Browsing by Author "Mengi, Yalcin"

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A Gfdm Based Computational Model for the Analysis of Tunnels Under Gravitational Loadings
(Pergamon-elsevier Science Ltd, 2024) Mengi, Yalcin; Korkut, Fuat
Based on an impedance relation, a new computational model is developed for the analysis of tunnels under gravitational loading. The shape of tunnel is arbitrary. The impedance matrix, representing the soil resistance, is evaluated through integration of the equations of elasticity by generalized finite difference method (GFDM). The rigidity matrix of tunnel ring is constructed by using two types of elements: plate and shell elements. The equations of these elements are evaluated through integration of the equations of higher order plate and shell theories again by GFDM. These element equations accommodate not only axial and bending deformations, but, also shear deformations in the ring. In the study, the rotational joint deformation is simulated through the use of rotational spring model and the slippage is considered by modifying the impedance matrix so that the tangential soil resistance force between the ring and soil medium vanishes. Some numerical results are presented, in nondimensional forms, for circular and square tunnels where the following three cases are considered for circular tunnels: a) the soil medium is infinite, the change in sigma v (vertical (in situ) compressional stress) in the vicinity of tunnel is disregarded b) the soil medium is infinite, the change in sigma v is taken into account c) the soil medium is halfspace (HS). In connection with the case of (a), a comparison is presented for the ring flexibility curves of radial displacement and section forces of circular ring with those reported in literature. In view of the interpretations of the results and comparisons, we think, the proposed model may be used reliably in the analysis of tunnels.
Interaction Analysis Revisited by Generalized Finite Difference Method With Perfectly Matched Layer
(Elsevier Sci Ltd, 2023) Mengi, Yalcin; Korkut, Fuat
A unified formulation is given for solid-solid interaction problems. For the description of the formulation, the embedded foundation problem is considered with interaction interface being taken as either flexible or rigid. Introducing a transfer function relating free field displacements at interaction interface to seismic excitation, a formula is established for the evaluation of all the elements of input matrix at a single step without using complicated scattering analysis. Some sample problems are considered in the study for the assessment of the formulation. In the in-plane problem, involving an infinitely long rigid embedded foundation under the influence of inclined P-SV or Rayleigh waves, it is found that the behavior of input motion functions for OvOcr for the reasons discussed in the study, where Ov and Ocr are respectively the inclination and critical angles for SV waves. The computations in the work are carried out by generalized finite difference method (GFDM) together with perfectly matched layer (PML).
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 Fft Algorithm for Circumferential Coordinate in Axisymmetric Analysis of Solids by Generalized Finite Difference Method
(Elsevier Sci Ltd, 2023) Korkut, Fuat; Mengi, Yalcin
A formulation is presented for GFDM analysis of axisymmetric viscoelastic bodies under general loading conditions. The proposed formulation reduces the dimension of analysis by one by using complex Fourier series for circumferential coordinate ((0) dependency) of field variables. For 0 (Fourier) transform computations, the discrete Fourier transform formulas with FFT algorithm are employed. Radiational effects are accounted for through the use of perfectly matched layer (PML) with the equation being modified in accordance with the proposed formulation. For the assessment of the formulation, several sample problems are presented. The results indicate its capability in estimating the response even for that requiring sensitive analysis, such as, those in wave propagation analysis.
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.