Publications

  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: In this paper, mechanical responses of isolated microtubules are investigated. Microtubules can be defined as bio-composite structures that are a component of the cytoskeleton in eukaryotic cells and play important roles in cellular processes. They have superior mechanical properties such as high rigidity and flexibility. In order to model the microtubules such as a hollow beam, a trigonometric shear deformation beam model is employed on the basis of modified strain gradient theory. The governing equations and related boundary conditions are derived by implementing Hamilton’s principle. A detailed parametric study is performed to investigate the influences of shear deformation, material length scale parameter-to-outer radius ratio, aspect ratio and shear modulus ratio on mechanical responses of microtubules. It is observed that microstructure-dependent behavior is more considerable when material length scale parameters are closer to the outer diameter of microtubules. Also, it can be stated that effects of shear deformation become more significant for smaller shear modulus and aspect ratios.
    Composite Structures 12/2014; 118:9–18. · 3.12 Impact Factor
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: A shear deformation beam model and new shear correction factors are presented for nonhomogeneous microbeams. The governing equations and corresponding boundary conditions in bending and buckling are obtained by implementing minimum total potential energy principle. Bending and buckling problems of a simply supported functionally graded microbeam are analytically solved by Navier solution procedure. Several comparative results are given for different material property gradient index, thickness-to-material length scale parameter ratio (or vice versa), slenderness ratio and shear correction factors. It is observed that size effect and shear deformation are more significant for lower values of thickness-to-material length scale parameter and slenderness ratios, respectively.
    Composite Structures 06/2014; · 3.12 Impact Factor
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: In this paper, a new microstructure-dependent sinusoidal beam model for buckling of microbeams is presented using modified strain gradient theory. This microbeam model can take into consideration microstructural and shear deformation effects. The equilibrium equations and corresponding boundary conditions in buckling are derived with the minimum total potential energy principle. Buckling problem of a simply supported microbeam subjected to an axial compressive force is analytically solved by Navier solution procedure. Influences of thickness-to-length scale parameter and slenderness ratios on buckling behavior are discussed in detail. It is observed that the size dependency becomes more important when the thickness of the microbeam is closer to material length scale parameter. Also, it can be said that the effects of shear deformation are more considerable for short and thick beams with lower slenderness ratios.
    International Journal of Mechanical Sciences 04/2014; · 1.61 Impact Factor
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: The longitudinal free vibration problem of a micro-scaled bar is formulated using the strain gradient elasticity theory. The equation of motion together with initial conditions, classical and non-classical corresponding boundary conditions for a micro-scaled elastic bar is derived via Hamilton's principle. The resulting higher-order equation is solved for clamped-clamped and clamped-free boundary conditions. Effects of the additional length scale parameters on the frequencies are investigated. It is observed that size effect is more significant when the ratio of the microbar diameter to the additional length scale parameter is small. It is also observed that the difference between natural frequencies predicted by current and classical models becomes more prominent for both lower values of slenderness ratio of the microbar and for higher modes.
    Journal of Vibration and Control 03/2014; 20(4):606-616. · 4.36 Impact Factor
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: Thermo-mechanical size-dependent buckling analysis of embedded functionally graded (FG) microbeams is performed based on sinusoidal shear deformation beam and modified couple stress theories. It is assumed that material properties vary smoothly and continuously throughout the thickness. Winkler elastic foundation model is used to simulate the interaction between FG microbeam and elastic medium. The governing equations and corresponding boundary conditions are obtained with the aid of minimum total potential energy principle. The buckling characteristics of simply supported embedded FG microbeams in thermal environment are investigated. The obtained results are compared with the results of simple beam theory with no shear deformation effects and classical theory. Influences of thickness-to-material length scale parameter ratio, material property gradient index, slenderness ratio, temperature change and Winkler parameter on critical buckling loads of embedded FG microbeams are discussed in detail.
    International Journal of Engineering Science. 01/2014; 85:90–104.
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: The buckling problem of linearly tapered micro-columns is investigated on the basis of modified strain gradient elasticity theory. Bernoulli-Euler beam theory is used to model the non-uniform micro column. Rayleigh-Ritz solution method is utilized to obtain the critical buckling loads of the tapered cantilever micro-columns for different taper ratios. Some comparative results for the cases of rectangular and circular cross-sections are presented in graphical and tabular form to show the differences between the results obtained by modified strain gradient elasticity theory and those achieved by modified couple stress and classical theories. From the results, it is observed that the differences between critical buckling loads achieved by classical and those predicted by non-classical theories are considerable for smaller values of the ratio of the micro-column thickness (or diameter) at its bottom end to the additional material length scale parameters and the differences also increase due to increasing of the taper ratio.
    Structural Engineering & Mechanics 10/2013; 48(2):195-205. · 0.80 Impact Factor
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: The buckling behavior of size-dependent microbeams made of functionally graded materials (FGMs) for different boundary conditions is investigated on the basis of Bernoulli–Euler beam and modified strain gradient theory. The higher-order governing differential equation for buckling with all possible classical and non-classical boundary conditions is obtained by a variational statement. The effects of the power of the material property variation function, boundary conditions, slenderness ratio, ratio of additional material length scale parameters for two constituents, beam thickness-to-additional material length scale parameter ratio on the buckling response of FGM microbeams are investigated. Some comparative results are presented in tabular and graphical form in order to show the differences between the results obtained by the present model and those predicted by modified couple stress and classical continuum models.
    Acta Mechanica 01/2013; · 1.25 Impact Factor
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: A new size-dependent higher-order shear deformation beam model is developed based on modified strain gradient theory. The model captures both the microstructural and shear deformation effects without the need for any shear correction factors. The governing equations and boundary conditions are derived by using Hamilton's principle. The static bending and free vibration behavior of simply supported microbeams are investigated. Analytical solutions including Poisson effect for deflections under point and uniform loads and for first three natural frequencies are obtained by Navier solution. The results are compared with other beam theories and other classical and non-classical models. A detailed parametric study is carried out to show the influences of thickness-to-material length scale parameter ratio, slenderness ratio and shear deformation on deflections and natural frequencies of microbeams. It is observed that effect of shear deformation becomes more significant for both smaller slenderness ratios and higher modes.
    International Journal of Engineering Science 01/2013; 70:1-14. · 1.69 Impact Factor
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: Analytical solutions for bending, buckling, and vibration of micro-sized plates on elastic medium using the modified couple stress theory are presented. The governing equations for bending, buckling and vibration are obtained via Hamilton’s principles in conjunctions with the modified couple stress and Kirchhoff plate theories. The surrounding elastic medium is modeled as the Winkler elastic foundation. Navier’s method is being employed and analytical solutions for the bending, buckling and free vibration problems are obtained. Influences of the elastic medium and the length scale parameter on the bending, buckling, and vibration properties are discussed.
    Meccanica 01/2013; 48(4). · 1.75 Impact Factor
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: Longitudinal free vibration analysis of axially functionally graded microbars is investigated on the basis of strain gradient elasticity theory. Functionally graded materials can be defined as nonhomogeneous composites which are obtained by combining of two different materials in order to obtain a new desired material. In this study, material properties of microbars are assumed to be smoothly varied along the axial direction. Rayleigh-Ritz solution technique is utilized to obtain an approximate solution to the free longitudinal vibration problem of strain gradient microbars for clamped-clamped and clamped-free boundary conditions. A parametric study is carried out to show the influences of additional material length scale parameters, material ratio, slenderness ratio and ratio of Young's modulus on natural frequencies of axially functionally graded microbars.
    Composites Part B Engineering 01/2013; 55:263-268. · 2.14 Impact Factor
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: Free vibration of single-layered graphene sheet (SLGS) resting on an elastic matrix as Pasternak foundation model is investigated by using the modified couple stress theory. Governing equation of motion for SLGS is obtained via thin plate theory in conjunction with Hamilton’s principle. All edges simply supported boundary condition is considered. Analytical solution of the resulting equation is obtained via Fourier series approach. Effects of the material length scale parameter and elastic matrix parameters on vibration frequencies of SLGS are investigated. The influence of the mode numbers on frequencies for two-different matrix parameters and aspect ratio of graphene sheet are also studied. Numerical results reveal that the frequency values increase significantly with the increase of the material length scale parameter. It has been shown that scale effects are quite significant on frequencies especially when length and width of the SLGS is smaller and in higher modes of vibration and need to be included in the mechanical modeling of SLGS.
    Materials and Design 12/2012; 42:164–171. · 2.91 Impact Factor
  • Murat Gürses, Bekir Akgöz, Ömer Civalek
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    ABSTRACT: In the present study, free vibration analysis of nano-sized annular sector plate is analyzed using the nonlocal continuum theory. The method of discrete singular convolution (DSC) is used for numerical computations. Firstly, equation of motion of thin plates is formulated via nonlocal elasticity. Then, irregular physical domain is transformed into a rectangular domain by using geometric coordinate transformation. The DSC procedures are then applied to discretization of the transformed set of governing equations and related boundary conditions. The effects of nonlocal parameter, mode numbers, sector angle and radius ratio on the vibration frequencies are investigated in detail. It is seen that the size effects are significant in vibration analysis of nano-scaled annular sector plates and need to be included in the mechanical model.
    Applied Mathematics and Computation 11/2012; 219(6):3226–3240. · 1.35 Impact Factor
  • B.akgÖz, Ö.cİvalek
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    ABSTRACT: This paper is concerned with the bending analysis of single-walled carbon nanotubes (CNT) based on modified couple stress and strain gradient elasticity theories and Euler–Bernoulli beam theory. The size effect is taken into consideration using the modified couple stress and strain gradient elasticity theories. The governing equations and boundary conditions are derived using the variational approach. Deflections of CNT are obtained and presented in graphical form. Results are presented to show the effect of small-scale effect on bending of CNT. It is the first time in the literature, analytical expression and their solutions for the bending analysis based on strain gradient elasticity and couple stress theories are given for CNT under uniformly distributed load and concentrated end load.
    International Journal of Computational Methods 07/2012; 09(02). · 0.48 Impact Factor
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: This paper comments on the recently published work dealing with the static and dynamic analysis of micro beams by using the strain gradient elasticity theory (International Journal of Engineering Science, 47, 487–498, 2009) by Kong et al. (2009). The authors give the non-zero elements related to deviatoric stretch gradient tensor and higher-order stress. The values of η131(1) and τ131(1) are taken as zero by Kong et al. (2009). We present the non-zero terms in this comment. Consequently, we presented some results for cantilever beam in order to show the effect of these non-zero terms on the tip deflections of micro-sized beam.
    International Journal of Engineering Science - INT J ENG SCI. 01/2012;
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: Bending analysis of micro-sized beams based on the Bernoulli-Euler beam theory is presented within the modified strain gradient elasticity and modified couple stress theories. The governing equations and the related boundary conditions are derived from the variational principles. These equations are solved analytically for deflection, bending, and rotation responses of micro-sized beams. Propped cantilever, both ends clamped, both ends simply supported, and cantilever cases are taken into consideration as boundary conditions. The influence of size effect and additional material parameters on the static response of micro-sized beams in bending is examined. The effect of Poisson’s ratio is also investigated in detail. It is concluded from the results that the bending values obtained by these higher-order elasticity theories have a significant difference with those calculated by the classical elasticity theory. KeywordsStrain gradient elasticity–Micro beams–Static analysis–Size effect–Modified couple stress–Bernoulli-Euler beam–Poisson’s ratio
    Archive of Applied Mechanics 01/2012; 82(3):423-443. · 1.44 Impact Factor
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: n the present study, a single elastic beam model based on strain gradient elasticity and modified couple stress theories is presented for bending analysis of microtubules (MTs). The small scale effect is taken into consideration using the strain gradient elasticity and couple stress theories in conjunction with the Bernoulli-Euler beam model. The governing equation and boundary conditions are derived using the variational approach. Governing equation is solved by analytically for simple supported boundary conditions, firstly. Analytical results are given to show the size effect on bending of microtubules. It is hoped that the research in the manuscript may present a benchmark in the study of bending analysis of micro-scaled systems such as microtubules.
    Advances in Vibration Engineering 01/2012; 11(4):385-400. · 0.20 Impact Factor
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: A class of higher-order continuum theories, such as modified couple stress, nonlocal elasticity, micropolar elasticity (Cosserat theory) and strain gradient elasticity has been recently employed to the mechanical modeling of micro- and nano-sized structures. In this article, however, we address stability problem of micro-sized beam based on the strain gradient elasticity and couple stress theories, firstly. Analytical solution of stability problem for axially loaded nano-sized beams based on strain gradient elasticity and modified couple stress theories are presented. Bernoulli–Euler beam theory is used for modeling. By using the variational principle, the governing equations for buckling and related boundary conditions are obtained in conjunctions with the strain gradient elasticity. Both end simply supported and cantilever boundary conditions are considered. The size effect on the critical buckling load is investigated.
    International Journal of Engineering Science 11/2011; 49(11):1268-1280. · 1.69 Impact Factor
  • Bekir Akgöz, Ömer Civalek
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    ABSTRACT: In this paper, size effect of microtubules (MTs) is studied via modified strain gradient elasticity theory for buckling. MTs are modeled by Bernoulli–Euler beam theory. By using the variational principle, the governing equations for buckling and related boundary conditions are obtained in conjunctions with the strain gradient elasticity. The size effect for buckling analysis of MTs is investigated and results are presented in graph form. The results obtained by strain gradient elasticity theory are discussed through the numerical simulations. The results based on the modified couple stress theory, nonlocal elasticity theory and classical elasticity theories have been also presented for comparison purposes.Highlights► Buckling of microtubules using strain gradient elasticity theory is presented. ► In literature only nonlocal elasticity theory has been used by this time. ► Size effect on buckling of Microtubules (MTs) is studied. ► The results based on the modified couple stress theory are also presented.
    Current Applied Physics 09/2011; 11(5):1133-1138. · 2.03 Impact Factor
  • B. Akgöz, Civalek
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    ABSTRACT: In this paper, higher-order continuum theories are proposed for the buckling analysis of single walled carbon nanotubes (SWCNT). Modified strain gradient elasticity and modified couple stress theories are proposed. The governing equations for buckling and related boundary conditions are obtained in conjunctions with the strain gradient elasticity and variational principle. Detailed formulations and analytical solutions are presented for cantilever boundary conditions. Some new results are computed for buckling analysis of carbon nanotubes in order to show the scale effect.
    Journal of Computational and Theoretical Nanoscience 08/2011; 8(9):1821-1827. · 1.03 Impact Factor
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    ABSTRACT: This paper presents nonlinear static analysis of a rectangular laminated composite thick plate resting on nonlinear two-parameter elastic foundation with cubic nonlinearity. The plate formulation is based on first-order shear deformation theory (FSDT). The governing equation of motion for a rectangular laminated composite thick plate is derived by using the von Karman equation. The nonlinear static deflections of laminated plates on elastic foundation are investigated using the discrete singular convolution method. The effects of foundation and geometric parameters of plates on nonlinear deflections are investigated. The validity of the present method is demonstrated by comparing the present results with those available in the literature.Highlights► Large deflection analysis of laminated composite plates are investigated. ► As foundation, nonlinear elastic models have been used firstly. ► The effects of three-parameter foundation are investigated in detail.
    International Journal of Pressure Vessels and Piping 01/2011; 88:290-300. · 0.93 Impact Factor

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