• Title, Summary, Keyword: Variational formulation

IMAGE SEGMENTATION BASED ON THE STATISTICAL VARIATIONAL FORMULATION USING THE LOCAL REGION INFORMATION

• Park, Sung Ha;Lee, Chang-Ock;Hahn, Jooyoung
• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.2
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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.

A variationally coupled Element-Free Galerkin Method(EFGM) -Boundary Element Method(BEM) (무요소법과 경계요소법의 변분적 조합)

• 이상호;김명원
• Proceedings of the Computational Structural Engineering Institute Conference
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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.

CONVERGENCE ANALYSIS OF PARALLEL S-ITERATION PROCESS FOR A SYSTEM OF VARIATIONAL INEQUALITIES USING ALTERING POINTS

• JUNG, CHAHN YONG;KUMAR, SATYENDRA;KANG, SHIN MIN
• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.381-396
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• 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.

Variational Formulation for Shape Optimization of Spatial Beam Structures (정식화를 이용한 3차원 구조물의 형상 최적설계)

• 최주호;김종수
• Proceedings of the Computational Structural Engineering Institute Conference
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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.

Study on the Generalization of the Extended Framework of Hamilton's Principle in Transient Continua Problems (확장 해밀턴 이론의 일반화에 대한 고찰)

• Kim, Jinkyu;Shin, Jinwon
• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.5
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• pp.421-428
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• 2016
• The present work extends the recent variational formulation to more general time-dependent problems. Thus, based upon recent works of variational formulation in dynamics and pure heat diffusion in the context of the extended framework of Hamilton's principle, formulation for fully coupled thermoelasticity is developed first, then, with thermoelasticity-poroelasticity analogy, poroelasticity formulation is provided. For each case, energy conservation and energy dissipation properties are discussed in Fourier transform domain.

MIXED QUASI VARIATIONAL INEQUALITIES INVOLVING FOUR NONLINEAR OPERATORS

• Honam Mathematical Journal
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• v.42 no.1
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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.

The Development of Incompatible Finite Elements for Plane Stress/Strain Using Multivariable Variational formulation (다변수 변분해법에 의한 비적합 4절점 사각형 평면응력 및 평면변형률 요소의 개발)

• 주상백;신효철
• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.11
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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.

Extension of the variational theory of complex rays to orthotropic shallow shell structures

• Cattabiani, Alessandro;Barbarulo, Andrea;Riou, Herve;Ladeveze, Pierre
• Advances in aircraft and spacecraft science
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• v.3 no.3
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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.

A Mixed Variational Principle of Fully Anisotropic Linear Elasticity (이방성탄성문제의 혼합형변분원리)

• 홍순조
• Computational Structural Engineering
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• v.4 no.2
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• pp.87-94
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• 1991
• In this paper, a mixed variational principle applicable to the linear elasticity of inhomogeneous anisotropic materials is presented. For derivation of the general variational principle, a systematic procedure for the variational formulation of linear coupled boundary value problems developed by Sandhu et al. is employed. Consistency condition of the field operators with the boundary operators results in explicit inclusion of boundary conditions in the governing functional. Extensions of admissible state function spaces and specialization to a certain relation in the general governing functional lead to the desired mixed variational principle. In the physical sense, the present variational principle is analogous to the Reissner's recent formulation obtained by applying Lagrange multiplier technique followed by partial Legendre transform to the classical minimum potential energy principle. However, the present one is more advantageous for the application to the general anisotropic materials since Reissner's principle contains an implicit function which is not easily converted to an explicit form.

WEAK SOLUTIONS OF THE EQUATION OF MOTION OF MEMBRANE WITH STRONG VISCOSITY

• Hwang, Jin-Soo;Nakagiri, Shin-Ichi
• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.443-453
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• 2007
• We study the equation of a membrane with strong viscosity. Based on the variational formulation corresponding to the suitable function space setting, we have proved the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.