• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권2호
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• pp.129-142
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• 2014

We propose a variational segmentation model based on statistical information of intensities in an image. The model consists of both a local region-based energy and a global region-based energy in order to handle misclassification which happens in a typical statistical variational model with an assumption that an image is a mixture of two Gaussian distributions. We find local ambiguous regions where misclassification might happen due to a small difference between two Gaussian distributions. Based on statistical information restricted to the local ambiguous regions, we design a local region-based energy in order to reduce the misclassification. We suggest an algorithm to avoid the difficulty of the Euler-Lagrange equations of the proposed variational model.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 가을 학술발표회 논문집
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• pp.11-18
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• 2001

In this paper, a new algorithm of coupling Element-Free Galerkin Method(EFGM) and Boundary Element Method(BEM) using the variational formulation is presented. A global variational coupling formulation of EFGM-BEM is achieved by combining the variational form on each subregion. In the formulation, Lagrange multiplier method is introduced to satisfy the compatibility conditions between EFGM subregion and BEM subregion. Some numerical examples are studied to verify accuracy and efficiency of the proposed method, in which numerical performance of the method is compared with that of conventional method such as EFGM-BEM direct coupling method, EFGM and BEM. The proposed method incorporating the merits of EFGM and BEM is expected to be applied to special engineering problems such as the crack propogation problems in very large domain, and underground structures with joints.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.717-731
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• 2021

In this paper, we introduce and study a new class of random generalized nonlinear implicit variational-like inclusion with random fuzzy mappings in a real separable Hilbert space and give its fixed point formulation. Using the fixed point formulation and the proximal mapping technique for strongly maximal monotone mapping, we suggest and analyze a random iterative scheme for finding the approximate solution of this class of inclusion. Further, we prove the existence of solution and discuss the convergence analysis of iterative scheme of this class of inclusion. Our results in this paper improve and generalize several known results in the literature.

• Journal of applied mathematics & informatics
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• 제5권1호
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• pp.73-90
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• 1998

In this paper we introduce and study a number of new classes of quasi variational inequalities. using essentially the projection technique and its variant forms we prove that the gen-eralized set-valued mixed quasivariational inequalities are equivalent to the fixed point problem and the Wiener-Hopf equations(normal maps). This equivalence enables us to suggest a number of iterative algorithms solving the generalized variational inequalities. As a special case of the generalized set-valued mixed quasi variational in-equalities we obtain a class of quasi variational inequalities studied by Siddiqi Husain and Kazmi [35] but there are several inaccuracies in their formulation of the problem the statement and the proofs of the problem the statement and the proofs of their results. We have removed these inaccuracies. The correct formulation of thir results can be obtained as special cases from our main results.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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• pp.123-130
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• 2002

A general formulation for shape design sensitivity analysis over three dimensional beam structure is developed based on a variational formulation of the beam in linear elasticity. Sensitivity formula is derived based on variational equations in cartesian coordinates using the material derivative concept and adjoint variable method for the displacement and Von-Mises stress functionals. Shape variation is considered for the beam shape in general 3-dimensional direction as well as for the orientation angle of the beam cross section. In the sensitivity expression, the end points evaluation at each beam segment is added to the integral formula, which are summed over the entire structure. The sensitivity formula can be evaluated with generality and ease even by employing piecewise linear design velocity field despite the bending model is fourth order differential equation. For the numerical implementation, commercial software ANSYS is used as analysis tool for the primal and adjoint analysis. Once the design variable set is defined using ANSYS language, shape and orientation variation vector at each node is generated by making finite difference to the shape with respect to each design parameter, and is used for the computation of sensitivity formula. Several numerical examples are taken to show the advantage of the method, in which the accuracy of the sensitivity is evaluated. The results are found excellent even by employing a simple linear function for the design velocity evaluation. Shape optimization is carried out for the geometric design of an archgrid and tilted bridge, which is to minimize maximum stress over the structure while maintaining constant weight. In conclusion, the proposed formulation is a useful and easy tool in finding optimum shape in a variety of the spatial frame structures.

• 한국전산구조공학회논문집
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• 제29권5호
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• pp.421-428
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• 2016

논문은 동역학의 새로운 변분이론인 확장 해밀턴 이론을 열 탄성과 공극 탄성에 적용하여 더욱 일반화하는 것에 그 주요 목적이 있다. 이를 위해 열 탄성학에 대한 이론 적용이 우선적으로 검토되었고, 열 탄성-공극 탄성의 유사성을 바탕으로 공극 탄성에까지 그 이론이 확장되었으며, 각 경우에 대한 푸리에 변환을 통해 그 적정성을 확인하였다.

• 호남수학학술지
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• 제42권1호
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• pp.17-35
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• 2020

In this paper we introduce and consider a new class of variational inequalities with four operators. This class is called the extended general mixed quasi variational inequality. We show that the extended general mixed quasi variational inequality is equivalent to the fixed point problem. We use this alternative equivalent formulation to discuss the existence of a solution of extended general mixed quasi variational inequality and also develop several iterative methods for solving extended general mixed quasi variational inequality and its variant forms. We consider the convergence analysis of the proposed iterative methods under appropriate conditions. We also introduce a new class of resolvent equation, which is called the extended general implicit resolvent equation and establish an equivalent relation between the extended general implicit resolvent equation and the extended general mixed quasi variational inequality. Some special cases are also discussed.

• 대한기계학회논문집
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• 제18권11호
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• pp.2871-2882
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• 1994

Two kinds of 4-node plane stress/strain finite elements are presented in this work. They are derived from the modified Hellinger-Reissner variational principle so as to employ the internal incompatible displacement and independent stress fields, or the incompatible displacement and strain fields. The introduced incompatible functions are selected to satisfy the constant strain condition. The elements are evaluated on several problems of bending and material incompressibility with regular and distorted elements. The results show that the new elements perform excellently in the calculation of deformation and stresses.

• Advances in aircraft and spacecraft science
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• 제3권3호
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• pp.317-330
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• 2016

Nowadays, the interest of aerospace and automotive industries on virtual testing of medium-frequency vibrational behavior of shallow shell structures is growing. The development of software capable of predicting the vibrational response in such frequency range is still an open question because classical methods (i.e., FEM, SEA) are not fully suitable for the medium-frequency bandwidth. In this context the Variational Theory of Complex Rays (VTCR) is taking place as an ad-hoc technique to address medium-frequency problems. It is a Trefftz method based on a weak variational formulation. It allows great flexibility because any shape function that satisfies the governing equations can be used. This work further develops such theory. In particular, orthotropic materials are introduced in the VTCR formulation for shallow shell structures. A significant numerical example is proposed to show the strategy.

• 전산구조공학
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• 제4권2호
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• pp.87-94
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• 1991

본고에서는 Sandhu등에 의해 개발된 다변수경계치문제의 변분모델화 방법을 이용하여 범함수의 독립변수로써 변위와 응력을 동시에 포함하는 이방성탄성문제의 혼합형변분원리(Mixed Variational Principle)를 유도한다. 탄성방정식을 내적공간에서 self-adjoint한 미분연산자매트릭스 방정식으로 표시한 후 다변수 경계치문제의 변분이론을 적용하므로써 일반적 범함수가 구해지며, 이때에 지배방정식의 미분연산자와 경계조건식의 연산자의 일관성 (Consistency)을 유지하므로써 경계조건도 체계적으로 범함수내에 포함시킬 수 있다. 이 일반적 범함수에서 미분연산자의 self-adjointness성질을 이용하여 응력함수의 도함수를 제거하고 탄성방정식중 특정식이 항상, 정확히 만족된다고 가정하므로써 원하는 혼합형변분원리의 범함수를 유도할 수 있다. 여기에서 유도된 변분원리는 최근 Reissner에 의해 개발된 변분원리와 유사한 물리적 의미를 가지나 유도방법이 다를 뿐 아니라 일반적 이방성탄성체에 적용할 때 보다 편리한 형태로 된다. 이 혼합형변분원리는 다양하게 응용될 수 있으나, 복합재료적층판과 같은 이질성, 이방성 평판이론, 또는 쉘이론의 유도에 유용하게 사용할 수 있다.