• Steel and Composite Structures
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• v.39 no.1
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• pp.1-20
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• 2021

An exact solution based on refined third-order theory (TOT) has been presented for functionally graded porous curved beams having deep curvature. The displacement field of the refined TOT is derived by imposing the shear free conditions at the outer and inner surfaces of curved beams. The properties of the two phase composite are tailored according the power law rule and the effective properties are computed using Mori-Tanaka homogenization scheme. The equations of motion as well as consistent boundary conditions are derived using the Hamilton's principle. The curved beam stiffness coefficients (A, B, D) are obtained numerically using six-point Gauss integration scheme without compromising the accuracy due to deepness (1 + z/R) terms. The porosity has been modeled assuming symmetric (even) as well as asymmetric (uneven) distributions across the cross section of curved beam. The programming has been performed in MATLAB and is validated with the results available in the literature as well as 2D finite element model developed in ABAQUS. The effect of inclusion of 1 + z/R terms is studied for deflection, stresses and natural frequencies for FG curved beams of different radii of curvature. Results presented in this work will be useful for comparison of future studies.

• Advances in nano research
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• v.15 no.6
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• pp.551-565
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• 2023

Coupled porous curved beams, due to their low weight and high flexibility, have many applications in engineering. This study investigates the vibration behavior of coupled porous curved beams in different boundary conditions. The system consists of two curved beams connected by a mid-layer of elastic springs. These beams are made of various materials, such as homogenous steel foam, and composite materials with PMMA (polymethyl methacrylate) and SWCNT (single-walled carbon nanotube) used as the matrix and nanofillers, respectively. To obtain equivalent material properties, the role of mixture (RoM) was employed, followed by the implementation of the porosity function. The system's governing equations were obtained by employing FSDT and Hamilton's law. To investigate thermal vibration, temperature was implemented as a load in the governing equations. The GDQ method was used to solve these equations. To demonstrate the applicability of the GDQ method in calculating the frequencies of the system and the correctness of the developed program, a validation study was conducted. After validation, numerous examples were presented to investigate the behavior of single and coupled curved beams in various material properties and boundary conditions. The results indicate that the frequencies of the curved beams and the system depend highly on the amount of porosity (n) and the distribution pattern. The system frequencies decreased with an increase in the porosity coefficient. The stiffness of the springs had no effect on the first mode frequency but increased frequencies of other modes in a specific range. The frequencies of the system decreased with an increase in environmental temperature.

• Steel and Composite Structures
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• v.50 no.2
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• pp.149-158
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• 2024

Considering that different boundary conditions can have an important impact on structural vibration characteristics. In this paper, the nonlinear forced vibration behavior of functionally graded material (FGM) doubly curved shells with initial geometric imperfections under different boundary conditions is studied. Considering initial geometric imperfections and von Karman geometric nonlinearity, the nonlinear governing equations of FGM doubly curved shells are derived using Reissner's first order shear deformation (FOSD) theory. Three different boundary conditions of four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS) were studied, and a system of nonlinear ordinary differential equations was obtained with the help of Galerkin principle. The nonlinear forced vibration response of the FGM doubly curved shell is obtained by using the modified Lindstedt Poincare (MLP) method. The accuracy of this method was verified by comparing it with published literature. Finally, the effects of curvature ratio, power law index, void coefficient, prestress, and initial geometric imperfections on the resonance of FGM doubly curved shells under different boundary conditions are fully discussed. The relevant research results can provide certain guidance for the design and application of doubly curved shell.

• Restorative Dentistry and Endodontics
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• v.22 no.1
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• pp.388-395
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• 1997

Maintaining the original canal path during instrumentation is a challenge in narrow curved canals. This study compared the maintenance of the original canal path of curved root canals during instrumentation with two kinds of stainless steel K-files(Brassler USA & Mani Japan), K-flexofiles(Maillefer Swiss) and Ni-Ti files(Brassler USA, Savannah, GA) using circumferential filing technique to # 40 MAF on 60 extracted human molars. Buccal and mesial canals with minimal initial curvature of 20 degrees were used. The maximal initial curvature was 41.5 degrees. Sixty curved canals divided into four groups according to file type(Group 1 : Ni-Ti file, Group 2 : K-flexofile, Group 3: K-file(Brassler), Group 4 : K-file(Mani)). Radiographs of canals were obtained before and after canal shaping. And postoperative radiographs were compared with preoperative radiographs using superimposition method. Data analysis was performed using Covariance analysis and paired-comparison test. The results observed were as follow ; 1. The angle of curvature was better maintained with Ni-Ti file than with stainless steel files. (p<0.01) 2. There was no significant difference in maintaining canal curvature between K-flexofile, Brassler$^{(R)}$ K-file and Mani$^{(R)}$ K-file, although there was some differences in mean values of postoperative canal curvature. 3. Paired-comparison t test revealed significant differences within each of the three stainless steel file types when comparing the mean differences before and after instrumentation, but no significant differences were observed within Ni-Ti file group.

• Journal of Korean Tunnelling and Underground Space Association
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• v.6 no.4
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• pp.279-290
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• 2004

The differential quadrature method (DQM) for a system of coupled differential equations governing the elastic stability of thin-walled curved members is presented, and is applied to computation of the eigenvalues of out-of-plane buckling of curved beams subjected to uniformly distributed radial loads including a warping contribution. Critical loads with warping, which were found to be significant, are calculated for a single-span wide-flange beam with various end conditions, opening angles, and stiffness parameters. The results are compared with the exact methods available. New results are given for the case of both ends clamped and clamped-simply supported ends without comparison since no data are available The differential quadrature method gives good accuracy and stability compared with previous theoretical results.

• Wind and Structures
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• v.19 no.6
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• pp.649-663
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• 2014

The present paper discusses the characteristics of unsteady aerodynamic forces on long-span curved roofs. A forced vibration test is carried out in a wind tunnel to investigate the effects of wind speed, vibration amplitude, reduced frequency of vibration and rise/span ratio of the roof on the unsteady aerodynamic forces. Because the range of parameters tested in the wind tunnel experiment is limited, a CFD simulation is also made for evaluating the characteristics of unsteady aerodynamic forces on the vibrating roof over a wider range of parameters. Special attention is paid to the effect of reduced frequency of vibration. Based on the results of the wind tunnel experiment and CFD simulation, the influence of the unsteady aerodynamic forces on the dynamic response of a full-scale long-span curved roof is investigated on the basis of the spectral analysis.

• Steel and Composite Structures
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• v.20 no.5
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• pp.983-997
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• 2016

The aim of this study is to investigate the impact behavior and impact-induced damage of sandwich composites made of E-glass/epoxy face sheets and PVC foam. The studies were carried out on square flat and curved sandwich panels with two different radius of curvatures. Impact tests were performed under impact energies of 10 J, 25 J and 80 J using an instrumented drop-weight machine. Contact force and displacement versus time and contact force- displacement graphs of sandwich panels were presented to determine the panel response. Through these graphs, the energy absorbing capacity of the sandwich panels was determined. The impact responses and failure modes of flat and curved sandwich panels were compared and the effect of curvature on sandwich composite panel was demonstrated. Testing has shown that the maximum contact force decrease while displacement increases with increasing of panel curvature and curved panels exhibits mixed failure mode, with cylindrical and cone cracking.

• Steel and Composite Structures
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• v.26 no.5
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• pp.607-620
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• 2018

Vibration analysis of deep curved FG nano-beam has been carried out based on modified couple stress theory. Material properties of curved Timoshenko beam are assumed to be functionally graded in radial direction. Governing equations of motion and related boundary conditions have been obtained via Hamilton's principle. In a parametric study, influence of length scale parameter, aspect ratio, gradient index, opening angle, mode number and interactive influences of these parameters on natural frequency of the beam, have been investigated. It was found that, considering geometrical deepness term leads to an increase in sensitivity of natural frequency about variation of aforementioned parameters.

• Journal of the Society of Naval Architects of Korea
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• v.44 no.5
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• pp.474-481
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• 2007

A three-dimensional finite element model has been used to simulate the bead on plate welding of curved steel plates having curvature in the welding direction. By using traditional method such as thermal-elastic-plastic(TEP) finite element analysis. the weld-induced deformation can be accurately predicted. However, three-dimensional finite element analysis is not practical in analyzing the weld-induced deformation of large and complex structures such as ship structures in view of computing time and cost. In this study, used is the equivalent loading method based on inherent strain to illustrate the effect of the longitudinal curvature upon the weld-induced deformation of curved plates.

• Structural Engineering and Mechanics
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• v.36 no.6
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• pp.679-695
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• 2010

In-plane vibrations of slightly curved beams having cracks are investigated numerically and experimentally. The curvature of the beam is circular and stays in the plane of vibration. Specimens made of steel with different lengths but with the same radius of curvature are used in the experiments. Cracks are opened using a hand saw having 0.4 mm thickness. Natural frequencies depending on location and depth of the cracks are determined using a Bruel & Kjaer 4366 type accelerometer. Then the beam is assumed as a Rayleigh type slightly curved beam in finite element method (FEM) including bending, extension and rotary inertia. A flexural rigidity equation given in literature for straight beams having a crack is used in the analysis. Frequencies are obtained numerically for different crack locations and depths. Experimental results are presented and compared with the numerical solutions. The natural frequencies are affected too much due to larger moments when the crack is around nodes. The effect can be neglected when it is at the location of maximum displacements. When the crack is close to the clamped end, the decrease in the frequencies in all modes is very high. The consistency of the results and validity of the equations are discussed.