• Structural Engineering and Mechanics
• /
• v.64 no.4
• /
• pp.403-411
• /
• 2017

In this article, analytical solution for free vibration of micro composite laminated beam on elastic medium based on modified couple stress are presented. The surrounding elastic medium is modeled as the Winkler elastic foundation. The governing equations and boundary conditions are obtained by using the principle of minimum potential energy for EulerBernoulli beam. For investigating the effect of different parameters including material length scale, beam thickness, some numerical results on different cross ply laminated beams such as (90,0,90), (0,90,0), (90,90,90) and (0,0,0) are presented on elastic medium. Free vibration analysis of a simply supported beam is considered utilizing the Fourier series. Also, the fundamental frequency is obtained using the principle of Hamilton for four types of cross ply laminations with hinged-hinged boundary conditions and different beam theories. The fundamental frequency for different thin beam theories are investigated by increasing the slenderness ratio and various foundation coefficients. The results prove that the modified couple stress theory increases the natural frequency under the various foundation for free vibration of composite laminated micro beams.

• Structural Engineering and Mechanics
• /
• v.73 no.2
• /
• pp.209-223
• /
• 2020

This paper investigates the buckling behavior of carbon nanotube-reinforced composite plates supported by Kerr foundation model. In this foundation elastic of Kerr consisting of two spring layers interconnected by a shearing layer. The plates are reinforced by single-walled carbon nanotubes with four types of distributions of uniaxially aligned reinforcement material. The analytical equations are derived and the exact solutions for buckling analyses of such type's plates are obtained. The mathematical models provided, and the present solutions are numerically validated by comparison with some available results in the literature. Effect of various reinforced plates parameters such as aspect ratios, volume fraction, types of reinforcement, parameters constant factors of Kerr foundation and plate thickness on the buckling analyses of carbon nanotube-reinforced composite plates are studied and discussed.

• Steel and Composite Structures
• /
• v.32 no.2
• /
• pp.173-187
• /
• 2019

This study is concerned with the stability of laminated composite plates modelled using Eringen's nonlocal differential model (ENDM) and a novel refined-hyperbolic-shear-deformable plate theory. The plate is assumed to be lying on the Pasternak elastic foundation and is under the influence of an in-plane magnetic field. The governing equations and boundary conditions are obtained through Hamilton's principle. An analytical approach considering Navier series is used to fine the critical bucking load. After verifying with existing results for the reduced cases, the present model is then used to study buckling of the laminated composite plate. Numerical results demonstrate clearly for the first time the roles of size effects, magnetic field, foundation parameters, moduli ratio, geometry, lay-up numbers and sequences, fiber orientations, and boundary conditions. These results could be useful for designing better composites and can further serve as benchmarks for future studies on the laminated composite plates.

• Steel and Composite Structures
• /
• v.20 no.3
• /
• pp.513-543
• /
• 2016

Third order shear deformation theory is used to evaluate electro-elastic solution of a sandwich plate with considering functionally graded (FG) core and composite face sheets made of piezoelectric layers. The plate is resting on the Pasternak foundation and subjected to normal pressure. Short circuited condition is applied on the top and bottom of piezoelectric layers. The governing differential equations of the system can be derived using Hamilton's principle and Maxwell's equation. The Navier's type solution for a sandwich rectangular thick plate with all edges simply supported is used. The numerical results are presented in terms of varying the parameters of the problem such as two elastic foundation parameters, thickness ratio ($h_p/2h$), and power law index on the dimensionless deflection, critical buckling load, electric potential function, and the natural frequency of sandwich rectangular thick plate. The results show that the dimensionless natural frequency and critical buckling load diminish with an increase in the power law index, and vice versa for dimensionless deflection and electrical potential function, because of the sandwich thick plate with considering FG core becomes more flexible; while these results are reverse for thickness ratio.

• Steel and Composite Structures
• /
• v.17 no.1
• /
• pp.1-19
• /
• 2014

Buckling and vibration characteristics of circular laminated plates under in-plane edge loads and resting on Winkler-type foundation are solved by the Ritz method. Inclusive numerical data are presented for the first three eigen-frequencies as a function of in-plane load for different classical edge conditions. Moreover, the effects of fiber orientation on the natural frequencies and critical buckling loads of laminated angle-ply plates with stacking sequence of $[({\beta}/-{\beta}/{\beta}/-{\beta})]_s$, are studied. Also, selected deformation mode shapes are illustrated. The correctness of results is established using finite element software as well as by comparison with the existing results in the literature.

• Computers and Concrete
• /
• v.22 no.6
• /
• pp.501-514
• /
• 2018

The paper presents the thermo-mechanically induced non-linear response of multiwall carbon nanotube reinforced laminated composite beam (MWCNTRCB) supported by elastic foundation using higher order shear deformation theory and von-Karman non-linear kinematics. The elastic properties of MWCNT reinforced composites are evaluated using Halpin-Tsai model by considering MWCNT reinforced polymer matrix as new matrix by dispersing in it and then reinforced with E-glass fiber in an orthotropic manner. The laminated beam is supported by Pasternak elastic foundation with Winkler cubic nonlinearity. A generalized static analysis is formulated using finite element method (FEM) through principle of minimum potential energy approach.

• The Journal of Advanced Prosthodontics
• /
• v.4 no.1
• /
• pp.37-42
• /
• 2012

PURPOSE. The influence of the modified process in the fiber-reinforced post and resin core foundation treatment on the fracture resistance and failure pattern of premolar was tested in this study. MATERIALS AND METHODS. Thirty-six human mandibular premolars were divided into 4 groups (n = 9). In group DCT, the quartz fibre post (D.T. Light-post) was cemented with resin cement (DUO-LINK) and a core foundation was formed with composite resin (LIGHT-CORE). In group DMO and DMT, resin cement (DUO-LINK) was used for post (D.T. Lightpost) cementation and core foundation; in group DMO, these procedures were performed simultaneously in one step, while DMT group was accomplished in separated two steps. In group LCT, the glass fiber post (LuxaPost) cementation and core foundation was accomplished with composite resin (LuxaCore-Dual) in separated procedures. Tooth were prepared with 2 mm ferrule and restored with nickel-chromium crowns. A static loading test was carried out and loads were applied to the buccal surface of the buccal cusp at a 45 degree inclination to the long axis of the tooth until failure occurred. The data were analyzed with MANOVA (${\alpha}$= .05). The failure pattern was observed and classified as either favorable (allowing repair) or unfavorable (not allowing repair). RESULTS. The mean fracture strength was highest in group DCT followed in descending order by groups DMO, DMT, and LCT. However, there were no significant differences in fracture strength between the groups. A higher prevalence of favorable fractures was detected in group DMT but there were no significant differences between the groups. CONCLUSION. The change of post or core foundation method does not appear to influence the fracture strength and failure patterns.

• Steel and Composite Structures
• /
• v.43 no.5
• /
• pp.581-601
• /
• 2022

The main objective of this research work is to investigate the free vibration behavior of annular sandwich plates resting on the Kerr foundation at thermal conditions. This sandwich configuration is composed of two FGM face sheets as coating layer and a porous GPLRC (GPL reinforced composite) core. It is supposed that the GPL nanofillers and the porosity coefficient vary continuously along the core thickness direction. To model closed-cell FG porous material reinforced with GPLs, Halpin-Tsai micromechanical modeling in conjunction with Gaussian-Random field scheme is used, while the Poisson's ratio and density are computed by the rule of mixtures. Besides, the material properties of two FGM face sheets change continuously through the thickness according to the power-law distribution. To capture fundamental frequencies of the annular sandwich plate resting on the Kerr foundation in a thermal environment, the analysis procedure is with the aid of Reddy's shear-deformation plate theory based high-order shear deformation plate theory (HSDT) to derive and solve the equations of motion and boundary conditions. The governing equations together with related boundary conditions are discretized using the generalized differential quadrature (GDQ) method in the spatial domain. Numerical results are compared with those published in the literature to examine the accuracy and validity of the present approach. A parametric solution for temperature variation across the thickness of the sandwich plate is employed taking into account the thermal conductivity, the inhomogeneity parameter, and the sandwich schemes. The numerical results indicate the influence of volume fraction index, GPLs volume fraction, porosity coefficient, three independent coefficients of Kerr elastic foundation, and temperature difference on the free vibration behavior of annular sandwich plate. This study provides essential information to engineers seeking innovative ways to promote composite structures in a practical way.

• Steel and Composite Structures
• /
• v.46 no.4
• /
• pp.553-563
• /
• 2023

In the current research, the nonlinear free vibrations of curved pipes made of functionally graded (FG) carbon nanotube reinforced composite (CNTRC) materials are investigated. It is assumed that the FG-CNTRC curved pipe is supported on a three-parameter nonlinear elastic foundation and is subjected to a uniform temperature rise. Properties of the curved nanocomposite pipe are distributed across the radius of the pipe and are given by means of a refined rule of mixtures approach. It is also assumed that all thermomechanical properties of the nanocomposite pipe are temperature-dependent. The governing equations of the curved pipe are obtained using a higher order shear deformation theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the pipe. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large deflection in the curved nanocomposite pipe. For the case of nanocomposite curved pipes which are simply supported in flexure and axially immovable, the motion equations are solved using the two-step perturbation technique. The closed-form expressions are provided to obtain the small- and large-amplitude frequencies of FG-CNTRC curved pipes rested on a nonlinear elastic foundation in thermal environment. Numerical results are given to explore the effects of CNT distribution pattern, the CNT volume fraction, thermal environment, nonlinear foundation stiffness, and geometrical parameters on the fundamental linear and nonlinear frequencies of the curved nanocomposite pipe.

• Coupled systems mechanics
• /
• v.9 no.3
• /
• pp.201-217
• /
• 2020

This paper employs differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT) for studying free vibrational characteristics of porous functionally graded (FG) nanoplates coupled by visco-elastic foundation. A secant function based refined plate theory is used for mathematical modeling of the nano-size plate. Two scale factors are included in the formulation for describing size influences based on NSGT. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. Visco-elastic foundation is presented based on three factors including a viscous layer and two elastic layers.The governing equations achieved by Hamilton's principle are solved implementing DQM. The nanoplate vibration is shown to be affected by porosity, temperature rise,scale factors and viscous damping.