• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.145-153
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• 2017

In this article, a novel simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) beams is proposed. The beauty of this theory relies on its 2-unknowns displacement field as the Euler-Bernoulli beam theory, which is even less than the Timoshenko beam theory. A shear correction factor is, therefore, not needed. Equations of motion are obtained via Hamilton's principle. Analytical solutions for the bending and free vibration analysis are given for simply supported beams. Efficacy of the proposed model is shown through illustrative examples for bending and dynamic of FG beams. The numerical results obtained are compared with those of other higher-order shear deformation beam theory results. The results obtained are found to be accurate.

• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.601-609
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• 1997

Bending and vibration results for a laminated plate base on a simplified higher-order plate theory with four variables are presented. Assuming a constant in-plane rotation tensor through the thickness in Reddy's higher-order shear deformation theory it is shown that a simpler higher-order theory can be obtained with the reduction of one variable without significant loss in the accuracy. This simple higher-order shear deformation theory is then used for predicting the natural frequencies and deflection of simply-supported laminated composite plates. The results obtained for antisymmetrical laminated composite plates compare favorably with third-order and first-order shear deformation theory. The information presented should be useful to composite-structure designers, to researchers seeking to obtain better correlation between theory and experiment and to numerical analysts in checking out their programs.

• Advances in materials Research
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• v.6 no.1
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• pp.13-26
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• 2017

In this work we introduce a higher-order hyperbolic shear deformation model for bending and frees vibration analysis of functionally graded beams. In this theory and by making a further supposition, the axial displacement accounts for a refined hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the beam boundary surfaces, so no need of any shear correction factors (SCFs). The material properties are continuously varied through the beam thickness by the power-law distribution of the volume fraction of the constituents. Based on the present refined hyperbolic shear deformation beam model, the governing equations of motion are obtained from the Hamilton's principle. Analytical solutions for simply-supported beams are developed to solve the problem. To verify the precision and validity of the present theory some numerical results are compared with the existing ones in the literature and a good agreement is showed.

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.761-769
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• 2018

In this paper, we study the Carbon/Glass hybrid laminated composite plates, where the buckling behavior is examined using an accurate and simple refined higher order shear deformation theory. This theory takes account the shear effect, where shear deformation and shear stresses will be considered in determination of critical buckling load under different boundary conditions. The most interesting feature of this new kind of hybrid laminated composite plates is that the possibility of varying components percentages, which allows us for a variety of plates with different materials combinations in order to overcome the most difficult obstacles faced in traditional laminated composite plates like (cost and strength). Numerical results of the present study are compared with three-dimensional elasticity solutions and results of the first-order and the other higher-order theories issue from the literature. It can be concluded that the proposed theory is accurate and simple in solving the buckling behavior of hybrid laminated composite plates and allows to industrials the possibility to adjust the component of this new kind of plates in the most efficient way (reducing time and cost) according to their specific needs.

• Structural Engineering and Mechanics
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• v.84 no.6
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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.

• Advances in materials Research
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• v.8 no.4
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• pp.313-335
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• 2019

The objective of the present paper is to investigate the bending and free vibration behavior of functionally graded material (FGM) sandwich rectangular plates using an efficient and simple higher order shear deformation theory. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The most interesting feature of this theory is that it does not require the shear correction factor. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Steel and Composite Structures
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• v.30 no.6
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• pp.567-576
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• 2019

Time-dependent creep analysis of a rotating functionally graded cantilever beam with trapezoidal longitudinal cross section subjected to thermal and inertia loading is investigated using first-order shear deformation theory (FSDT). The model described in this paper is a simple simulation of a turbine blade working under creep condition. The material is a metal based composite reinforced by a ceramic where the creep properties of which has been described by the Sherby's constitutive model. All mechanical and thermal properties except Poisson's ratio are assumed to be variable longitudinally based on the volume fraction of constituent. The principle of virtual work as well as first order shear deformation theory is used to derive governing equations. Longitudinal distribution of displacements and stresses are investigated for various volume fractions of reinforcement. Method of successive elastic solution is employed to obtain history of stresses and creep deformations. It is found that stresses and displacements approach their steady state values after 40000 hours. The results presented in this paper can be used for selection of appropriate longitudinal distribution of reinforcement to achieve the desired stresses and displacements.

• Steel and Composite Structures
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• v.32 no.3
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• pp.389-410
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• 2019

In this article, a simple quasi-3D shear deformation theory is employed for thermo-mechanical bending analysis of functionally graded material (FGM) sandwich plates. The displacement field is defined using only 5 variables as the first order shear deformation theory (FSDT). Unlike the other high order shear deformation theories (HSDTs), the present formulation considers a new kinematic which includes undetermined integral variables. The governing equations are determined based on the principle of virtual work and then they are solved via Navier method. Analytical solutions are proposed to provide the deflections and stresses of simply supported FGM sandwich structures. Comparative examples are presented to demonstrate the accuracy of the present theory. The effects of gradient index, geometrical parameters and thermal load on thermo-mechanical bending response of the FG sandwich plates are examined.

• Coupled systems mechanics
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• v.6 no.3
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• pp.251-272
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• 2017

In this paper, the thermo-mechanical vibration characteristics of functionally graded (FG) nanobeams subjected to three types of thermal loading including uniform, linear and non-linear temperature change are investigated in the framework of third-order shear deformation beam theory which captures both the microstructural and shear deformation effects without the need for any shear correction factors. Material properties of FG nanobeam are assumed to be temperature-dependent and vary gradually along the thickness according to the power-law form. Hence, applying a third-order shear deformation beam theory (TSDBT) with more rigorous kinetics of displacements to anticipate the behaviors of FG nanobeams is more appropriate than using other theories. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton's principle and they are solved applying analytical solution. The obtained results are compared with those predicted by the nonlocal Euler-Bernoulli beam theory and nonlocal Timoshenko beam theory and it is revealed that the proposed modeling can accurately predict the vibration responses of FG nanobeams. The obtained results are presented for the thermo-mechanical vibration analysis of the FG nanobeams such as the effects of material graduation, nonlocal parameter, mode number, slenderness ratio and thermal loading in detail. The present study is associated to aerospace, mechanical and nuclear engineering structures which are under thermal loads.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.19-31
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• 2018

In this paper, a new quasi-3D sinusoidal shear deformation theory for functionally graded (FG) plates is proposed. The theory considers both shear deformation and thickness-stretching influences by a trigonometric distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower faces of the plate without employing any shear correction coefficient. The advantage of the proposed model is that it posses a smaller number of variables and governing equations than the existing quasi-3D models, but its results compare well with those of 3D and quasi-3D theories. This benefit is due to the use of undetermined integral unknowns in the displacement field of the present theory. By employing the Hamilton principle, equations of motion are obtained in the present formulation. Closed-form solutions for bending and free vibration problems are determined for simply supported plates. Numerical examples are proposed to check the accuracy of the developed theory.