• Steel and Composite Structures
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• 제23권1호
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• pp.41-51
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• 2017

A $C^0$ FE model developed based on an efficient higher order zigzag theory is used for hygrothermal analysis of laminated composite plates. The $C^0$ FE model satisfies the inter-laminar shear stress continuity at the interfaces and zero transverse shear stress conditions at plate top and bottom. In this model the first derivatives of transverse displacement have been treated as independent variables to circumvent the problem of $C^1$ continuity associated with the above plate theory. In the present theory the above mentioned $C^0$ continuity of the present element is compensated in the stiffness matrix formulation by using penalty parameter approach. In order to avoid stress oscillations observed in the displacement based finite element, the stress field derived from temperature/moisture fields (initial strains) must be consistent with total strain field. Special steps are introduced by field consistent approach (e.g., sampling at gauss points) to compensate this problem. A nine noded $C^0$ continuous isoparametric element is used in the proposed FE model. Comparison of present numerical results with other existing solutions shows that the proposed FE model is efficient, accurate and free of locking.

• Steel and Composite Structures
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• 제25권5호
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• pp.535-544
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• 2017

Box sections are symmetrical sections and they have high moment of inertia in both directions, therefore they are good members in tall building structures. For the rigid connection in structures with box column continuity plates are used on level of beam flanges in column. Assembly of the continuity plates is a difficult and unreliable work due to lack of weld or high welding and cutting in the fourth side of column in panel zone, so the use of experimental stiffeners have been considered by researchers. This paper presented an experimental investigation on connection in box columns. The proposed connection has been investigated in four cases which contain connection without internal and external stiffeners(C-0-00), connection with continuity plates(C-I-CP), connection with external vase shape stiffener (C-E-VP) and connection with surrounding plates(C-E-SP). The results show that the connections with vase plates and surrounding plates can respectively increase the ultimate strength of the connection up to 366% and 518% than the connection without stiffeners, in case connection with the continuity plates this parameter increases about 39%. In addition, the proposed C-E-VP and C-E-SP connection provide a rigid and safe connection to acquire rigidity of 95% and 98% respectively. But C-I-CP connection is classified as semi-rigid connections.

• Structural Engineering and Mechanics
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• 제11권2호
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• pp.123-132
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• 2001

An improved version of the Element-free Galerkin method (EFGM) is presented here for addressing the problem of transverse shear locking in shear-deformable beams with a high length over thickness ratio. Based upon Timoshenko's theory of thick beams, it has been recognized that shear locking will be completely eliminated if the rotation field is constructed to match the field of slope, given by the first derivative of displacement. This criterion is applied directly to the most commonly implemented version of EFGM. However in the numerical process to integrate strain energy, the second derivative of the standard Moving Least Square (MLS) shape functions must be evaluated, thus requiring at least a $C^1$ continuity of MLS shape functions instead of $C^0$ continuity in the conventional EFGM. Yet this hindrance is overcome effortlessly by only using at least a $C^1$ weight function. One-dimensional quartic spline weight function with $C^2$ continuity is therefore adopted for this purpose. Various numerical results in this work indicate that the modified version of the EFGM does not exhibit transverse shear locking, reduces stress oscillations, produces fast convergence, and provides a surprisingly high degree of accuracy even with coarse domain discretizations.

• Structural Engineering and Mechanics
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• 제89권2호
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• pp.199-211
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• 2024

The loading capacity of engineering structures/components reduces after the initiation and propagation of crack eventually leads to the final failure. Hence, it becomes essential to deal with the crack and its effects at the design and simulation stages itself, by detecting the prone area of the fracture. The phase-field (PF) method has been accepted widely in simulating fracture problems in complex geometries. However, most of the PF methods are formulated with second order continuity theoryinvolving C⁰ continuity. In the present study, PF method based on fourth-order (i.e., higher order) theory, maintaining C¹ continuity has been proposed for ductile fracture simulation. The formulation includes fourth-order derivative terms of phase field variable, varying between 0 and 1. Applications of fourth-order PF theory to ductile fracture simulation resulted in novelty in this area. The proposed formulation is numerically solved using a two-dimensional finite element (FE) framework in 3-layered manner system. The solutions thus obtained from the proposed fourth order theory for different benchmark problems portray the improvement in the accuracy of the numerical results and are well matched with experimental results available in the literature. These results are also compared with second-order PF theory and a comparison study demonstrated the robustness of the proposed model in capturing ductile behaviour close to experimental observations.

• Structural Engineering and Mechanics
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• 제8권6호
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• pp.623-637
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• 1999

This paper presents a four-noded quadrilateral $C^0$ strain plate element for the analysis of thick laminated composite plates. The element formulation is based on: 1) the third-order shear deformation theory; 2) assumed strain element formulation; and 3) interrelated edge displacements and rotations along element boundaries. Unlike the existing displacement-type composite plate elements based on the third-order theory, which rely on the $C^1$-continuity formulation, the present plate element is of $C^0$-continuity, and its element stiffness matrix is evaluated explicitly. Because of the third-order expansion of the in-plane displacements through the thickness, the resulting theory and hence elements do not need shear correction factors. The explicit element stiffness matrix makes the present element more computationally efficient than the composite plate elements using numerical integration for the analysis of thick layered composite plates.

• 열처리공학회지
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• 제10권1호
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• pp.47-54
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• 1997

Flake graphite cast irons with the high damping capacity have been used for the control of vibration and noise occuring in the members of various mechanical structures under vibrating conditions. However, the damping capacity which is morphological characteristics of graphite is one of the important factors in reducing the vibration and noise, but hardly any work has deal with this problem. Therefore, the authors have examined the damping capacity of various cast irons with alloying elements and studied the influences of the matrix, mechanical properties and morphological characteristics of graphite. The main results obtained are as follows: Effects of Ni on the damping capacities and mechanical properties are investigated in 3.9%C-0.3% Cu gray cast iron. At 0.2% Ni content, specific damping capacity showed the maximum value, and decreased with further increase in Ni content, Graphite continuity also showed same behavior. This indicates that the specific damping capacity has a close relation with graphite continuity. On the other hand, the damping capacity in pearlite matrix showed superior to that in ferrite. In contrast, with increasing the Ni content, both tensile strength and hardness increased due to the decrease of graphite length and eutectic cell size.

• 대한수학회지
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• 제50권1호
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• pp.189-202
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• 2013

On the unit ball of $\mathbb{C}^n$, the space of those holomorphic functions satisfying the mean Lipschitz condition $${\int}_0^1\;{\omega}_p(t,f)^q\frac{dt}{t^1+{\alpha}q}\;<\;{\infty}$$ is characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where ${\omega}_p(t,f)$ denotes the $L^p$ modulus of continuity defined in terms of the unitary transformations of $\mathbb{C}^n$.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1999년도 추계 학술대회논문집
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• pp.108-114
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• 1999

In this paper. a new automatic multi=block grid generation technique for general 2D regions is introduced. According to this simple and robust method, the domain of interest is first triangulated by using Delaunay triangulation of boundary points, and then geometric information of those triangles is used to obtain block topology. Once block boundaries are obtained. structured grid for each block is generated such that grid lines have $C^0-continuity$ across inter-block boundaries. In the final step of the present method, an elliptic grid generation method is applied to smoothen grid distribution for each block and also to re-locale the inter-block boundaries, and eventually to achieve a globally smooth multi-block structured grid system with $C^1-continuity$.

• 대한수학회보
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• 제46권4호
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• pp.701-712
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• 2009

In this paper, we study the simultaneous approximation to functions in $C^m$[0, 1] by neural networks with a squashing function and the complexity related to the simultaneous approximation using a Bernstein polynomial and the modulus of continuity. Our proofs are constructive.

• 한국전산구조공학회논문집
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• 제31권5호
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• pp.275-282
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• 2018

등기하 해석법을 이용한 고유치 해석은 유한요소를 이용한 결과보다 고차 모드에서 더 정확한 결과를 주는 것으로 알려져 있다. 이는 유한요소법이 차수에 상관없이 요소 간에 $C^0$ 연속성을 보이는 것과 다르게 등기하 해석법은 p차 요소에 대해서 $C^{p-1}$의 연속성을 보장하기 때문이다. 본 논문에서는 이러한 장점을 이용하여 등기하 해석법을 이용하여 모드 기반의 축소 모델을 구성하고 동적 거동 해석을 수행하였다. 축소 모델 구성을 위해 Craig-Bampton(CB) 기법을 적용하였다. 수치 예제를 통해 간단한 봉 요소에 대해 등기하 해석법과 유한요소 해석법을 적용하여 요소의 차수에 따른 고유치 해석 결과를 비교분석하였다. 등기하 해석법에 중첩 노트를 허용하여 요소 간 연속성을 조절하고, 요소 간 연속성이 줄어듦에 따라 고차 모드에서의 수치 오차가 커짐을 확인하였다. 동적 거동 해석을 위한 축소 모델에 높은 차수의 외력이 주어지는 경우 요소간 연속성이 높은 등기하해석법을 사용하면, 해의 정확도를 높일 수 있다.