• Steel and Composite Structures
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• v.33 no.5
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• pp.717-727
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• 2019

This paper is motivated by the lack of studies in the technical literature concerning to vibration analysis of a single-layered graphene sheet (SLGS) with corner cutout based on the nonlocal elasticity model framework of classical Kirchhoff thin plate. An isogeometric analysis (IGA) based upon non-uniform rational B-spline (NURBS) is employed for approximation of the L-shape SLGS deflection field. Trimming technique is employed to create the cutout in geometry of L-shape plate. The L-shape plate is assumed to be Free (F) in the straight edges of cutout while any arbitrary boundary conditions are applied to the other four straight edges including Simply supported (S), Clamped (C) and Free (F). The Numerical studies are carried out to express the influences of the nonlocal parameter, cutout dimensions, boundary conditions and mode numbers on the variations of the natural frequencies of SLGS. It is precisely shown that these parameters have considerable effects on the free vibration behavior of the system. In addition, numerical results are validated and compared with those achieved using other analysis, where an excellent agreement is found. The effectiveness and the accuracy of the present IGA approach have been demonstrated and it is shown that the IGA is efficient, robust and accurate in terms of nanoplate problems. This study serves as a benchmark for assessing the validity of numerical methods used to analyze the single-layered graphene sheet with corner cutout.

• Steel and Composite Structures
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• v.20 no.3
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• pp.623-649
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• 2016

Most of the early studies on plates vibration are focused on two-dimensional theories, these theories reduce the dimensions of problems from three to two by introducing some assumptions in mathematical modeling leading to simpler expressions and derivation of solutions. However, these simplifications inherently bring errors and therefore may lead to unreliable results for relatively thick plates. The main objective of this research paper is to present 3-D elasticity solution for free vibration analysis of continuously graded carbon nanotube-reinforced (CGCNTR) rectangular plates resting on two-parameter elastic foundations. The volume fractions of oriented, straight single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. In this study, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes (CNTs). The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The formulations are based on the three-dimensional elasticity theory. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence of the method is demonstrated and comparison studies are carried out to establish its very high accuracy and versatility. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and results reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. The novelty of the present work is to exploit Eshelby-Mori-Tanaka approach in order to reveal the impacts of the volume fractions of oriented CNTs, different CNTs distributions, various coefficients of foundation and different combinations of free, simply supported and clamped boundary conditions on the vibrational characteristics of CGCNTR rectangular plates. The new results can be used as benchmark solutions for future researches.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.34C no.4
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• pp.36-44
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• 1997

An efficient context-free multiple-object segmentation using attention operator based on modified generalized symmetry transform is proposed and implemented by modifying a radial basis function network. By using the difference of intensity gradient, instead of te intensity gradient itself, in generalized symmetry tranform so as to make the attention operator to preserve the edges of the objects shape, an efficient context-free multiple-object segementation is proposed in which no a priori shape informtion on the objects is requried. The attention operator is implemented by using a modified radial basis function network which can reflect symmetry, and by using te edge pyramid of the input image, both of the local and the global symmetry of the objects are reflected simultaneously to make the multiple-object with different sizes be segmented with a singel fixed-size $n\timesm$ can be done with O(n) complexity. The simulaton results show that the proposed algorithm can efficiently be used in context-free multiple-object segmentation even for the low contrast IR images as well as for the images from the camera.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.623-628
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• 2004

In this study, the assumed-mode method using characteristic polynomials of Timoshenko beam is applied for the free vibration analysis of rectangular stiffened plates. The polynomial is derived considering the rotational constraint along the boundary edges of plate and the orthogonal relation of Timoshenko beam functions, which enables to simplify the free vibration analysis of plate structure having various boundary conditions. To verify the validity and effectiveness of the adopted method, numerical analysis for cross-stiffened plates were carried out and its results were compared with those obtained by the general purpose FEA software.

• Proceedings of the KWS Conference
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• 2007.11a
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• pp.20-22
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• 2007

Welding-induced buckling distortion at the free edge of thin-plated panels has been studied. Welding distortion at free edges causes the additional man hours to straighten for the easy adjusting works of the following assembly stage. Therefore, it is necessary to develop a free-edge distortion control method. It is the purpose in the study to evaluate the effectiveness of buckling distortion prevention of the current design practice and design modification.

• Computational Structural Engineering
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• v.7 no.4
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• pp.151-158
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• 1994

The free vibrations of thermally buckled, simply supported, symmetrically laminated, rectangular, and quasi-isotropic plates are investigated. The nonlinear postbuckling analysis is performed by the finite element method based on the first order shear deformable plate theory with the use of von Karman type nonlinear strains and the Duhamel-Newman type constitutive law. The postbuckling solutions are used to obtain free vibration responses of buckled plates. Several numerical examples for quasi-isotropic laminated plates are considered. The effects of width-to-thickness ratios and aspect ratios on the free vibration characteristics of buckled plates are investigated.

• Journal of KSNVE
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• v.9 no.2
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• pp.273-284
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• 1999

The cylindrical shells are used as primary components of complex structures such as airplane fuselages and nuclear pressure vessels. Recently the free vibration analysis of these structures are investigated by many researchers. The engineering informations on experimental validation of the free vibration behavior on the simply supported cylindrical shells are very few. The experimental methods for realizing the physical boundary condition of simply supported edges are examined. Natural frequencies and mode shapes of the isotropic and plain weave composite simply supported shells are obtained by modal tests. A theoretical and finite element analysis are also performed in order to validate the experimental results. The experimental results indicate that the simply supported boundary conditions with bolts along the circumferential direction of shell in both ends are well achieved. Those are shown to agree with the analytical results and with the finite element analysis results. These methods can be used to realize other experimental simple support boundary conditions.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.959-986
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• 2023

Zhai and Lin recently proved that if G is an n-vertex connected 𝜃(1, 2, r + 1)-free graph, then for odd r and n ⩾ 10r, or for even r and n ⩾ 7r, one has ${\rho}(G){\leq}{\sqrt{{\lfloor}{\frac{n^2}{4}}{\rfloor}}}$, and equality holds if and only if G is $K_{{\lceil}{\frac{n}{2}}{\rceil},{\lfloor}{\frac{n}{2}}{\rfloor}}$. In this paper, for large enough n, we prove a sharp upper bound for the spectral radius in an n-vertex H-free non-bipartite graph, where H is 𝜃(1, 2, 3) or 𝜃(1, 2, 4), and we characterize all the extremal graphs. Furthermore, for n ⩾ 137, we determine the maximum number of edges in an n-vertex 𝜃(1, 2, 4)-free non-bipartite graph and characterize the unique extremal graph.

• Structural Engineering and Mechanics
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• v.7 no.4
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• pp.377-386
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• 1999

The stress distribution in a symmetrically laminated composite plate subjected to in-plane compression are evaluated using finite element analysis. Six different finite element models are created for the study of stresses in the plate after buckling. Two finite element modelling approaches are adopted to obtain the stress distribution. The first approach starts with a full model of shell elements from which sub-models of solid elements are spin-off The second approach adopts a full model of solid elements at the beginning from which sub-models of solid elements are created. All sub-models have either 1-element thickness or 14-element thickness. Both techniques show high interlaminar direct and shear stresses at the free edges. The study also provides vital information of the distribution of all components of stresses along the unloaded edges in length direction and also in the thickness direction of the plate.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.04a
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• pp.106-112
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• 1996

In this paper, the propagation of elastic wave generated by loading impact to plates made of isotropic or anisotropic material was studied. And the influence of boundary conditions(free or clamped edge) upon the reflection of elastic wave of isotropic plate such as aluminum plate showed circular interferometric fringe pattern, whereas that of anisotropic plate such as epoxy composite laminates showed elliptical one. And the transverse displacement curves obtained from experiment and theory for both plates agreed well. Also, the waves reflected from the boundary edges showed much differences according to the boundary condition of edges.