• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.14 no.11
• /
• pp.5930-5938
• /
• 2013

The sigmoid functionally graded mateiral(S-FGM) theory is reformulated using the nonlocal elatictiry of Erigen. The equation of equilibrium of the nonlocal elasticity are derived. This theory has ability to capture the both small scale effects and sigmoid function in terms of the volume fraction of the constituents for material properties through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported boundary conditions. Numerical solutions of biaxial buckling of nano-scale plates are presented using this theory to illustrate the effects of nonlocal theory and power law index of sigmoid function on buckling load. The relations between nonlocal and local theories are discussed by numerical results. Further, effects of (i) power law index, (ii) length, (iii) nonlocal parameter, (iv) aspect ratio and (v) mode number on nondimensional biaxial buckling load are studied. To validate the present solutions, the reference solutions are discussed.

• Structural Engineering and Mechanics
• /
• v.81 no.2
• /
• pp.179-194
• /
• 2022

The bending, buckling and free vibration responses of functionally graded material (FGM) beams are investigated semi-analytically by the scaled boundary finite element method (SBFEM) in this paper. In the concepts of the SBFEM, the dimension of computational domain can be reduced by one, therefore only the axial dimension of the beam is discretized using the higher order spectral element, which reduces the amount of calculation and greatly improves the calculation efficiency. The governing equation of FGM beams is derived in detail by the means of the principle of virtual work. Compared with the higher-order beam theory, fewer parameters and simpler control equations are used. And the governing equation is transformed into a first-order ordinary differential equation by introducing intermediate variables. Analytical solutions of the governing equation can be obtained by pade series expansion in the direction of thickness. Numerical example are compared with the numerical solutions provided by the previous researchers to verify the accuracy and applicability of the proposed method. The results show that the proposed formulations can quickly converge to the reference solutions by increasing the order of higher order spectral elements, and high accuracy can be achieved by using a small number of the elements. In addition, the influence of the structural sizes, material properties and boundary conditions on the mechanical behaviors of FG beams subjected to different load types is discussed.

• Advances in concrete construction
• /
• v.9 no.6
• /
• pp.569-576
• /
• 2020

Employment of the wave propagation approach with the combination of Pasternak foundation equation gives birth to the shell frequency equation. Mathematically, the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. A cylindrical shell is placed on the elastic foundation of Pasternak. For isotropic materials, the physical properties are same everywhere, whereas the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. The influence of the elastic foundation, wave number, length and height-to-radius ratios is investigated with different boundary conditions. The frequencies of length-to-radius and height-to-radius ratio are counter part of each other. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down for the variations of wave number. It is found that due to inducting the elastic foundation of Pasternak, the frequencies increases. It is also exhibited that the effect of frequencies is investigated by varying the surfaces with stainless steel and nickel as a constituent material. MATLAB software is utilized for the vibration of functionally graded cylindrical shell with elastic foundation of Pasternak and the results are verified with the open literature.

• Advances in materials Research
• /
• v.8 no.3
• /
• pp.155-177
• /
• 2019

In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate with new definition of porosity distribution taking into account composition and the scheme of the sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Material properties of FGM layers are assumed to vary continuously across the plate thickness according to either power-law or sigmoid function in terms of the volume fractions of the constituents. The face layers are considered to be FG across each face thickness while the core is made of a ceramic homogeneous layer. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinusoidal loading has been obtained by using the Navier method. Numerical results are presented to show the effect of the material distribution, the sandwich plate geometry and the porosity on the deflections and stresses of FG sandwich plates. The validity of the present theory is investigated by comparing some of the present results with other published results.

• Advances in materials Research
• /
• v.7 no.2
• /
• pp.83-103
• /
• 2018

In this paper, the problem of interfacial stresses in damaged reinforced concrete beams strengthened with bonded prestressed functionally graded material plate and subjected to a uniformly distributed load, arbitrarily positioned single point load, or two symmetric point loads is developed using linear elastic theory. The adopted model takes into account the adherend shear deformations by assuming a linear shear stress through the depth of the damaged RC beam. This solution is intended for application to beams made of all kinds of materials bonded with a thin FGM plate. The results show that there exists a high concentration of both shear and normal stress at the ends of the functionally graded material plate, which might result in premature failure of the strengthening scheme at these locations. Finally, numerical comparisons between the existing solutions and the present new solution enable a clear appreciation of the effects of various parameters of the beams on the distributions of the interfacial stresses.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.15 no.2
• /
• pp.1109-1117
• /
• 2014

We study free vibration analysis of sigmoid functionally graded materials(S-FGM) nano-scale plates, using a nonlocal elasticity theory of Eringen in this paper. This theory has ability to capture the both small scale effects and sigmoid function in terms of the volume fraction of the constituents for material properties through the plate thickness. Numerical solutions of S-FGM nano-scale plate are presented using this theory to illustrate the effect of nonlocal theory on natural frequency of the S-FGM nano-scale plates. The relations between nonlocal and local theories are discussed by numerical results. Further, effects of (i) power law index (ii) nonlocal parameters, (iii) elastic modulus ratio and (iv) thickness and aspect ratios on nondimensional frequencies are investigated. In order to validate the present solutions, the reference solutions are compared and discussed. The results of S-FGM nano-scale plates using the nonlocal theory may be the benchmark test for the free vibration analysis.

• Structural Engineering and Mechanics
• /
• v.85 no.2
• /
• pp.233-246
• /
• 2023

Bending and buckling analysis of multi-directional porous functionally graded sandwich plate has been performed for two cases namely: FG skin with homogeneous core and FG core with homogeneous skin. The principle of virtual displacements 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 validation of the present study has been performed with those available in the literature. The composition of metal-ceramic-based FGM changes in longitudinal and transverse directions according to the power law. Different porosity laws, such as uniform distribution, unevenly and logarithmically uneven distributions were used to mimic the imperfections in the functionally graded material that were introduced during the fabrication process. Several sandwich plates schemes were studied based on the plate's symmetry and the thickness of each layer. The effects of grading parameters and porosity laws on the bending and buckling of sandwich plates were examined.

• Geomechanics and Engineering
• /
• v.16 no.1
• /
• pp.1-9
• /
• 2018

In this paper an efficient and simple refined shear deformation theory is presented for the free vibration of Functionally Graded Plates Under Various Boundary Conditions. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. The plates are considered of the type having two opposite sides simply-supported, and the two other sides having combinations of simply-supported, clamped, and free boundary conditions. The mechanical properties of functionally graded material are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion are derived using Hamilton's principle. The results of this theory are compared with those of other shear deformation theories. Various numerical results including the effect of boundary conditions, power-law index, plate aspect ratio, and side-to-thickness ratio on the free vibration of FGM plates are presented.

• Nuclear Engineering and Technology
• /
• v.54 no.12
• /
• pp.4491-4498
• /
• 2022

The thermal stress between W plasma-facing material (PFM) and Cu heat sink in fusion reactors can be significantly reduced by using a W-Cu functionally graded material (W-Cu FGM) interlayer. However, there is still considerable stress at the joining interface between W and W-Cu FGM in the W/W-Cu FGM/Cu portions. In this work, we fabricate W skeletons with continuous gradients in porosity by a modified sedimentation method. Sintering densification behavior and pore characteristics of the sedimented W skeletons at different sintering temperatures were investigated. After Cu infiltration, the final W-Cu FGM was obtained. The results indicate that the pore size and porosity in the W skeleton decrease gradually with the increase of sintering temperature, but the increase of skeleton sintering temperature does not reduce the gradient range of composition distribution of the final prepared W-Cu FGM. And W-Cu FGM with composition distribution from pure W to W-20.5wt.% Cu layer across the section was successfully obtained. The thickness of the pure W layer is about one-fifth of the whole sample thickness. In addition, the prepared W-Cu FGM has a relative density of 94.5 % and thermal conductivity of 185 W/(m·K). The W-Cu FGM prepared in this work may provide a good solution to alleviate the thermal stress between W PFM and Cu heat sink in the fusion reactors.

• Structural Engineering and Mechanics
• /
• v.67 no.1
• /
• pp.33-43
• /
• 2018

The dynamic output-feedback robust control method based on linear matrix inequality (LMI) method is presented for suppressing vibration response of a functionally graded material (FGM) beam with piezoelectric actuator/sensor layers in this paper. Based on the reduced model obtained by using direct mode truncation, the linear fractional state space representation of a piezoelectric FGM beam with material properties varying through the thickness is developed by considering both the inherent uncertainties in constitution material properties as well as material distribution and the model error due to mode truncation. The dynamic output-feedback robust H-infinity control law is implemented to suppress the vibration response of the piezoelectric FGM beam and the LMI method is utilized to convert control problem into convex optimization problem for efficient computation. In numerical studies, the flexural vibration control of a cantilever piezoelectric FGM beam is considered to investigate the accuracy and efficiency of the proposed control method. Compared with the efficient linear quadratic regulator (LQR) widely employed in literatures, the proposed robust control method requires less control voltage applied to the piezoelectric actuator in the case of same control performance for the controlled closed-loop system.