• Coupled systems mechanics
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• 제8권3호
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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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• 제66권4호
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• pp.487-494
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• 2018

The purpose of the present paper is to study the bending and free vibration of Functionally Graded Material (FGM) plate using user-defined material subroutine on the finite element software ABAQUS. The FGM plate is simply supported and subjected to sinusoidal and uniform load. The Poisson's ratio is kept constant. The results obtained compared to those available in the literature show the convergence, the exactitude and the efficiency of the method used with various power index of the materials.

• Steel and Composite Structures
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• 제23권1호
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• pp.1-16
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• 2017

This paper is presented to solve the buckling problem of functionally graded truncated conical shells subjected to displacement-dependent pressure which remains normal to the shell middle surface throughout the deformation process by the semi-analytical finite strip method. Material properties are assumed to be temperature dependent, and 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 governing equations are derived based on first-order shear deformation theory which accounts for through thickness shear flexibility with Sanders-type of kinematic nonlinearity. The element linear and geometric stiffness matrices are obtained using virtual work expression for functionally graded materials. The load stiffness also called pressure stiffness matrix which accounts for variation of load direction is derived for each strip and after assembling, global load stiffness matrix of the shell which may be un-symmetric is formed. The un-symmetric parts which are due to load non-uniformity and unconstrained boundaries have been separated. A detailed parametric study is carried out to quantify the effects of power-law index of functional graded material and shell geometry variations on the difference between follower and non-follower lateral buckling pressures. The results indicate that considering pressure stiffness which arises from follower action of pressure causes considerable reduction in estimating buckling pressure.

• Steel and Composite Structures
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• 제19권6호
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• pp.1421-1447
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• 2015

In this paper, the effect of material-temperature dependent on the wave propagation of a cantilever beam composed of functionally graded material (FGM) under the effect of an impact force is investigated. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. Material properties of the beam are temperature-dependent and change in the thickness direction. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Euler-Bernoulli beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain and frequency domain by using Newmark average acceleration method. In order to establish the accuracy of the present formulation and results, the comparison study is performed with the published results available in the literature. Good agreement is observed. In the study, the effects of material distributions and temperature rising on the wave propagation of the FGM beam are investigated in detail.

• Structural Engineering and Mechanics
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• 제55권6호
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• pp.1087-1097
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• 2015

In this paper, the effect of functionally graded material (FGM) coatings on the fracture behavior of semi-elliptical cracks in cylinders is assessed. The objective is to calculate the stress intensity factor (SIF) of a longitudinal semi-elliptical crack on the wall of an aluminum cylinder with FGM coating. A three-dimensional finite element method (FEM) is used for constructing the mechanical models and analyzing the SIFs of cracks. The effect of many geometrical parameters such as relative depth, crack aspect ratio, FG coating thickness to liner thickness as well as the mechanical properties of the FG coating on the SIF of the cracks is discussed. For a special case, the validity of the FE model is examined. The results indicated that there is a particular crack aspect ratio in which the maximum value of SIFs changes from the deepest point to the surface point of the crack. Moreover, it was found that the SIFs decrease by increasing the thickness ratio of the cylinder. But, the cylinder length has no effect on the crack SIFs.

• Structural Engineering and Mechanics
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• 제61권4호
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• pp.551-561
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• 2017

As FGM (functionally graded material) bars which vibrate in axial or longitudinal direction have great potential for applications in diverse engineering fields, developing a reliable mathematical model that provides very reliable vibration and wave characteristics of a FGM axial bar, especially at high frequencies, has been an important research issue during last decades. Thus, as an extension of the previous works (Hong et al. 2014, Hong and Lee 2015) on three-layered FGM axial bars (hereafter called FGM bars), an enhanced spectral element model is proposed for a FGM bar model in which axial and radial displacements in the radial direction are treated more realistic by representing the inner FGM layer by multiple sub-layers. The accuracy and performance of the proposed enhanced spectral element model is evaluated by comparison with the solutions obtained by using the commercial finite element package ANSYS. The proposed enhanced spectral element model is also evaluated by comparison with the author's previous spectral element model. In addition, the effects of Poisson's ratio on the dynamics and wave characteristics in example FGM bars are numerically investigated.

• Computers and Concrete
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• 제25권4호
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• pp.283-291
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• 2020

The present paper researches post-buckling behaviors of geometrically imperfect concrete beam resting on elastic foundation reinforced with graphene oxide powders (GOPs) based on finite element method (FEM). Distribution of GOPs are considered as uniform and linearly graded through the thickness. Geometric imperfection is considered as first buckling mode shape of the beam, the GOP reinforced beam is rested in initial position. The material properties of GOP reinforced composite have been calculated via employment of Halpin-Tsai micromechanical scheme. The provided refined beam element verifies the shear deformation impacts needless of any shear correction coefficient. The post-buckling load-deflections relations have been calculated via solving the governing equations having cubic non-linearity implementing FEM. Obtained findings indicate the importance of GOP distributions, GOP weight fraction, matrix material, geometric imperfection, shear deformation and foundation parameters on nonlinear buckling behavior of GOP reinforced beam.

• Structural Engineering and Mechanics
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• 제58권3호
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• pp.423-442
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• 2016

This study considers a functionally graded (FG) elastic layer resting on homogeneous elastic substrate under axisymmetric static loading. The shear modulus of the FG layer is assumed to vary in an exponential form through the thickness. In solution, the FG layer is approximated into a multilayered medium consisting of thin homogeneous sublayers. Stiffness matrices for a typical homogeneous isotropic elastic layer and a half-space are first obtained by solving the axisymmetric elasticity equations with the aid of Hankel's transform. Global stiffness matrix is, then, assembled by considering the continuity conditions at the interfaces. Numerical results for the displacements and the stresses are obtained and compared with those of the classical elasticity and the finite element solutions. According to the results of the study, the approach employed here is accurate and efficient for elasto-static problems of FGMs.

• Structural Engineering and Mechanics
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• 제51권2호
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• pp.299-313
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• 2014

In the first part of this paper, the influences of some of crack parameters on natural frequencies of a cracked cantilever Functionally Graded Beam (FGB) are studied. A cantilever beam is modeled using Finite Element Method (FEM) and its natural frequencies are obtained for different conditions of cracks. Then effect of variation of depth and location of cracks on natural frequencies of FGB with single and multiple cracks are investigated. In the second part, two Multi-Layer Feed Forward (MLFF) Artificial Neural Networks (ANNs) are designed for prediction of FGB's Cracks' location and depth. Particle Swarm Optimization (PSO) and Back-Error Propagation (BEP) algorithms are applied for training ANNs. The accuracy of two training methods' results are investigated.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2004년도 춘계학술발표대회 논문집
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• pp.279-283
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• 2004

Thermal postbuckling and vibration analyses of functionally graded plates (FG plates) are performed. The nonlinear finite element equation based on the first-order shear deformation plate theory is formulated for the FG plate. The von Karman strain-displacement relation is used to account for the thermal large deflection. The incremental method considering the effect of the initial deflection and the initial stress is adopted for temperature-dependent material properties of functionally graded materials. The numerical result shows characteristics of the thermal postbuckling and vibration of FG plates in the pre- and post- buckled regions.