• Computers and Concrete
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• 제18권1호
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• pp.17-37
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• 2016

This paper compares the arc-length and explicit dynamic solution methods for nonlinear finite element analysis of prestressed concrete members subjected to monotonically increasing loads. The investigations have been conducted using an L-shaped, prestressed concrete spandrel beam, selected as a highly nonlinear problem from the literature to give insight into the advantages and disadvantages of these two solution methods. Convergence problems, computational effort, and quality of the results were investigated using the commercial finite element package ABAQUS. The work in this paper demonstrates that a static analysis procedure, based on the arc-length method, provides more accurate results if it is able to converge on the solution. However, it experiences convergence problems depending upon the choice of mesh configuration and the selection of concrete post-cracking response parameters. The explicit dynamic solution procedure appears to be more robust than the arc-length method in the sense that it provides acceptable solutions in cases when the arc-length approach fails, however solution accuracy may be slightly lower and computational effort may be significantly larger. Furthermore, prestressing forces must be introduced into the finite element model in different ways for the explicit dynamic and arc-length solution procedures.

• 대한토목학회논문집
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• 제28권1B호
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• pp.111-114
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• 2008

파랑의 분산관계식에서 상대수심이 반복적으로 표현되는 순환 관계를 이용하여 파랑분산식의 양해를 개발하였다. 순환 관계를 이용한 해의 초기값으로 Eckart(1951), Hunt(1979)의 해와 심해와 천해에서의 해를 사용했다. 순환해 가운데 심해에서의 해를 초기값으로 사용한 해를 제외하고는 모두 참값으로 수렴하였다. 특히, Hunt의 해를 초기값으로 사용한 해는 다른 해보다 더 빠르게 수렴했다. 순환해는 휴대용 계산기를 사용하여 손 쉽고 빠르게 구할 수 있는 장점이 있다. 선형파의 변형을 예측하기 위하여 해석 해를 사용할 경우 파랑분산식의 양해를 사용해야 하는 데 본 연구에서 개발한 순환해를 사용하면 기존의 양해를 사용한 것보다 더 정확한 해석 해를 도출할 것이다.

• 대한수학회논문집
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• 제36권3호
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• pp.549-555
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• 2021

We show the solvability of the ordinary differential equations describing curves on sphere or hyperbolic space. Making use of the geometric properties of the equations, we derive explicit solution formulae.

• Communications for Statistical Applications and Methods
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• 제16권3호
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• pp.409-419
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• 2009

본 연구에서는 영상흐림보정를 위한 EM 알고리즘의 일반형 해를 제공한다. 주어진 관측영상의 크기가 크거나 많은 반복을 필요로 할 때, EM 알고리즘의 반복은 매우 오랜시간이 걸리며 비실용적이다. 본 연구에서는 복원 영상의 유효영역 밖에서 약간의 근사로부터 해를 일반형으로 나타내고, 이것을 이산형 유한 푸리에 변환을 이용하여 EM 알고리즘의 반복과정을 사용하지 않으면서 매우 유효한 복원영상을 즉시 계산하는 방법을 제공한다.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1996년도 자동차부품 제작기술의 진보
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• pp.97-109
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• 1996

In the present work computations are carried out for analysis of complicated sheet metal forming process such as forming of a rear hinge. Finite element formulation using dynamic explicit time integration scheme and step-wise combined Implicit/Explicit scheme are introduced for numerical analysis of sheet metal forming process. The rigid-plastic finite element method based on membrane elements has long been employed as a useful numerical technique for the analysis of sheet metal forming because of its time effectiveness. The explicit scheme in general use is based on the elastic-plastic modelling of material requiring large computation time. In finite element simulation of sheet metal forming processes, the robustness and stability of computation are important requirements since the computation time and convergency become major points of consideration besides the solution accuracy due to the complexity of geometry and boundary conditions. The implicit scheme employs a more reliable and rigorous scheme in considering the equilibrium at each step of deformation, while in the explicit scheme the problem of convergency is eliminated at the cost of solution accuracy. The explicit approach and the implicit approach have merits and demerits, respectively. In order to combine the merits of these two methods a step-wise combined implicit/explicit scheme has been developed.

• 한국정밀공학회지
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• 제13권12호
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• pp.86-98
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• 1996

An combined implicit/explicit scheme for the analysis of sheet forming problems has been proposed in this work. In finite element simulation of sheet metal forming processes, the robustness and stability of computation are important requirements since the computation time and convergency become major points of consideration besides the solution accuracy due to the complexity of geometry and boundary conditions. The implicit scheme dmploys a more reliable and rigorous scheme in considering the equilibrium at each step of deformation, while in the explict scheme the problem of convergency is elimented at thecost of solution accuracy. The explicit approach and the implicit approach have merits and demerits, respectively. In order to combine the merits of these two methods a step-wise combined implici/explicit scheme has been developed. In the present work, the rigid-plastic finite element method using bending energy augmented membraneelements(BEAM)(1) is employed for computation. Computations are carried out for some typical sheet forming examples by implicit, combined implicit/explicit schemes including deep drawing of an oil pan, front fender and fuel tank. From the comparison between the methods the advantages and disadvantages of the methods are discussed.

• 대한수학회보
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• 제55권6호
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• pp.1909-1920
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• 2018

In the paper, the authors find a common solution to three series of differential equations related to the generating function of the Bernoulli numbers of the second kind and present a recurrence relation, an explicit formula in terms of the Stirling numbers of the first kind, and a determinantal expression for the Bernoulli numbers of the second kind.

• East Asian mathematical journal
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• 제31권1호
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• pp.91-101
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• 2015

An explicit expression of the optimal investment strategy corresponding to the HARA utility function under the constant elasticity of variance (CEV) model has been given by Jung and Kim [6]. In this paper we give an explicit expression of the optimal solution for the extended logarithmic utility function. And we prove an a.s. convergence of the HARA solutions to the extended logarithmic one.

• 대한수학회지
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• 제53권1호
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• pp.89-114
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• 2016

In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.

• Structural Engineering and Mechanics
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• 제75권5호
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• pp.541-557
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• 2020

A novel family of controllable, dissipative structure-dependent integration methods is derived from an eigen-based theory, where the concept of the eigenmode can give a solid theoretical basis for the feasibility of this type of integration methods. In fact, the concepts of eigen-decomposition and modal superposition are involved in solving a multiple degree of freedom system. The total solution of a coupled equation of motion consists of each modal solution of the uncoupled equation of motion. Hence, an eigen-dependent integration method is proposed to solve each modal equation of motion and an approximate solution can be yielded via modal superposition with only the first few modes of interest for inertial problems. All the eigen-dependent integration methods combine to form a structure-dependent integration method. Some key assumptions and new techniques are combined to successfully develop this family of integration methods. In addition, this family of integration methods can be either explicitly or implicitly implemented. Except for stability property, both explicit and implicit implementations have almost the same numerical properties. An explicit implementation is more computationally efficient than for an implicit implementation since it can combine unconditional stability and explicit formulation simultaneously. As a result, an explicit implementation is preferred over an implicit implementation. This family of integration methods can have the same numerical properties as those of the WBZ-α method for linear elastic systems. Besides, its stability and accuracy performance for solving nonlinear systems is also almost the same as those of the WBZ-α method. It is evident from numerical experiments that an explicit implementation of this family of integration methods can save many computational efforts when compared to conventional implicit methods, such as the WBZ-α method.