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Civalek, Omer,Ozturk, Baki Techno-Press 2010 Geomechanics & engineering Vol.2 No.1
The current study presents a mathematical model and numerical method for free vibration of tapered piles embedded in two-parameter elastic foundations. The method of Discrete Singular Convolution (DSC) is used for numerical simulation. Bernoulli-Euler beam theory is considered. Various numerical applications demonstrate the validity and applicability of the proposed method for free vibration analysis. The results prove that the proposed method is quite easy to implement, accurate and highly efficient for free vibration analysis of tapered beam-columns embedded in Winkler- Pasternak elastic foundations.
Discrete singular convolution for buckling analyses of plates and columns
Civalek, Omer,Yavas, Altug Techno-Press 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.
Civalek, Omer,Ersoy, Hakan Techno-Press 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.
Civalek, Omer,Uzun, Busra,Yayli, M. Ozgur Techno-Press 2022 Advances in nano research Vol.12 No.5
In the current work, static and free torsional vibration of functionally graded (FG) nanorods are investigated using Fourier sine series. The boundary conditions are described by the two elastic torsional springs at the ends. The distribution of functionally graded material is considered using a power-law rule. The systems of equations of the mechanical response of nanorods subjected to deformable boundary conditions are achieved by using the modified couple stress theory (MCST) and taking the effects of torsional springs into account. The idea of the study is to construct an eigen value problem involving the torsional spring parameters with small scale parameter and functionally graded index. This article investigates the size dependent free torsional vibration based on the MCST of functionally graded nano/micro rods with deformable boundary conditions using a Fourier sine series solution for the first time. The eigen value problem is constructed using the Stokes' transform to deformable boundary conditions and also the convergence and accuracy of the present methodology are discussed in various numerical examples. The small size coefficient influence on the free torsional vibration characteristics is studied from the point of different parameters for both deformable and rigid boundary conditions. It shows that the torsional vibrational response of functionally graded nanorods are effected by geometry, small size effects, boundary conditions and material composition. Furthermore, for all deformable boundary conditions in the event of nano-sized FG nanorods, the incrementing of the small size parameters leads to increas the torsional frequencies.
Civalek, Omer,Ulker, Mehmet Techno-Press 2005 Structural Engineering and Mechanics, An Int'l Jou Vol.19 No.5
The non-linear static and dynamic response of doubly curved thin isotropic shells has been studied for the step and sinusoidal loadings. Dynamic analogues Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by the numerical examples. Numerical examples demonstrate the satisfactory accuracy, efficiency and versatility of the presented approach.
Nonlinear dynamic response of MDOF systems by the method of harmonic differential quadrature (HDQ)
Civalek, Omer Techno-Press 2007 Structural Engineering and Mechanics, An Int'l Jou Vol.25 No.2
A harmonic type differential quadrature approach for nonlinear dynamic analysis of multi-degree-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.
Civalek, Omer,Ozturk, Baki Techno-Press 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.