• Steel and Composite Structures
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• 제4권4호
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• pp.281-301
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• 2004

The paper begins by presenting a unified variational approach to the lateral-torsional buckling (LTB) analysis of doubly symmetric prismatic and tapered thin-walled beams with open cross-sections, which accounts for the influence of the pre-buckling deflections. This approach (i) extends the kinematical assumptions usually adopted for prismatic beams, (ii) consistently uses shell membrane theory in general coordinates and (iii) adopts Trefftz's criterion to perform the bifurcation analysis. The proposed formulation is then applied to investigate the influence of the pre-buckling deflections on the LTB behaviour of prismatic and web-tapered I-section simply supported beams and cantilevers. After establishing an interesting analytical result, valid for prismatic members with shear centre loading, several elastic critical moments/loads are presented, discussed and, when possible, also compared with values reported in the literature. These numerical results, which are obtained by means of the Rayleigh-Ritz method, (i) highlight the qualitative differences existing between the LTB behaviours of simply supported beams and cantilevers and (ii) illustrate how the influence of the pre-buckling deflections on LTB is affected by a number of factors, namely ($ii_1$) the minor-to-major inertia ratio, ($ii_2$) the beam length, ($ii_3$) the location of the load point of application and ($ii_4$) the bending moment diagram shape.

• 대한교통학회지
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• 제20권6호
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• pp.99-113
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• 2002

교통량배분문제 가운데 다중계층 교통량배분문제는 유일해가 보장되지 않는 대표적 사례로 최근 들어 모형의 정식화 및 해법에 관해서 활발하게 전개되고 있다. 정식화에 있어서는 변동부등식이나 고정점 문제를 활용한 정식화가 보편적으로 활용되고 있으나 해법(알고리즘)에 관한 연구는 미흡한 실정이다. 본 연구에서는 변동부등식으로 정의된 다중계층 이용자균형 교통량배분문제의 해법으로서 GA알고리즘과 대각화알고리즘, 군집화알고리즘을 조합한 Hybrid Algorithm을 개발, 제안한다. GA알고리즘과 군집화알고리즘은 해의 탐색을 전역적이면서도 효과적으로 수행하기 위해서 도입된 대각화 알고리즘의 보완적 알고리즘이라 할 수 있다. 본 연구에서는 또한, 다중계층 이용자균형 교통량배분문제의 해법으로서의 제안된 AMSA(The Algorithm of Multiclass Static User Equilibrium Assignment)의 특징을 예제풀이를 통해서 설명하고 있다.

• Structural Engineering and Mechanics
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• 제30권1호
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• pp.119-129
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• 2008

A small strain and elastoplastic formulation of Polygonal Element Method (PEM) is developed for efficient analysis of elastoplastic solids. In this work, the polygonal elements are constructed based on traditional triangular finite meshes. The construction method of polygonal mesh can directly utilize the sophisticated triangularization algorithm and reduce the difficulty in generating polygonal elements. The Wachspress rational finite element basis function is used to construct the approximations of polygonal elements. The incremental variational form and a von Mises type model are used for non-linear elastoplastic analysis. Several small strain elastoplastic numerical examples are presented to verify the advantages and the accuracy of the numerical formulation.

• Structural Engineering and Mechanics
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• 제33권5호
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• pp.573-588
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• 2009

In this paper a four-node hybrid stress element is proposed for analysing arbitrarily shaped plates on a two parameter elastic foundation. The element is developed by combining a hybrid plate stress element and a soil element. The formulation is based on Hellinger-Reissner variational principle in which both inter element compatible boundary displacement and equilibrated stress fields for the plate as well as the foundation are chosen separately. This formulation also allows a low order polynomial interpolation functions. Numerical examples are presented to show that the validity and efficiency of the present element for the plate analysis resting on an elastic foundation. In these examples the effect of soil depth, interaction between closed plates on soil parameters, comparison with Winkler hypothesis is investigated.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1994년도 추계학술대회 논문집
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• pp.44-54
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• 1994

A variational formulation and the associated finite elemet equations have been derived for general three-dimensional deformation of a planar anisotropic rigid-plastic sheet metal which obeys the strain-rate potential proposed by BARLAT et al [13]. By using the natural convected coordinate system, the effect of geometric change and the rotation of planar anisotropic axes are considered efficiently. In order to check the validity of present formulation, a cylindrical cup and a square cup deep drawing test was modeled. good agreement was found between the FE simulation and the experiment. The results have shown that the present formulation for planar anisotropic deformation can be efficiently applied to the analysis of sheet metal working processes for planar anisotropic nonferrous metals.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2000년도 가을 학술발표회논문집
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• pp.238-245
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• 2000

A general formulation for shape design sensitivity analysis over a plane arch structure is developed based on a variational formulation of curved beam in linear elasticity. Sensitivity formula is derived using the material derivative concept and adjoint variable method for the stress defined at a local segment. Obtained sensitivity expression, which can be computed by simple algebraic manipulation of the solution variables, is well suited for numerical implementation since it does not involve numerical differentiation. Due to the complete description for the shape and its variation of the arch, the formulation can manage more complex design problems with ease and gives better optimum design than before. Several examples are taken to show the advantage of the method, in which the accuracy of the sensitivity is evaluated. Shape optimization is also conducted with two design problems to illustrate the excellent applicability.

• Interaction and multiscale mechanics
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• 제6권2호
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• pp.83-105
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• 2013

In this paper, a multi-scale meshfree-enriched finite element formulation is presented for the analysis of acoustic wave propagation problem. The scale splitting in this formulation is based on the Variational Multi-scale (VMS) method. While the standard finite element polynomials are used to represent the coarse scales, the approximation of fine-scale solution is defined globally using the meshfree enrichments generated from the Generalized Meshfree (GMF) approximation. The resultant fine-scale approximations satisfy the homogenous Dirichlet boundary conditions and behave as the "global residual-free" bubbles for the enrichments in the oscillatory type of Helmholtz solutions. Numerical examples in one dimension and two dimensional cases are analyzed to demonstrate the accuracy of the present formulation and comparison is made to the analytical and two finite element solutions.

• Structural Engineering and Mechanics
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• 제38권3호
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• pp.261-281
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• 2011

A new method of formulation of a class of elements that are immune to mesh distortion effects is proposed here. The simple three-noded bar element with an offset of the internal node from the element center is employed here to demonstrate the method and the principles on which it is founded upon. Using the function space approach, the modified formulation is shown here to be superior to the conventional isoparametric version of the element since it satisfies the completeness requirement as the metric formulation, and yet it is in agreement with the best-fit paradigm in both the metric and the parametric domains. Furthermore, the element error is limited to only those that are permissible by the classical projection theorem of strains and stresses. Unlike its conventional counterpart, the modified element is thus not prone to any errors from mesh distortion. The element formulation is symmetric and thus satisfies the requirement of the conservative nature of problems associated with all self-adjoint differential operators. The present paper indicates that a proper mapping set for distortion immune elements constitutes geometric and displacement interpolations through parametric and metric shape functions respectively, with the metric components in the displacement/strain replaced by the equivalent geometric interpolation in parametric co-ordinates.

• Nuclear Engineering and Technology
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• 제55권6호
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• pp.2172-2194
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• 2023

A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are proposed to accelerate the within-group and power iterations. Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (k_eff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time-step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2-3.

• 대한기계학회논문집A
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• 제23권6호
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• pp.1018-1025
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• 1999

For the effective analysis of two dimensional plane problems with geometrical discontinuities, singular finite element has been proposed. The element matrix equation was formulated on the basis of hybrid variational principle and Trefftz function sets derived consistently from the complex theory of plane elasticity by introducing a conformal mapping function. In order to suggest the accuracy characteristics of the proposed singular finite element, typical plane problems were analyzed and these results were compared with exact solutions. The singular finite element gives the comparatively exact values of stress concentration factors or stress intensity factors and can be effectively used for the analysis of mechanical structures containing various geometrical discontinuities.