• Steel and Composite Structures
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• 제30권1호
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• pp.13-29
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• 2019

This work presents the buckling investigation of functionally graded plates resting on two parameter elastic foundations by using a new hyperbolic plate theory. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only four unknowns and which is even less than the first order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT) by introducing undetermined integral terms, hence it is unnecessary to use shear correction factors. The governing equations are derived using Hamilton's principle and solved using Navier's steps. The validation of the proposed theoretical model is performed to demonstrate the efficacy of the model. The effects of various parameters like the Winkler and Pasternak modulus coefficients, inhomogeneity parameter, aspect ratio and thickness ratio on the behaviour of the functionally graded plates are studied. It can be concluded that the present theory is not only accurate but also simple in predicting the critical buckling loads of functionally graded plates on elastic foundation.

• 한국지반공학회논문집
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• 제39권12호
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• pp.75-91
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• 2023

GPR을 활용한 지중 매설관로의 비파괴 탐사에 있어서 다중 관로의 경우 관로에 의한 음영영역이 탐사결과에 많은 영향을 미친다. 다중 관로의 음영영역은 관로들의 위치 및 직경에 의해 변화되며 음영영역 내에서는 신호가 전파되지 못하기 때문에 탐지가 불가능하다. 본 연구에서는 FDTD 수치해석을 활용하여 다중 관로의 배치 및 직경에 따라 쌍곡선 형태로 나타나는 관로신호의 특성을 분석하였다. 관로의 배치는 수평, 수직, 대각 배치로 총 3가지 형태에 대한 분석을 수행하였으며, AGC를 활용하여 신호를 증폭하고 각각의 배치형태에서 나타나는 음영영역과 신호 특성의 차이를 분석하였다. 수평 배치에서는 두 관로가 근접할수록 두 쌍곡선 형태 사이에 새로운 쌍곡선 형태가 나타난다. 수직 배치에서는 쌍곡선 좌우 신호가 탐색 가능하여 이를 활용하면 하단 관로를 탐지가능할 것으로 보이나, 상단 관로의 직경이 하단 관로보다 큰 경우에는 탐지가 힘들 것으로 판단된다. 대각 배치의 경우, 지표면의 음영영역의 위치에 따라 다른 특성을 보인다. 장비의 가탐범위 내에 음영영역이 존재하는 경우 신호의 비대칭형태의 신호 특성을 보이며, 음영영역이 가탐범위 외부에 존재하는 경우에는 두 관로의 신호 특성에 영향을 거의 미치지 않는 것으로 나타났다.

• 대한수학회지
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• 제33권3호
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• pp.625-639
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• 1996

A convex $RP^n$-structure on a smooth anifold M is a representation of M as a quotient of a convex domain $\Omega \subset RP^n$ by a discrete group $\Gamma$ of collineations of $RP^n$ acting properly on $\Omega$. When M is a closed surface of genus g > 1, then the equivalence classes of such structures form a moduli space $B(M)$ homeomorphic to an open cell of dimension 16(g-1) (Goldman [2]). This cell contains the Teichmuller space $T(M)$ of M and it is of interest to know what of the rich geometric structure extends to $B(M)$. In [3], a symplectic structure on $B(M)$ is defined, which extends the symplectic structure on $T(M)$ defined by the Weil-Petersson Kahler form.

• 대한수학회보
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• 제55권4호
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• pp.1051-1063
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• 2018

The real moment-angle complex (or, more generally, real polyhedral product) and its real toric space have recently attracted much attention in toric topology. The aim of this paper is to give two interesting remarks regarding real polyhedral products and real toric spaces. That is, we first show that Moore's conjecture holds to be true for certain real polyhedral products. In general, real polyhedral products show some drastic difference between the rational and torsion homotopy groups. Our result shows that at least in terms of the homotopy exponent at a prime this is not the case for real polyhedral products associated to a simplicial complex whose minimal missing faces are all k-simplices with $k{\geq}2$. Moreover, we also show a structural theorem for a finite group G acting simplicially on the real toric space. In other words, we show that G always contains an element of order 2, and so the order of G should be even.

• 대한수학회논문집
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• 제9권4호
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• pp.945-950
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• 1994

Although the study of the limit points of discrete groups of M$\ddot{o}$bius transformations has been a fertile area for many decades, there are some very natural topological properties of the limit points which appear not to have been previously examined. Let $\Gamma$ be a nonelementary discrete group of hyperbolic isometries acting on the Poincare disc $B^m, m \geq 2$, and let $p \in \partial B^m$ be a limit point of $\Gamma$. By a neighborhood of p, we will always mean an open neighborhood of p in $\partial B^m$.

• 대한수학회보
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• 제34권4호
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• pp.549-560
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• 1997

For positive integers $n_i \geq 2, i = 1, 2, 3, 4$, such that $\Sigma \frac{n_i}{1} < 2$, there exists a quadrilateral $P = P_1 P_2 P_3 P_4$ in the hyperbolic plane $H^2$ with the interior angle $\frac{n_i}{\pi}$ at $P_i$. Let $\Gamma \subset Isom(H^2)$ be the (discrete) group generated by reflections in each side of $P$. Then the quotient space $H^2/\gamma$ is a differentiable orbifold of type $(^* n_1 n_2 n_3 n_4)$. It will be shown that the deformation space of $Rp^2$-structures on this orbifold can be mapped continuously and bijectively onto the cell of dimension 4 - \left$\mid$ {i$\mid$n_i = 2} \right$\mid$$.

• 대한수학회지
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• 제40권3호
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• pp.461-486
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• 2003

It is known that the CR geometries of Levi non-degen-erate hypersurfaces in $\C^n$ and of the elliptic or hyperbolic CR submanifolds of codimension two in $\C^4$ share many common features. In this paper, a special class of normalized coordinates is introduced for any CR manifold M which is one of the above three kinds and it is shown that the explicit expression in these coordinates of an isotropy automorphism $f{\in}Aut(M)_o {\subset}Aut(M),\;o{\in}M$, is equal to the expression of a corresponding element of the automorphism group of the homogeneous model. As an application of this property, an extension theorem for CR maps is obtained.

• Journal of Electrical Engineering and Technology
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• 제11권1호
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• pp.215-226
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• 2016

Modeling, control and implementation of a real redundant robot with five Degrees Freedom (DOF) of the SCARA (Selective Compliant Assembly Robot Arm) manipulator type is presented. Through geometric methods and structural and functional considerations, the inverse kinematics for redundant robot can be obtained. By means of a modification of the classical sliding mode control law through a hyperbolic function, we get a new algorithm which enables reducing the chattering effect of the real actuators, which together with the learning and adaptive controllers, is applied to the model and to the real robot. A simulation environment including the actuator dynamics is elaborated. A 5 DOF robot, a communication interface and a signal conditioning circuit are designed and implemented for feedback. Three control laws are executed in: a simulation structure (together with the dynamic model of the SCARA type redundant manipulator and the actuator dynamics) and a real redundant manipulator of the SCARA type carried out using MatLab/Simulink programming tools. The results, obtained through simulation and implementation, were represented by comparative curves and RMS indices of the joint errors, and they showed that the redundant manipulator, both in the simulation and the implementation, followed the test trajectory with less pronounced maximum errors using the adaptive controller than the other controllers, with more homogeneous motions of the manipulator.

• Structural Engineering and Mechanics
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• 제13권2호
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• pp.187-209
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• 2002

The infrastructure system in the United States has been aging faster than the resource available to restore them. Therefore decision for allocating the resources is based in part on the condition of the structural system. This paper proposes to use neural network to predict the overall rating of the structural system because of the successful applications of neural network to other fields which require a "symptom-diagnostic" type relationship. The goal of this paper is to illustrate the potential of using neural network in civil engineering applications and, particularly, in bridge evaluations. Data collected by the Tennessee Department of Transportation were used as "test bed" for the study. Multi-layer feed forward networks were developed using the Levenberg-Marquardt training algorithm. All the neural networks consisted of at least one hidden layer of neurons. Hyperbolic tangent transfer functions were used in the first hidden layer and log-sigmoid transfer functions were used in the subsequent hidden and output layers. The best performing neural network consisted of three hidden layers. This network contained three neurons in the first hidden layer, two neurons in the second hidden layer and one neuron in the third hidden layer. The neural network performed well based on a target error of 10%. The results of this study indicate that the potential for using neural networks for the evaluation of infrastructure systems is very good.

• Structural Engineering and Mechanics
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• 제68권5호
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• pp.527-536
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• 2018

The free vibration frequency responses of the graded flat and curved (cylindrical, spherical, hyperbolic and elliptical) panel structures investigated in this research considering the rectangular and tilted planforms under unlike temperature loading. For the numerical implementation purpose, a micromechanical model is prepared with the help of Voigt's methodology via the power-law type of material model. Additionally, to incur the exact material strength, the temperature-dependent properties of each constituent of the graded structure included due to unlike thermal environment. The deformation kinematics of the rectangular/tilted graded shallow curved panel structural is modeled via higher-order type of polynomial functions. The final form of the eigenvalue equation of the heated structure obtained via Hamilton's principle and simultaneously solved numerically using finite element steps. To show the solution accuracy, a series of comparison the results are compared with the published data. Some new results are exemplified to exhibit the significance of power-law index, shallowness ratio, aspect ratio and thickness ratio on the combined thermal eigen characteristics of the regular and tilted graded panel structure.