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Nonlinear dynamic response of MDOF systems by the method of harmonic differential quadrature (HDQ)
Ömer Civalek 국제구조공학회 2007 Structural Engineering and Mechanics, An Int'l Jou Vol.25 No.2
A harmonic type differential quadrature approach for nonlinear dynamic analysis of multidegree-of-freedom systems has been developed. A series of numerical examples is conducted to assess the performance of the HDQ method in linear and nonlinear dynamic analysis problems. Results are compared with the existing solutions available from other analytical and numerical methods. In all cases, the results obtained are quite accurate.
Discrete singular convolution for buckling analyses of plates and columns
Ömer Civalek,Altu Yava 국제구조공학회 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.29 No.3
In the present study, the discrete singular convolution (DSC) method is developed for buckling analysis of columns and thin plates having different geometries. Regularized Shannon’s delta (RSD) kernel is selected as singular convolution to illustrate the present algorithm. In the proposed approach, the derivatives in both the governing equations and the boundary conditions are discretized by the method of DSC. The results obtained by DSC method were compared with those obtained by the other numerical and analytical methods.
Ömer Civalek,Engin Emsen 국제구조공학회 2009 Steel and Composite Structures, An International J Vol.9 No.1
In this study, a simple approach for bending analysis of Reissner-Mindlin plates is presented using the four-node quadrilateral domain transformation based on discrete singular convolution. In the proposed approach, irregular physical domain is transformed into a rectangular domain by using the geometric coordinate transformation. The DSC procedures are then applied to discrete the governing equations and boundary conditions. The accuracy of the proposed method is verified by comparison with known solutions obtained by other numerical or analytical methods. Results for Reissner-Mindlin plates show a satisfactory agreement with the analytical and numerical solutions.
Ömer Civalek,Baki Ozturk 국제구조공학회 2010 Structural Engineering and Mechanics, An Int'l Jou Vol.36 No.3
A methodology on application of the discrete singular convolution (DSC) technique to the free vibration analysis of thin plates with curvilinear quadrilateral platforms is developed. In the proposed approach, 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 boundary conditions. For demonstration of the accuracy and convergence of the method, some numerical examples are provided on plates with different geometry such as elliptic, trapezoidal having straight and parabolic sides, sectorial, annular sectorial, and plates with four curved edges. The results obtained by the DSC method are compared with those obtained by other numerical and analytical methods. The method is suitable for the problem considered due to its generality, simplicity, and potential for further development.
Ömer Civalek 국제구조공학회 2006 Steel and Composite Structures, An International J Vol.6 No.4
The discrete singular convolution (DSC) algorithm for determining the frequencies of the free vibration of single isotropic and orthotropic laminated conical shells is developed by using a numerical solution of the governing differential equations of motion based on Love’s first approximation thin shell theory. By applying the discrete singular convolution method, the free vibration equations of motion of the composite laminated conical shell are transformed to a set of algebraic equations. Convergence and comparison studies are carried out to check the validity and accuracy of the DSC method. The obtained results are in excellent agreement with those in the literature.
Ömer Civalek,Hakan Ersoy 국제구조공학회 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.29 No.4
In the present study, free vibration analysis of thick annular plates is analyzed by discrete singular convolution method. The Mindlin plate theory is employed. The material is isotropic, homogeneous and obeys Hook’s law. In this paper, discrete singular convolution method is used for discretization of equations of motion. Axisymmetric frequency values are presented illustrating the effect of radius ratio and thickness to radius ratio of the annular plate. The influence of boundary conditions on the frequency characteristics is also discussed. Comparing results with those in the literature validates the present analysis. It is shown that the obtained results are very accurate by this approach.
Bekir Akgöz,Ömer Civalek 국제구조공학회 2011 Steel and Composite Structures, An International J Vol.11 No.5
In the present manuscript, geometrically nonlinear free vibration analysis of thin laminated plates resting on non-linear elastic foundations is investigated. Winkler-Pasternak type foundation model is used. Governing equations of motions are obtained using the von Karman type nonlinear theory. The method of discrete singular convolution is used to obtain the discretised equations of motion of plates. The effects of plate geometry, boundary conditions, material properties and foundation parameters on nonlinear vibration behavior of plates are presented.
Application of strain gradient elasticity theory for buckling analysis of protein microtubules
Bekir Akgöz,Ömer Civalek 한국물리학회 2011 Current Applied Physics Vol.11 No.5
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.