• Smart Structures and Systems
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• v.14 no.2
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• pp.225-246
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• 2014

The present paper develops piezo-thermo-elastic analysis of a thick spherical shell for generalized functionally graded piezoelectric material. The assumed structure is loaded under thermal, electrical and mechanical loads. The mechanical, thermal and electrical properties are graded along the radial direction based on a power function with three different non homogenous indexes. Primarily, the non homogenous heat transfer equation is solved by applying the general boundary conditions, individually. Substitution of stress, strain, electrical displacement and material properties in equilibrium and Maxwell equations present two non homogenous differential equation of order two. The main objective of the present study is to improve the relations between mechanical and electrical loads in hollow spherical shells especially for functionally graded piezoelectric materials. The obtained results can evaluate the effect of every non homogenous parameter on the mechanical and electrical components.

• Coupled systems mechanics
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• v.2 no.3
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• pp.215-230
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• 2013

This paper investigates the pull-in instability of functionally graded poly-SiGe micro-beams under the combined electrostatic and intermolecular forces and temperature change. The exponential distribution model and Voigt model are used to analyze the functionally graded materials (FGMs). Principle of virtual work is used to derive the nonlinear governing differential equation which is then solved using differential quadrature method (DQM). A parametric study is conducted to show the significant effects of material composition, geometric nonlinearity, temperature change and intermolecular Casimir force.

• Structural Engineering and Mechanics
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• v.71 no.1
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• pp.89-98
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• 2019

In this study, the mechanical bending behaviors of functionally graded porous nanobeams are investigated. Four types of porosity which are, the classical power porosity function, the symmetric with mid-plane cosine function, bottom surface distribution and top surface distribution are proposed in analysis of nanobeam for the first time. A comparison between four types of porosity are illustrated. The effect of nano-scale is described by the differential nonlocal continuum theory of Eringen by adding the length scale into the constitutive equations as a material parameter comprising information about nanoscopic forces and its interactions. The graded material is designated by a power function through the thickness of nanobeam. The beam is simply-supported and is assumed to be thin, and hence, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Numerical results show effects of porosity type, material graduation, and nanoscale parameters on the static deflection of nanobeam.

• Coupled systems mechanics
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• v.8 no.3
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• pp.259-271
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• 2019

This paper presents forced vibration analysis of sandwich deep beams made of functionally graded material (FGM) in face layers and a porous material in core layer. The FGM sandwich deep beam is subjected to a harmonic dynamic load. The FGM in the face layer is graded though the layer thickness. In order to get more realistic result for the deep beam problem, the plane solid continua is used in the modeling of The FGM sandwich deep beam. The equations of the problem are derived based the Hamilton procedure and solved by using the finite element method. The novelty in this paper is to investigate the dynamic responses of sandwich deep beams made of FGM and porous material by using the plane solid continua. In the numerical results, the effects of different material distributions, porosity coefficient, geometric and dynamic parameters on the dynamic responses of the FGM sandwich deep beam are investigated and discussed.

• Structural Engineering and Mechanics
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• v.77 no.6
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• pp.797-807
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• 2021

A new simple solution for critical buckling of FG sandwich plates under axial and biaxial loads is presented using new modified power-law formulations. Both even and uneven distributions of porosity are taken into account in this study. Material properties of the sandwich plate faces are assumed to be graded in the thickness direction according to a modified power-law distribution in terms of the volume fractions of the constituents. Equilibrium and stability equations of FG sandwich plate with various boundary conditions are derived using the higher-order shear deformation plate theory. The results reveal that the distribution shape of the porosity, the gradient index, loading type and functionally graded layers thickness have significant influence on the buckling response of functionally graded sandwich plates.

• Geomechanics and Engineering
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• v.31 no.3
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• pp.329-337
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• 2022

In this paper, the thermal post-buckling characteristics of functionally graded (FG) pipes with initial geometric imperfection are studied. Considering the influence of initial geometric defects, temperature and geometric nonlinearity, Euler-Lagrange principle is used to derive the nonlinear governing equations of the FG pipes. Considering three different boundary conditions, the two-step perturbation method is used to solve the nonlinear governing equations, and the expressions of thermal post-buckling responses are also obtained. Finally, the correctness of this paper is verified by numerical analyses, and the effects of initial geometric defects, functional graded index, elastic foundation, porosity, thickness of pipe and boundary conditions on thermal post-buckling response are analyzed. It is found that, bifurcation buckling exists for the pipes without initial geometric imperfection. In contrast, there is no bifurcation buckling phenomenon for the pipes with initial geometric imperfection. Meanwhile, the elastic stiffness can significantly improve thermal post-buckling load and thermal post-buckling strength. The larger the porosity, the greater the thermal buckling load and the thermal buckling strength.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.11a
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• pp.443-444
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• 2010

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.1
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• pp.13-20
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• 2008

Graded layers in which two different constituent particles are mixed are inserted into functionally graded material such that the volume fractions of constituent particles vary continuously and functionally over the entire material domain. The material properties of this dual-phase graded region, which is essential for the numerical analysis of the thermo-mechanical behavior of FGM, have been predicted by traditional homogenization methods. But, these methods are limited to predict the global equivalent material properties of FGMs because the detailed geometry information such as the particel shape and the dispersion structure is not considered. In this context, this study intends to investigate the characteristics of these homogenization methods through the finite element analysis utilizing the discrete micromechanics models of the graded layer, for various volume fractions and external loading conditions.

• Steel and Composite Structures
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• v.14 no.1
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• pp.85-104
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• 2013

The present work deals with the thermomechanical bending response of functionally graded plates resting on Winkler-Pasternak elastic foundations. Theoretical formulations are based on a recently developed refined trigonometric shear deformation theory (RTSDT). The theory accounts for trigonometric distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the present refined trigonometric shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modelled as two-parameter Pasternak foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermomechanical behavior of functionally graded plates. It can be concluded that the proposed theory is accurate and efficient in predicting the thermomechanical bending response of functionally graded plates.

• Structural Engineering and Mechanics
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• v.66 no.5
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• pp.557-568
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• 2018

An investigation is made in the present work on the post-buckling and geometrically nonlinear behaviors of moderately thick perfect and imperfect rectangular plates made-up of functionally graded materials. Spectral collocation approach based on Legendre basis functions is developed to analyze the functionally graded plates while they are subjected to end-shortening strain. The material properties in this study are varied through the thickness according to the simple power law distribution. The fundamental equations for moderately thick rectangular plates are derived using first order shear deformation plate theory and taking into account both geometric nonlinearity and initial geometric imperfections. In the current study, the domain of interest is discretized with Legendre-Gauss-Lobatto nodes. The equilibrium equations will be obtained by discretizing the Von-Karman's equilibrium equations and also boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Due to effect of geometric nonlinearity, the final set of equilibrium equations is nonlinear and therefore the quadratic extrapolation technique is used to solve them. Since the number of equations in this approach will always be more than the number of unknown coefficients, the least squares technique will be used. Finally, the effects of boundary conditions, initial geometric imperfection and material properties are investigated and discussed to demonstrate the validity and capability of proposed method.