• Structural Engineering and Mechanics
• /
• 제65권5호
• /
• pp.523-533
• /
• 2018

In this study, the dynamic response of a functionally graded material (FGM) circular plate in contact with incompressible fluid under the harmonic load is investigated. Analysis of the plate is based on First-order Shear Deformation Plate Theory (FSDT). The governing equation of the oscillatory behavior of the fluid is obtained by solving Laplace equation and satisfying its boundary conditions. A new set of admissible functions, which satisfy both geometrical and natural boundary conditions, are developed for the free vibration analysis of moderately thick circular plate. The Chebyshev-Ritz Method is employed together with this set of admissible functions to determine the vibrational behaviors. The modal superposition approach is used to determine the dynamic response of the plate exposed to harmonic loading. Numerical results of the force vibrations and the effects of the different geometrical parameters on the dynamic response of the plate are investigated. Finally, the results of this research in the limit case are compared and validated with the results of other researches and finite element model (FEM).

• 한국재료학회:학술대회논문집
• /
• 한국재료학회 2008년도 춘계학술발표대회 및 제14회 신소재 심포지엄
• /
• pp.42.2-42.2
• /
• 2008

• Structural Engineering and Mechanics
• /
• 제49권5호
• /
• pp.569-595
• /
• 2014

In this paper, a novel semi-energy finite strip method (FSM) is developed based on the concept of first order shear deformation theory (FSDT) in order to attempt the post-buckling solution for thin and relatively thick functionally graded (FG) plates under uniform end-shortening. In order to study the effects of through-the-thickness shear stresses on the post-buckling behavior of FG plates, two previously developed finite strip methods, i.e., semi-energy FSM based on the concept of classical laminated plate theory (CLPT) and a CLPT full-energy FSM, are also implemented. Moreover, the effects of aspect ratio on initial post-buckling stiffness of FG rectangular plates are studied. It has been shown that the variation of the ratio of initial post-buckling stiffness to pre-buckling stiffness ($S^*/S$) with respect to aspects ratios is quite independent of volume fractions of constituents in thin FG plates. It has also been seen that the universal curve representing the variation of ($S^*/S$) with aspect ratio of a FG plate demonstrate a saw shape curve. Moreover, it is revealed that for the thin FG plates in contrast to relatively thick plates, the variations of non-dimensional load versus end-shortening is independent of ceramic-metal volume fraction index. This means that the post-buckling behavior of thin FG plates and the thin pure isotropic plates is similar. The results are discussed in detail and compared with those obtained from finite element method (FEM) of analysis. The study of the results may have a great influence in design of FG plates encountering post-buckling behavior.

• Advances in nano research
• /
• 제14권4호
• /
• pp.375-389
• /
• 2023

In this study, free vibration analysis of functionally graded (FG) porous truncated conical shell panels reinforced by graphene platelets (GPLs) has been investigated for the first time. Additionally, the effect of three different types of porosity distribution and five different types of GPLs patterns on dynamic response of the shell are also studied. Halpin-Tsai micromechanical model and Voigt's rule are used to determine Young modulus, shear modulus and Poisson's ratio with mass densities of the shell, respectively. The main novelties of present study are: applying 3D elasticity theory and the finite element method in conjunction with Rayleigh-Ritz method to give more accurate results unlike other simplified shell theories, and also presenting a general 3D solution in cylindrical coordinate system that can be used for analyses of different structures such as circular, annular and annular sector plates, cylindrical shells and panels, and conical shells and panels. A convergence study is performed to justify the correctness of the obtained solution and numerical results. The impact of porosity and GPLs patterns, the volume of voids, the weight fraction of graphene nanofillers, semi vertex and span angles of the cone, and various boundary conditions on natural frequencies of the functionally graded panel have been comprehensively studied and discussed. The results show that the most important parameter on dynamic response of FG porous truncated conical panel is the weight fraction of nanofiller and adding 1% weight fraction of nanofiller could increase 57% approximately the amounts of natural frequencies of the shell. Moreover, the porosity distribution has great effect on the value of natural frequency of structure rather than the porosity coefficient.

• Computers and Concrete
• /
• 제27권3호
• /
• pp.199-210
• /
• 2021

The aim of this paper was to examine the continuous and discontinuous contact problems between the functionally graded (FG) layer pressed with a uniformly distributed load and homogeneous half plane using an analytical method and FEM. The FG layer is made of non-homogeneous material with an isotropic stress-strain law with exponentially varying properties. It is assumed that the contact at the FG layer-half plane interface is frictionless, and only the normal tractions can be transmitted along the contacted regions. The body force of the FG layer is considered in the study. The FG layer was positioned on the homogeneous half plane without any bonds. Thus, if the external load was smaller than a certain critical value, the contact between the FG layer and half plane would be continuous. However, when the external load exceeded the critical value, there was a separation between the FG layer and half plane on the finite region, as discontinuous contact. Therefore, there have been some steps taken in this study. Firstly, an analytical solution for continuous and discontinuous contact cases of the problem has been realized using the theory of elasticity and Fourier integral transform techniques. Then, the problem modeled and two-dimensional analysis was carried out by using ANSYS package program based on FEM. Numerical results for initial separation distance and contact stress distributions between the FG layer and homogeneous half plane for continuous contact case; the start and end points of separation and contact stress distributions between the FG layer and homogeneous half plane for discontinuous contact case were provided for various dimensionless quantities including material inhomogeneity, distributed load width, the shear module ratio and load factor for both methods. The results obtained using FEM were compared with the results found using analytical formulation. It was found that the results obtained from analytical formulation were in perfect agreement with the FEM study.

• 한국복합재료학회:학술대회논문집
• /
• 한국복합재료학회 2000년도 춘계학술발표대회 논문집
• /
• pp.97-100
• /
• 2000

A FEA(finite element analysis) model was proposed to study stress and strain distributions in thick composites with various types of fiber waviness under tensile and compressive loadings. Three types of model were considered in this study: uniform fiber waviness, graded fiber waviness and localized fiber waviness models. In the analysis, both material and geometrical nonlinearities due to fiber waviness were incorporated into the model utilizing energy density and incremental method. The strain distributions of uniform fiber waviness model were strongly influenced whereas the stress distributions were little influenced by fiber waviness. The stress and strain distributions of graded and localized fiber waviness models showed more complex distributions than those of uniform fiber waviness model due to the variation of fiber waviness along the thickness and length directions. It was concluded that the stress and strain distributions of composites with fiber waviness were significantly affected by types of fiber waviness.

• 한국소음진동공학회논문집
• /
• 제15권4호
• /
• pp.474-482
• /
• 2005

A theoretical method is presented to investigate the thermoelastic and dynamic response of functionally graded material (FGM) rectangular plates made up of metal and ceramic. The temperature is assumed to be constant in the plane of the plate and to vary in the thickness direction only. Material properties are assumed to be temperature-dependant, and vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The third order shear deformation theory (TSDT) to account for rotary inertia and transverse shear strains is adopted to formulate the theoretical model. The modal analysis technique is used to develop the analytic solutions of the dynamic problem. The effect of material compositions and temperature fields is examined. The present theoretical results are verified by comparing with those from finite element analysis by ANSYS.

• Structural Engineering and Mechanics
• /
• 제58권3호
• /
• pp.515-532
• /
• 2016

The elastoplastic response of functionally graded material (FGM) beams resting on a nonlinear elastic foundation to an eccentric axial load is investigated by using the finite element method. The FGM is assumed to be formed from ceramic and metal phases with their volume fraction vary in the thickness direction by a power-law function. A bilinear elastoplastic behavior is assumed for the metallic phase, and the effective elastoplastic properties of the FGM are evaluated by Tamura-Tomota-Ozawa (TTO) model. Based on the classical beam theory, a nonlinear finite beam element taking the shift in the neutral axis position into account is formulated and employed in the investigation. An incremental-iterative procedure in combination with the arc-length control method is employed in computing the equilibrium paths of the beams. The validation of the formulated element is confirmed by comparing the equilibrium paths obtained by using the present element and the one available in the literature. The numerical results show that the elastoplastic post-buckling of the FGM beams is unstable, and the post-buckling strength is higher for the beams associated with a higher ceramic content. Different from homogeneous beams, yielding in the FGM beam occurs in the layer near the ceramic layer before in the layer near metal surface. A parametric study is carried out to highlight the effect of the material distribution, foundation support and eccentric ratio on the elastoplastic response of the beams.

• Advances in nano research
• /
• 제6권3호
• /
• pp.219-242
• /
• 2018

In this study, static bending of an edge cracked cantilever nanobeam composed of functionally graded material (FGM) subjected to transversal point load at the free end of the beam is investigated based on modified couple stress theory. Material properties of the beam change in the height direction according to exponential distributions. The cracked nanobeam is modelled using a proper modification of the classical cracked-beam theory consisting of two sub-nanobeams connected through a massless elastic rotational spring. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new non-classical beam model reduces to the classical beam model when the length scale parameter is set to zero. The considered problem is investigated within the Euler-Bernoulli beam theory by using finite element method. In order to establish the accuracy of the present formulation and results, the deflections are obtained, and compared with the published results available in the literature. Good agreement is observed. In the numerical study, the static deflections of the edge cracked FGM nanobeams are calculated and discussed for different crack positions, different lengths of the beam, different length scale parameter, different crack depths, and different material distributions. Also, the difference between the classical beam theory and modified couple stress theory is investigated for static bending of edge cracked FGM nanobeams. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

• Structural Engineering and Mechanics
• /
• 제51권5호
• /
• pp.727-741
• /
• 2014

The functionally graded beam (FGB) is investigated in this study on both dynamic and static loading in case of resting on a soil medium rather than on the usual Winkler-Pasternak elastic foundation. The powerful ABAQUS software was used to model the problem applying finite element method. In the present study, two different soil models are taken into account. In the first model, the soil is assumed to be an elastic plane stress medium. In the second soil model, the Drucker-Prager yield criterion, which is one of the most well-known elastic-perfectly plastic constitutive models, is used for modelling the soil medium. The results are shown to evaluate the effects of the different soil models, stiffness values of the elastic soil medium on the normal and shear stress and free vibration properties. A comparison was made to those from the existing literature. Numerical results show that considering real soil as a continuum space affects the results of the bending and the modal properties significantly.