• Coupled systems mechanics
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• v.5 no.3
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• pp.269-283
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• 2016

A two new high-order shear deformation theory for bending analysis is presented for a simply supported, functionally graded plate with porosities resting on an elastic foundation. This porosities may possibly occur inside the functionally graded materials (FGMs) during their fabrication, while material properties varying to a simple power-law distribution along the thickness direction. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theories presented are variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. It is established that the volume fraction of porosity significantly affect the mechanical behavior of thick function ally graded plates. The validity of the two new theories is shown by comparing the present results with other higher-order theories. The influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.

• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.703-723
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• 2015

In this paper optimization of volume fraction distribution in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) and subjected to steady state thermal and mechanical loadings is considered. The finite element method with graded material properties within each element (graded finite elements) is used to model the structure. Volume fractions of constituent materials on a finite number of design points are taken as design variables and the volume fractions at any arbitrary point in the cylinder are obtained via cubic spline interpolation functions. The objective function selected as having the normalized effective stress equal to one at all points that leads to a uniform stress distribution in the structure. Genetic Algorithm jointed with interior penalty-function method for implementing constraints is effectively employed to find the global solution of the optimization problem. Obtained results indicates that by using the uniform distribution of normalized effective stress as objective function, considerably more efficient usage of materials can be achieved compared with the power law volume fraction distribution. Also considering uniform distribution of safety factor as design criteria instead of minimizing peak effective stress affects remarkably the optimum volume fractions.

• Steel and Composite Structures
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• v.29 no.3
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• pp.363-377
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• 2018

An efficient and free of shear locking finite element model is developed and employed to study free vibration of tapered bidirectional functionally graded material (BFGM) beams. The beam material is assumed to be formed from four distinct constituent materials whose volume fraction continuously varies along the longitudinal and thickness directions by power-law functions. The finite element formulation based on the first-order shear deformation theory is derived by using hierarchical functions to interpolate the displacement field. In order to improve efficiency and accuracy of the formulation, the shear strain is constrained to constant and the exact variation of the cross-sectional profile is employed to compute the element stiffness and mass matrices. A comprehensive parametric study is carried out to highlight the influence of the material distribution, the taper and aspect ratios as well as the boundary conditions on the vibration characteristics. Numerical investigation reveals that the proposed model is efficient, and it is capable to evaluate the natural frequencies of BFGM beams by using a small number of the elements. It is also shown that the effect of the taper ratio on the fundamental frequency of the BFGM beams is significantly influenced by the boundary conditions. The present results are of benefit to optimum design of tapered FGM beam structures.

• Geomechanics and Engineering
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• v.8 no.3
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• pp.305-321
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• 2015

In this paper, a new hyperbolic shear deformation plate theory based on neutral surface position is developed for the static analysis of functionally graded plates (FGPs). The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Based on the present new hyperbolic shear deformation plate theory and the neutral surface concept, the governing equations of equilibrium are derived from the principle of virtual displacements. Numerical illustrations concern flexural behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, aspect ratios and length to thickness ratios. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Advances in materials Research
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• v.5 no.4
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• pp.245-261
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• 2016

Thermo-mechanical buckling problem of functionally graded (FG) nanoplates supported by Pasternak elastic foundation subjected to linearly/non-linearly varying loadings is analyzed via the nonlocal elasticity theory. Two opposite edges of the nanoplate are subjected to the linear and nonlinear varying normal stresses. Elastic properties of nanoplate change in spatial coordinate based on a power-law form. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanoplate. The equations of motion for an embedded FG nanoplate are derived by using Hamilton principle and Eringen's nonlocal elasticity theory. Navier's method is presented to explore the influences of elastic foundation parameters, various thermal environments, small scale parameter, material composition and the plate geometrical parameters on buckling characteristics of the FG nanoplate. According to the numerical results, it is revealed that the proposed modeling can provide accurate results of the FG nanoplates as compared some cases in the literature. Numerical examples show that the buckling characteristics of the FG nanoplate are related to the material composition, temperature distribution, elastic foundation parameters, nonlocality effects and the different loading conditions.

• Structural Engineering and Mechanics
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• v.60 no.4
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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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• v.22 no.1
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• pp.91-112
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• 2016

In this paper, post-buckling behavior of sandwich plates with functionally graded (FG) face sheets under uniform temperature rise loading is examined based on both sinusoidal shear deformation theory and stress function. It is supposed that the sandwich plate is in contact with an elastic foundation during deformation, which acts in both compression and tension. Thermo-elastic non-homogeneous properties of FG layers change smoothly by the variation of power law within the thickness, and temperature dependency of material constituents is considered in the formulation. In the present development, Von Karman nonlinearity and initial geometrical imperfection of sandwich plate are also taken into account. By employing Galerkin method, analytical solutions of thermal buckling and post-buckling equilibrium paths for simply supported plates are determined. Numerical examples presented in the present study discuss the effects of gradient index, sandwich plate geometry, geometrical imperfection, temperature dependency, and the elastic foundation parameters.

• Smart Structures and Systems
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• v.26 no.5
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• pp.641-656
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• 2020

The finite element solutions of thermal buckling load values of the graded sandwich curved shell structure are reported in this research using a higher-order kinematic model including the shear deformation effect. The numerical buckling temperature has been computed using an in-house specialized code (MATLAB environment) prepared in the framework of the current mathematical formulation. In addition, the mathematical model includes the excess structural distortion under the influence of elevated environment via Green-Lagrange nonlinear strain. The corresponding eigenvalue equation has been solved to predict the critical buckling temperature of the graded sandwich structure. The numerical stability and the accuracy of the current solution have been confirmed by comparing with the available published results. Thereafter, the model is extended to bring out the influences of structural parameters i.e. the curvature ratio, core-face thickness ratio, support conditions, power-law indices and sandwich types on the thermal buckling behavior of graded sandwich curved shell panels.

• Composites Research
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• v.17 no.5
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• pp.78-84
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• 2004

In this paper, a study of thermal response of two types of functionally graded materials (FCM) plates composed of $\textrm{Al}_2\textrm{O}_3$ and Ti-6Al-4V is presented. The material properties of the functionally graded plates are assumed to vary continuously through the thickness of the plate according to a power law distribution of the volume fraction of the constituents. It is supposed that the top and bottom surfaces of the plate are heated and kept as constant thermal boundary conditions. The fundamental equations for rectangular plates of FGM are obtained using Hamilton's variational principles. The solution is obtained in terms of Navier Solution. The influence of volume fraction and temperature is studied on the static deflection and natural frequency of FCM plate.

• Steel and Composite Structures
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• v.37 no.5
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• pp.551-569
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• 2020

Vibration of vertically aligned-monolayered-nonuniform nanorods consist of functionally graded materials with elastic supports has not been investigated yet. To fill this gap, the problem is examined using the elasticity theories of Eringen and Gurtin-Murdoch. The geometrical and mechanical properties of the surface layer and the bulk are allowed to vary arbitrarily across the length. The nonlocal-surface energy-based governing equations are established using differential-type and integro-type formulations, and solved by employing the Galerkin method by exploiting admissible modes approach and element-free Galerkin (EFG). Through various comparison studies, the effectiveness of the EFG in capturing both nonlocal-differential/integro-based frequencies is proved. A constructive parametric study is also conducted, and the roles of nanorods' diameter, length, stiffness of both inter-rod's elastic layer and elastic supports, power-law index of both constituent materials and geometry, nonlocal and surface effects on the dominant frequencies are revealed.