Bending Response of Nanobeams Resting on Elastic Foundation

In the present study, the finite element method is developed for the static analysis of nano-beams under the Winkler foundation and the uniform load. The small scale effect along with Eringen's nonlocal elasticity theory is taken into account. The governing equations are derived based on the minimum potential energy principle. Galerkin weighted residual method is used to obtain the finite element equations. The validity and novelty of the results for bending are tested and comparative results are presented. Deflections according to different Winkler foundation parameters and small scale parameters are tabulated and plotted. As it can be seen clearly from figures and tables, for simply-supported boundary conditions, the effect of small scale parameter is very high when the Winkler foundation parameter is smaller. On the other hand, for clamped-clamped boundary conditions, the effect of small scale parameter is higher when the Winkler foundation parameter is high. Although the effect of the small scale parameter is adverse on deflection for simply-supported and clamped-clamped boundary conditions

Free vibration analysis of tapered beam-column with pinned ends embedded in Winkler-Pasternak elastic foundation

WOS: 000208451100004The 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.Scientific Research Projects Unit of Akdeniz UniversityThe financial support of the Scientific Research Projects Unit of Akdeniz University is gratefully acknowledged

Vibration analysis of plates with curvilinear quadrilateral domains by discrete singular convolution method

WOS: 000282139300002A 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 lour 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.Akdeniz UniversityThe financial support of the Scientific Research Projects Unit of Akdeniz University is gratefully acknowledged