever considered.

• Steel and Composite Structures
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• 제48권6호
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• pp.709-725
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• 2023

This paper uses a new type of deformation theory to establish the free vibration and static buckling equations of nanoplates resting on two-parameter elastic foundations, in which the flexoelectric effect is taken into account. The proposed approach used in this work is not only simpler than other higher-order shear deformation theories but also does not need any shear correction coefficients to describe exactly the mechanical responses of structures. The reliability of the theory is verified by comparing the numerical results of this work with those of analytical solutions. The results show that the flexoelectric effect significantly changes the natural frequency and the critical buckling load of the nanoplate compared with the case of neglecting this effect, especially when the plate thickness changes and with some different boundary conditions. These are new results that have not been mentioned in any publications but are meaningful in engineering practice.

• Steel and Composite Structures
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• 제26권5호
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• pp.557-572
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• 2018

In this paper, a refined higher-order shear deformation theory including the stretching effect is developed for the analysis of bending analysis of the simply supported functionally graded (FG) sandwich plates resting on elastic foundation. This theory has only five unknowns, which is even less than the other shear and normal deformation theories. The theory presented is variationally consistent, without the shear correction factor. The present one has a new displacement field which introduces undetermined integral variables. Equations of motion are obtained by utilizing the Hamilton's principles and solved via Navier's procedure. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.