• Journal of applied mathematics & informatics
• /
• 제7권3호
• /
• pp.813-831
• /
• 2000

In recent years, the theory of Wiener-Hopf equations has emerged as a novel and innovative technique for developing efficient and powerful numerical methods for solving variational inequalities and complementarity problems. In this paper, we provide an account of some of the fundamental aspects of the Wiener-Hopf equations with major emphasis on the formulation, computational algorithms, various generalizations and their applications. We also suggest some open problems for further research with sufficient information and references.

• 한국전산구조공학회논문집
• /
• 제27권1호
• /
• pp.37-43
• /
• 2014

동역학의 새로운 변분이론인 확장 해밀턴 이론은 수학물리학을 비롯한 공학에 있어 초기치-경계치 문제해석에 광범위하게 적용될수 있는 기반을 제공하는 것으로 본 논문에서는 이 이론을 기반으로 선형탄성 단자유도계에 적용한 새로운 수치해석법을 제안하였다. 곧, 변분이론의 특성을 감안해, 전체 time-step에 대한 수치해를 한번에 산정하는 해석법을 제안하였고, 주요 예제를 통해 이 해석법의 특성을 살펴보았다. 에너지 보존 시스템의 경우(비감쇠 시스템에 외력이 작용치 않는 경우), time-step에 관계없이 에너지와 모멘텀이 보존되는 symplecticity property를 가지고 있음을 확인할 수 있었고, 감쇠 시스템인 경우, time-step이 점점 작아질수록 정확한 해에 빠르게 수렴하는 것을 확인하였다.

• 대한기계학회논문집A
• /
• 제27권9호
• /
• pp.1579-1588
• /
• 2003

In this paper, the finite element equations for the transient linear viscoelastic stress analysis are presented in time domain, whose variational formulation is derived by using the Galerkin's method based on the equations of motion in time integral. Since the inertia terms are not included in the variational formulation, the time integration schemes such as the Newmark's method widely used in the classical dynamic analysis based on the equations of motion in time differential are not required in the development of that formulation, resulting in a computationally simple and stable numerical algorithm. The viscoelastic material is assumed to behave as a standard linear solid in shear and an elastic solid in dilatation. To show the validity of the presented method, two numerical examples are solved nuder plane strain and plane stress conditions and good results are obtained.

• Journal of applied mathematics & informatics
• /
• 제36권5_6호
• /
• pp.381-396
• /
• 2018

In this paper we have considered a system of mixed generalized variational inequality problems defined on two different domains in a Hilbert space. It has been shown that the solution of a system of mixed generalized variational inequality problems is equivalent to altering point formulation of some mappings. A new parallel S-iteration type process has been considered which converges strongly to the solution of a system of mixed generalized variational inequality problems.

• Nuclear Engineering and Technology
• /
• 제54권9호
• /
• pp.3181-3204
• /
• 2022

The variational nodal method for solving the neutron transport equation has evolved over 40 years. Based on a functional form of the Boltzmann neutron transport equation, the method now comprises a complete set of variants that can be employed for different problems. This paper presents an extensive review of the development of the variational nodal method. The emphasis is on summarizing the whole theoretical system rather than validating the methodologies. The paper covers the variational nodal formulation of the Boltzmann neutron transport equation, the Ritz procedure for various application purposes, the derivation of boundary conditions, the extension for adjoint and perturbation calculations, and treatments for anisotropic scattering sources. Acceleration approaches for constructing response matrices and solving the resulting system of algebraic equations are also presented.

• Structural Engineering and Mechanics
• /
• 제28권6호
• /
• pp.767-770
• /
• 2008

• Structural Engineering and Mechanics
• /
• 제21권5호
• /
• pp.571-590
• /
• 2005

An 8 node assumed stress hexahedral element with rotational degrees of freedom is proposed for static and free vibration analyses. The element formulation is based directly on an 8-node element. This direct formulation requires fewer computations than a similar element that is derived from an internal 20-node element in which the midside degrees of freedom are eliminated by expressing them in terms of displacements and rotations at corner nodes. The formulation is based on Hellinger-Reissner variational principle. Numerical examples are presented to show the validity and efficiency of the present element for static and free vibration analysis.

• Steel and Composite Structures
• /
• 제27권1호
• /
• pp.1-12
• /
• 2018

This paper presents a semi-analytical solution of simply supported horizontally composite curved I-beam by trigonometric series. The flexibility of the interlayer connectors between layers both in the tangential direction and in the radial direction is taken into account in the proposed formulation. The governing differential equations and the boundary conditions are established by applying the variational approach, which are solved by applying the Fourier series expansion method. The accuracy and efficiency of the proposed formulation are validated by comparing its results with both experimental results reported in the literature and FEM results.

• 한국전산구조공학회논문집
• /
• 제14권2호
• /
• pp.159-171
• /
• 2001

평면 아치 구조물에 대해 선형 탄성 변분방정식에 기반을 둔 설계민감도 해석을 위한 일반적 이론을 개발하였다. 아치 구조물내의 임의 마디에 정의된 응력범함수를 고려하였고 이에 대한 설계민감도 공식을 유도하기 위해 전미분(material derivative) 개념과 보조(adjoint) 변수 방법을 도입하였다. 얻어진 민감도 공식은 구조해석 결과를 얻고 나면 이들로부터 단순 대수연산을 통해 계산이 되므로 적용이 간편할 뿐 아니라 해의 정확도가 높은 잇점이 있다. 본 방법은 아치의 형상을 매개변수를 통해 표현하므로 얕은 아치에 국한하지 않고 어떠한 형상도 고려가 가능하며, 나아가서 아치의 형상변화를 형상에 대해 수직뿐 아니라 접선방향도 포함하여 일반적으로 고려하므로 다양한 형상설계가 가능하다. 몇 가지 예제에서 민감도 계산을 수행함으로써 본 방법의 정확도와 효율성을 입증하였으며, 두 가지의 설계최적화 문제를 대상으로 실제로 두께 및 형상최적설계를 수행하였다.

• 대한기계학회논문집A
• /
• 제20권7호
• /
• pp.2078-2086
• /
• 1996

This paper introduces two three-dimensional eight-node hexagonal elements obtained by using multivariable variational mehtod. Both of them are based on the modified hellinger-reissner principle to employ incompatible displacements and assumed stresses of assumed strains. The internal functions of element are introduced to as element formulation through two different methods : the first one uses the functions determined directly from the element boundary condition of the incompatible displacements ; while the second, being a kind of B-bar mehtod, employs the modification technique of strain-displacement matrix to pass the patch test. The elements are evaluated on the selective problems of bending and material incompressibility with regular and distorted meshes. The results show that the new elements perform with good accuracy in both of deformation and stress calculation and they are insensitive to distorted geometry of element.