• 대한수학회보
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• 제53권2호
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• pp.589-600
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• 2016

In this paper, we propose a new incremental gradient method for solving a regularized minimization problem whose objective is the sum of m smooth functions and a (possibly nonsmooth) convex function. This method uses an adaptive stepsize. Recently proposed incremental gradient methods for a regularized minimization problem need O(mn) storage, where n is the number of variables. This is the drawback of them. But, the proposed new incremental gradient method requires only O(n) storage.

• Structural Engineering and Mechanics
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• 제13권1호
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• pp.35-52
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• 2002

It was shown in the previous study (Lee and Bertero 1993) that incremental collapse can lead to the exhaustion of the plastic rotation capacity at critical regions in a structure when subjected to the number of load cycles and load intensities as expected during maximum credible earthquakes and that this type of collapse can be predicted using the shakedown analysis technique. In this study, a minimum-weight design methodology, which takes into account not only the prevention of this incremental collapse but also the requirements of the serviceability limit states, is proposed by using the shakedown analysis technique and a nonlinear programming algorithm (gradient projection method).

• 한국생산제조학회지
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• 제8권1호
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• pp.60-66
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• 1999

This study is to develop design sensitivity analysis method based on continuum theory for the actual buckling load of vehicle passenger compartment with respect to sizing design variables. For nonlinear structural analysis, both geometric and material nonlinear effects are considered. The total Lagrangian formulation for incremental equilibrium analysis and one-point linear eigenvalue problem for buckling analysis are utilized. Numerical methods are presented to evaluate design sensitivity expressions, using structural analysis results from FEM code. Optical design of vehicle passenger compartment with buckling constraint solved using Gradient projection method.

• Journal of Welding and Joining
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• 제16권2호
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• pp.111-121
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• 1998

It is well recognized that a excessive temperature gradient from the junction of head to skirt in axial direction in a hot pressure vessel can cause unpredicted high thermal stress at the junction and/or in axial direction of a skirt. this thermal stress resulting from axial thermal gradient may be a major cause of unsoundness of structural integrity. In case of cyclic operation of hot pressure vessels, the thermal stress becomes one of the primary design consideration because of the possibility of fracture as a result of cyclic thermal fatigue and progressively incremental plastic deformation. To perform thermal stress analysis of the junction and cylindrical skirt of a vessel, or, at least, to inspect quantitatively the magnitude and effect of thermal stress, the temperature profile of the vessel and skirt must be known. This paper demonstrated the temperature distribution and thermal stress analysis for the junction of skirt to head using F.E. analysis. Effect of air pocket in crotch space was quantitatively investigated to minimize the temperature gradient causing the thermal stress in axial direction. Effect of the skirt height on thermal stresses was also studied. Analysis results were compared with theoretical formulas to verify th applicability to the strength calculation in design field.

• Steel and Composite Structures
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• 제42권1호
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• pp.23-32
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• 2022

In this paper, a nonlinear numerical method to solve the large deflection problem is introduced. And the non-dimensional load-deflection behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates is parametrically investigated. The large deflection problem is formulated according to the von Kármán nonlinear theory and the (1,1,0)^* hierarchical model, and it is approximated by 2-D natural element method (NEM). The shear locking phenomenon is suppressed by the selectively reduced integration method. The nonlinear matrix equations are solved by combining the incremental loading scheme and the Newton-Raphson iteration method. The proposed method is validated from the benchmark experiments, where the propose method shows an excellent agreement with the reference methods. The nonlinear behavior of FG-CNTRC plates is evaluated in terms of the non-dimensional load-deflection curve, and it is parametrically investigated with respect to the existence/non-existence and gradient pattern of CNTs, the width-to-thickness and aspect ratios of plates and the type of boundary conditions. The non-dimensional central deflection is significantly reduced when CNTs and added, and it decreases with the volume fraction of CNTs. But, it shows a uniform increase in proportion to the width-to-thickness and aspect ratios. Both the gradient pattern of CNTs and the type of boundary conditions do also show the remarkable effects.

• 대한기계학회논문집A
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• 제35권9호
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• pp.1041-1050
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• 2011

미크론 단위의 크기를 갖는 구조물의 소성변형에서 나타나는 길이 효과를 고려하여 유한요소 해석을 하기 위하여 변형률 구배 소성이론을 이용하는 탄소성 유한요소 모델링 및 해석법을 제안하였다. 기존의 연구에서 주로 고차, 고자유도 및 혼합요소, 초 요소 등을 필요로 하였던 것에 비하여 본 논문에서는 이들을 배제하는 변위법 저차 평면 요소 및 삼차원 요소를 도입하였다. 이는 비선형 증분 해석의 프레임워크에서 계산된 소성 변형률의 절점 평균값으로 보간하여 적분점에서의 변형률 구배를 구하고 테일러 전위 모델에 의한 변형률 경화 구성방정식을 적용하므로서 가능하였다. 제안된 방법론은 선형 삼각 및 사각요소, 선형 사면체, 육면체 요소에 대해 적용되었으며 마이크로 굽힘, 마이크로 비틀림, 마이크로 기공과 같은 대표적인 길이 스케일 문제를 통하여 수치적으로 검증하였다. 본 논문에서 제안한 방법은 계산이 매우 쉬우면서도 실험값들과 비교해 볼 때, 변형률 구배 소성이론 즉, 길이 효과를 잘 나타내어 주었다.

• Structural Engineering and Mechanics
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• 제41권6호
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• pp.775-789
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• 2012

This paper focuses on post-buckling analysis of functionally graded Timoshenko beam subjected to thermal loading by using the total Lagrangian Timoshenko beam element approximation. Material properties of the beam change in the thickness direction according to a power-law function. The beam is clamped at both ends. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. As far as the authors know, there is no study on the post-buckling analysis of functionally graded Timoshenko beams under thermal loading considering full geometric non-linearity investigated by using finite element method. The convergence studies are made and the obtained results are compared with the published results. In the study, with the effects of material gradient property and thermal load, the relationships between deflections, end constraint forces, thermal buckling configuration and stress distributions through the thickness of the beams are illustrated in detail in post-buckling case.

• Structural Engineering and Mechanics
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• 제17권2호
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• pp.245-266
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• 2004

Incremental launching method is one of the highly competitive techniques for construction of concrete bridges. It avoids costly and time consuming form work and centralizes all construction activities in a small casting yard, thus saving in cost and time against conventional bridge construction. From the quality point of view, it eliminates the uncertainty of monolithic behaviour by allowing high repetitiveness and industrial environment. But, from analysis and design point of view, the most characteristic aspect of incrementally launched bridges is that, it has to absorb the stresses associated with the temporary supports that are gradually taken on by the deck during its launch. So, it is necessary to analyse the structure for each step of launching which is a tedious and time consuming process. Effect of support settlements or temperature variation makes the problem more complex. By using transfer matrix method, this problem can be handled efficiently with minimal computational effort. This paper gives insight into method of analysis, formulation for optimization of the structural system, effect of support settlement and temperature gradient, during construction, on the stress state of incrementally launched bridges.

• Steel and Composite Structures
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• 제15권5호
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• pp.481-505
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• 2013

This paper focuses on thermal post-buckling analysis of functionally graded beams with temperature dependent physical properties by using the total Lagrangian Timoshenko beam element approximation. Material properties of the beam change in the thickness direction according to a power-law function. The beam is clamped at both ends. In the case of beams with immovable ends, temperature rise causes compressible forces and therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. Also, the material properties (Young's modulus, coefficient of thermal expansion, yield stress) are temperature dependent: That is the coefficients of the governing equations are not constant in this study. This situation suggests the physical nonlinearity of the problem. Hence, the considered problem is both geometrically and physically nonlinear. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In this study, the differences between temperature dependent and independent physical properties are investigated for functionally graded beams in detail in post-buckling case. With the effects of material gradient property and thermal load, the relationships between deflections, critical buckling temperature and maximum stresses of the beams are illustrated in detail in post-buckling case.

• 대한기계학회논문집
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• 제16권9호
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• pp.1632-1642
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• 1992

본 연구에서는 방전가공(electric disharge machining, EDM) 또는 공기연마 분사기(air-abrasive jet machine, AJM) 가공에 의하여 인장 시험편 또는 외팔보 시험 편에 구멍깊이를 증가시켜 가면서 구멍을 뚫었다. 여기에서 방저가공(EDM)을 채택한 것은 구멍깊이를 직접 계측하는 것이 가능하여 구멍깊이 측정 오차에 기인하는 잔류응 력 측정오차를 최소화 할 수 있기 때문이며, 공기연마 분사기를 채택한 것은 구멍을 뚫는 동안 가공응력을 유발시키지 않기 때문이었다. 위 인장 시험편 또는 외팔보 시 험편을 이용하여 균일한 응력장과 두께 방향으로 변하는 선형적 구배응력장을 구현하 고, 이 때 각각 구멍깊이가 다른 원통형 막힘 구멍으로 부터 이완되는 스트레인을 계 측하였다. Schajer가 제안한 멱급수법과 최소장승법을 적용하여 균일응력장 또는 구 배 응력장에서 측정되는 스트레인을 잔류응력으로 환산하였으며, 환산된 잔류응력과 실제로 작용하는 응력을 비교하므로서 이론적으로 제시된 멱급수법과 최소자승법의 타 당성을 실험적으로 검토하는데 본 연구의 목적이 있다. 이 때 얕은 구멍깊이 (0.3∼ 1.2mm)에서 측정되는 스트레인을 이용하여 Schajer의 제안에 따라 잔류응력을 산정하 므로서, 잔류응력 계측 대상 구조물을 가급적 덜파괴시키며 잔류응력을 측정할 수 있 는지 여부를 실험적으로 검토하였다.