• Steel and Composite Structures
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• v.46 no.2
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• pp.263-277
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• 2023

Free vibration analysis of multi-directional porous functionally graded (FG) sandwich plate has been performed for two cases namely: FG skin with homogeneous core and FG core with homogeneous skin. Hamilton's principle was employed and the solution was obtained using Navier's technique. This theory imposes traction-free boundary conditions on the surfaces and does not require shear correction factors. The results obtained are validated with those available in the literature. The composition of metal-ceramic-based functionally graded material (FGM) changes in longitudinal and transverse directions according to the power law. Imperfections in the functionally graded material introduced during the fabrication process were modeled with different porosity laws such as evenly, unevenly distributed, and logarithmic uneven distributions. The effect of porosity laws and geometry parameters on the natural frequency was investigated. On comparing the natural frequency of two cases for perfect and imperfect sandwich plates a reverse trend in natural frequency result was seen. The finding shows a multidirectional functionally graded structures perform better compared to uni-directional gradation. Hence, critical grading parameters and imperfection types have been identified which will guide experimentalists and researchers in selecting fabrication routes for improving the performance of such structures.

• Structural Engineering and Mechanics
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• v.89 no.1
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• pp.13-22
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• 2024

The nonlinear snap-through buckling of functionally graded (FG) carbon nanotube reinforced composite (CNTRC) curved tubes is analytically investigated in this research. It is assumed that the FG-CNTRC curved tube is supported on a three-parameter nonlinear elastic foundation and is subjected to the uniformly distributed pressure and thermal loads. Properties of the curved nanocomposite tube are distributed across the radius of the pipe and are given by means of a refined rule of mixtures approach. It is also assumed that all thermomechanical properties of the nanocomposite tube are temperature-dependent. The governing equations of the curved tube are obtained using a higher-order shear deformation theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the tube. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large deflection in the curved tube. Equations of motion are solved using the two-step perturbation technique for nanocomposite curved tubes which are simply-supported and clamped. Closed-form expressions are provided to estimate the snap-buckling resistance of FG-CNTRC curved pipes rested on nonlinear elastic foundation in thermal environment. Numerical results are given to explore the effects of the distribution pattern and volume fraction of CNTs, thermal field, foundation stiffnesses, and geometrical parameters on the instability of the curved nanocomposite tube.

• Structural Engineering and Mechanics
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• v.75 no.2
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• pp.193-209
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• 2020

This paper presents a new hyperbolic shear deformation plate theory including the stretching effect for free vibration of the simply supported functionally graded plates in thermal environments. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. This theory has only five unknowns, which is even less than the other shear and normal deformation theories. The present one has a new displacement field which introduces undetermined integral variables. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume power laws of the constituents. The equation of motion of the vibrated plate obtained via the classical Hamilton's principle and solved using Navier's steps. The accuracy of the proposed solution is checked by comparing the present results with those available in existing literature. The effects of the temperature field, volume fraction index of functionally graded material, side-to-thickness ratio on free vibration responses of the functionally graded plates are investigated. It can be concluded that the present theory is not only accurate but also simple in predicting the natural frequencies of functionally graded plates with stretching effect in thermal environments.

• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.317-328
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• 2018

In this paper, a new refined quasi-three-dimensional (3D) shear deformation theory for the bending analysis of functionally graded plate is presented. The number of unknown functions involved in this theory is only four against five or more in the case of the other shear and normal deformation theories. Due to its quasi-3D nature, the stretching effect is taken into account in the formulation of governing equations. In addition, the effect of different micromechanical models on the bending response of these plates is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG plates whose properties vary continuously across the thickness according to a simple power law. The present theory accounts for both shear deformation and thickness stretching effects by a parabolic variation of displacements across the thickness, and the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The problem is solved for a plate simply supported on its edges and the Navier solution is used. The results of the present method are compared with others from the literature where a good agreement has been found. A detailed parametric study is presented to show the effect of different micromechanical models on the flexural response of a simply supported FG plates.

• Steel and Composite Structures
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• v.25 no.2
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• pp.157-175
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• 2017

The novelty of this work is the use of a new displacement field that includes undetermined integral terms for analyzing thermal buckling response of functionally graded (FG) sandwich plates. The proposed kinematic uses only four variables, which is even less than the first shear deformation theory (FSDT) and the conventional higher shear deformation theories (HSDTs). The theory considers a trigonometric variation of transverse shear stress and verifies the traction free boundary conditions without employing the shear correction factors. Material properties of the sandwich plate faces are considered to be graded in the thickness direction according to a simple power-law variation in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are assumed as uniform, linear and non-linear temperature rises within the thickness direction. An energy based variational principle is employed to derive the governing equations as an eigenvalue problem. The validation of the present work is checked by comparing the obtained results the available ones in the literature. The influences of aspect and thickness ratios, material index, loading type, and sandwich plate type on the critical buckling are all discussed.

• Coupled systems mechanics
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• v.8 no.5
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• pp.439-457
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• 2019

In this paper, a new application of a four variable refined plate theory to analyze the nonlinear bending of functionally graded plates exposed to thermo-mechanical loadings, is presented. This recent theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces, and similarly, the shear components do not contribute toward bending moments. The derived transverse shear strains has a quadratic variation across the thickness that satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. The solutions are achieved by minimizing the total potential energy. The non-linear strain-displacement relations in the von Karman sense are used to derive the effect of geometric non-linearity. It is concluded that the proposed theory is accurate and simple in solving the nonlinear bending behavior of functionally graded plates.

• Earthquakes and Structures
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• v.22 no.5
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• pp.447-460
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• 2022

In this article, wave propagation in functional gradation plates (FG) resting on an elastic foundation with two parameters is studied using a new quasi-three-dimensional (3D) higher shear deformation theory (HSDT). The new qausi-3D HSOT has only five variables in fields displacement, which means has few numbers of unknowns compared with others quasi-3D. This higher shear deformation theory (HSDT) includes shear deformation and effect stretching with satisfying the boundary conditions of zero traction on the surfaces of the FG plate without the need for shear correction factors. The FG plates are considered to rest on the Winkler layer, which is interconnected with a Pasternak shear layer. The properties of the material graded for the plates are supposed to vary smoothly, with the power and the exponential law, in the z-direction. By based on Hamilton's principle, we derive the governing equations of FG plates resting on an elastic foundation, which are then solved analytically to obtain the dispersion relations. Numerical results are presented in the form of graphs and tables to demonstrate the effectiveness of the current quasi-3D theory and to analyze the effect of the elastic foundation on wave propagation in FG plates.

• Steel and Composite Structures
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• v.43 no.6
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• pp.821-837
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• 2022

This research is devoted to study the effects of humidity and temperature on the bending behavior of functionally graded (FG) ceramic-metal porous plates resting on Pasternak elastic foundation using a quasi-3D hyperbolic shear deformation theory developed recently. The present plate theory with only four unknowns, takes into account both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the functionally graded plate without using shear correction factors. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. The governing differential equations are obtained using the "principle of virtual work". Analytically, the Navier method is used to solve the equations that govern a simply supported FG porous plate. The obtained results are checked by comparing the results determined for the perfect and imperfect FG plates with those available in the scientific literature. Effects due to material index, porosity factors, moisture and thermal loads, foundation rigidities, geometric ratios on the FG porous plate are all examined. Finally, this research will help us to design advanced functionally graded materials to ensure better durability and efficiency for hygro-thermal environments.

• Geomechanics and Engineering
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• v.34 no.3
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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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• v.89 no.3
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• pp.225-238
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• 2024

In this paper, a quasi-3D hyperbolic shear deformation theory for the bending responses of a functionally graded (FG) porous micro-beam is based on a modified couple stress theory requiring only one material length scale parameter that can capture the size influence. The model proposed accounts for both shear and normal deformation effects through an illustrative variation of all displacements across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the micro-beam. The effective material properties of the functionally graded micro-beam are assumed to vary in the thickness direction and are estimated using the homogenization method of power law distribution, which is modified to approximate the porous material properties with even and uneven distributions of porosity phases. The equilibrium equations are obtained using the virtual work principle and solved using Navier's technique. The validity of the derived formulation is established by comparing it with the ones available in the literature. Numerical examples are presented to investigate the influences of the power law index, material length scale parameter, beam thickness, and shear and normal deformation effects on the mechanical characteristics of the FG micro-beam. The results demonstrate that the inclusion of the size effects increases the microbeams stiffness, which consequently leads to a reduction in deflections. In contrast, the shear and normal deformation effects are just the opposite.