• Structural Engineering and Mechanics
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• v.23 no.1
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• pp.97-113
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• 2006

A simply supported hybrid plate consisting of top and bottom functionally graded elastic layers and an intermediate actuating or sensing homogeneous piezoelectric layer is investigated by an elasticity (piezoelasticity) method, which is based on state space formulations. The general spring layer model is adopted to consider the effect of bonding adhesives between the piezoelectric layer and the two functionally graded ones. The two functionally graded layers are inhomogeneous along the thickness direction, which are approached by laminate models. The effect of interlaminar bonding imperfections on the static bending and free vibration of the smart plate is discussed in the numerical examples.

• Computers and Concrete
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• v.33 no.1
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• pp.13-25
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• 2024

In this study, contact analysis in a functionally graded (FG) layer loaded with two circular punches is solved using the finite element method (FEM). The problem is consisted of a functionally graded layer that resting on an elastic semi-infinite plane and is loaded with two rigid punches of circular geometry. External loads P and Q are transferred to the layer via two rigid punches. The finite element model of the functionally graded layer is created using the ANSYS package program and a 2-dimensional analysis of the problem is analyzed. The contact lengths, obtained as a result of the analysis are compared with the analytical solution in the literature. In the study, the effects of parameters such as distances between punches, loads, inhomogenity parameter on contact zones, initial separation loads and distances, normal stresses, stresses across depth and contact stresses are investigated. As a result, in this study, it can be said that the magnitude of the stresses occurring in the FG layer is less than the homogeneous layer, therefore the life of FG materials will be longer than the homogeneous layer. When the distance between the punches is 2.25, the initial separation distance is 6.98, and when the distance between the punches is 4, the initial separation distance decreases to 6.10. In addition, when the load increased in the second punch, the initial separation load decreased from 55 to 18. The obtained results are presented in the form of graphs and tables.

• Steel and Composite Structures
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• v.15 no.2
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• pp.221-245
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• 2013

This paper presents an analytical solution to the thermomechanical bending analysis of functionally graded sandwich plates by using a new hyperbolic shear deformation theory in which the stretching effect is included. The modulus of elasticity of plates is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. The effects of functionally graded material (FGM) layer thickness, volume fraction index, layer thickness ratio, thickness ratio and aspect ratio on the deflections and stresses of functionally graded sandwich plates are investigated.

• Structural Engineering and Mechanics
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• v.51 no.4
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• pp.627-641
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• 2014

Functionally graded steels (FGSs) are a family of functionally graded materials (FGMs) consisting of ferrite (${\alpha}$), austenite (${\gamma}$), bainite (${\beta}$) and martensite (M) phases placed on each other in different configurations and produced via electroslag remelting (ESR). In this research, the flow stress of dual layer austenitic-martensitic functionally graded steels under hot deformation loading has been modeled considering the constitutive equations which describe the continuous effect of temperature and strain rate on the flow stress. The mechanism-based strain gradient plasticity theory is used here to determine the position of each layer considering the relationship between the hardness of the layer and the composite dislocation density profile. Then, the released energy of each layer under a specified loading condition (temperature and strain rate) is related to the dislocation density utilizing the mechanism-based strain gradient plasticity theory. The flow stress of the considered FGS is obtained by using the appropriate coefficients in the constitutive equations of each layer. Finally, the theoretical model is compared with the experimental results measured in the temperature range $1000-1200^{\circ}C$ and strain rate 0.01-1 s-1 and a sound agreement is found.

• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.727-740
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• 2006

A simple plane-strain solution is derived in this paper for the functionally graded multilayered isotropic elastic cylinder under static deformation. The solution is obtained using method of separation of variables and is expressed in terms of the summation of the Fourier series in the circumferential direction. While the solution for order n = 0 corresponds to the axisymmetric deformation, that for n = 2 includes the special deformation frequently utilized in the upper and lower bounds analysis. Numerical results for a three-phase cylinder with a middle functionally graded layer are presented for both axisymmetric (n = 0) and general (n = 2) deformations, under either the traction or displacement boundary conditions on the surface of the layered cylinder. The solution to the general deformation case (n = 2) is further utilized for the first time to find the upper and lower bounds of the effective shear modulus of the layered cylinder with a functionally graded middle layer. These results could be useful in the future study of cylindrical composites where FGMs and/or multilayers are involved.

• Structural Engineering and Mechanics
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• v.56 no.6
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• pp.1003-1020
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• 2015

In this study, free vibration analysis of an edge cracked multilayered symmetric sandwich beams made of functionally graded materials are investigated. Modelling of the cracked structure is based on the linear elastic fracture mechanics theory. Material properties of the functionally graded beams change in the thickness direction according to the power and exponential laws. To represent functionally graded symmetric sandwich beams more realistic, fifty layered beam is considered. Composition of each layer is different although each layer is isotropic and homogeneous. The considered problem is carried out within the Timoshenko first order shear deformation beam theory by using finite element method. A MATLAB code developed to calculate natural frequencies for clamped and simply supported conditions. The obtained results are compared with published studies and excellent agreement is observed. In the study, the effects of crack location, depth of the crack, power law index and slenderness ratio on the natural frequencies are investigated.

• Structural Engineering and Mechanics
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• v.78 no.2
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• pp.135-143
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• 2021

In this study, continuous contact problem in the functionally graded (FG) layer loaded with a FG flat punch resting on the elastic semi-infinite plane was analyzed by the finite element method (FEM). It was assumed that the shear modulus and density of the layer and punch varied according to exponentially throughout their depth. FG layer's weight was included to the problem and additionally all surfaces were considered as frictionless. Analysis of FG materials was performed with a special macro which was added to the ANSYS program. Firstly, the shear modulus of the punch was considered to be very rigid and the results of initial separation load (λcr) and distance (xcr) were compared with the analytical solution. Afterwards, results obtained from the contact analysis made according to the inhomogeneity parameters (β, γ) between FG punch-FG layer which had been unprecedented in the literature were discussed. As a result, FG punch's stress values at the punch edges where stress accumulations occurred were found to be smaller than the rigid punch. The security of the structure, longer life of the material and ease of production are directly related to the reduction of the stress values. The results obtained in this study are important in this respect. Also this work is the first study that investigates the effect of FG punch on the FG layer.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2005.11a
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• pp.66-69
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• 2005

Mechanical strength of functionally graded composite plates that composed of ceramic, functionally graded material and metal layers is investigated using 3-D finite element method. In FGM layer, material properties are assumed to be varied continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of a ceramic and metal. The 3-D finite element model is adopted by using an IS-node solid element to analyze more accurately the variation of material properties in the thickness direction. Numerical results are compared with those of the previous works. In addition, the displacements, the tensile stresses and the compressive stresses are analyzed for the variation of FGM thickness ratio and volume fraction distribution.Mechanical strength of functionally graded composite plates that composed of ceramic, functionally graded material and metal layers is investigated using 3-D finite element method. In FGM layer, material properties are assumed to be varied continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of a ceramic and metal. The 3-D finite element model is adopted by using an IS-node solid element to analyze more accurately the variation of material properties in the thickness direction. Numerical results are compared with those of the previous works. In addition, the displacements, the tensile stresses and the compressive stresses are analyzed for the variation of FGM thickness ratio and volume fraction distribution.

• Journal of Mechanical Science and Technology
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• v.14 no.3
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• pp.298-305
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• 2000

The functionally graded material (FGM) is the new concept for a heat resisting material. FGM consists of ceramics on one side and metal on the other. A composition and microstructure of an intermediate layer change continuously from ceramics to metal at the micron level. This study is carried out to analyze the thermal shock characteristics of functionally graded PSZ/ metal composites. Heat-resistant property was evaluated by gas burner heating test using $C_2H_2/O_2$ combustion flame. The ceramic surface was heated with burner flame and the bottom surface cooled with water flow. Also, the composition profile and the thickness of the graded layer were varied to study the thermo mechanical response. Furthermore, this study carried out the thermal stress analysis to investigate the thermal characteristics by the finite element method. Acoustic emission (AE) monitoring was performed to detect the microfracture process in a thermal shock test.

• Steel and Composite Structures
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• v.22 no.5
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• pp.975-999
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• 2016

This work investigates a thermomechanical bending analysis of functionally graded sandwich plates by proposing a novel quasi-3D type higher order shear deformation theory (HSDT). The mathematical model introduces only 5 variables as the first order shear deformation theory (FSDT). Unlike the conventional HSDT, the present one presents a novel displacement field which includes undetermined integral variables. The mechanical properties of functionally graded layers of the plate are supposed to change in the thickness direction according to a power law distribution. The core layer is still homogeneous and made of an isotropic ceramic material. The governing equations for the thermomechanical bending investigation are obtained through the principle of virtual work and solved via Navier-type method. Interesting results are determined and compared with quasi-3D and 2D HSDTs. The influences of functionally graded material (FGM) layer thickness, power law index, layer thickness ratio, thickness ratio and aspect ratio on the deflections and stresses of functionally graded sandwich plates are discussed.