Browsing by Author "Tokdemir, Turgut"

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On the Use of Complex Stretching Coordinates in Generalized Finite Difference Method With Applications in Inhomogeneous Visco-Elasto Dynamics
(Elsevier Sci Ltd, 2022) Korkut, Fuat; Mengi, Yalcin; Tokdemir, Turgut
In the study, in conjunction with perfectly matched layer (PML) analysis, an approach is proposed for the evaluation of complex derivatives directly in terms of complex stretching coordinates of points in PML. For doing this within the framework of generalized finite difference method (GFDM), a difference equation is formulated and presented, where both the function values and coordinates of data points might be complex. The use of the proposed approach is considered in the analysis of inhomogeneous visco-elasto-dynamic system and assessed through three example problems analyzed in Fourier space: the composite and inhomogeneous tube, layer and impedance problems. The GFDM results obtained for the tube and layer problems compare very closely and coincide almost exactly with the exact solution. In the impedance problems, rigid surface or embedded footings resting on a composite inhomogeneous half-space are considered. The influences of various types of inhomogeneities, as well as, of various geometric shapes of PML-(physical region) interfaces on impedance curves are examined.
The Use of Generalized Finite Difference Method in Perfectly Matched Layer Analysis
(Elsevier Science inc, 2018) Korkut, Fuat; Tokdemir, Turgut; Mengi, Yalcin
This study deals with the use of Generalized Finite Difference Method (GFDM) in Perfectly Matched layer (PML) analysis. There are two options for performing PML analysis. First option is to express PML equations in terms of real coordinates of the points in actual (real) PML region; the second is to use governing equations (expressed in terms of complex stretching coordinates) as they are in complex PML region. The first option is implemented in this study; the implementation of the second option is under way and will be reported in another study. For the integration of PML equations, the use of GFDM is proposed. Finally, the suggested procedure is assessed computationally by considering the compliance functions of surface and embedded rigid strip foundations. GFDM with PML results are compared to those obtained by using Finite Element Method (FEM) with PML and Boundary Element Method (BEM). Excellent matches in results showed the reliability of the proposed procedure in PML analysis. (C) 2018 Elsevier Inc. All rights reserved.
Viscoelastic Rod Using the Generalized Finite Difference Method
(2023) Tokdemir, Turgut; Korkut, Fuat
The finite difference method is quite extensively used to obtain the approximate solutions of many equations of mathematical physics. In this study, the precise algorithm in the time domain is combined with the generalized finite difference method to solve dynamic viscoelasticity problems. The numerical results obtained are satisfactory, and they are presented together with finite difference and finite element solutions.