• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.121-140
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• 2022

In this paper, we study the strong convergence of new methods for solving classical variational inequalities problems involving semistrictly quasimonotone and Lipschitz-continuous operators in a real Hilbert space. Three proposed methods are based on Tseng's extragradient method and use a simple self-adaptive step size rule that is independent of the Lipschitz constant. The step size rule is built around two techniques: the monotone and the non-monotone step size rule. We establish strong convergence theorems for the proposed methods that do not require any additional projections or knowledge of an involved operator's Lipschitz constant. Finally, we present some numerical experiments that demonstrate the efficiency and advantages of the proposed methods.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.595-619
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• 2022

The purpose of this paper is to introduce an iterative algorithm for approximating a solution of split equality variational inequality problem for pseudomonotone mappings in the setting of Banach spaces. Under certain conditions, we prove a strong convergence theorem for the iterative scheme produced by the method in real reflexive Banach spaces. The assumption that the mappings are uniformly continuous and sequentially weakly continuous on bounded subsets of Banach spaces are dispensed with. In addition, we present an application of our main results to find solutions of split equality minimum point problems for convex functions in real reflexive Banach spaces. Finally, we provide a numerical example which supports our main result. Our results improve and generalize many of the results in the literature.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.205-235
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• 2023

In this paper, we introduce and study an iterative technique for solving quasimonotone split variational inequality problems and fixed point problem in the framework of real Hilbert spaces. Our proposed iterative technique is self adaptive, and easy to implement. We establish that the proposed iterative technique converges strongly to a minimum-norm solution of the problem and give some numerical illustrations in comparison with other methods in the literature to support our strong convergence result.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.1
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• pp.37-43
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• 2014

The extended framework of Hamilton's principle provides a new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics in terms of mixed formulation. Based upon such framework, a new variational numerical method of linear elasticity is provided for the classical single-degree-of-freedom dynamical systems. For the undamped system, the algorithm is symplectic with respect to the time step. For the damped system, it is shown to be accurate with good convergence characteristics.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.255-267
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• 2007

In this work, by using Xu's inequality, Nalder's results, the notion of $(A,\;{\eta})-accretive$ mappings and the new resolvent operator technique associated with $(A,\;{\eta})-accretive$ mappings due to Lan et al., we study the existence of solutions for a new class of $(A,\;{\eta})-accretive$ variational inclusion problems with non-accretive set-valued mappings and the convergence of the iterative sequences generated by the algorithms in Banach spaces. Our results are new and extend, improve and unify the corresponding results in this field.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.6 s.165
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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.

• 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.

• Journal of Power System Engineering
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• v.10 no.4
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• pp.83-89
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• 2006

Curved beams are more efficient in transfer of loads than straight beams because the transfer is effected by bending, shear and membrane action. The finite element method is a versatile method for solving structural mechanics problems and curved beam problems have been solved using this method by many author. In this study, a new three-noded hybrid-mixed curved beam element is proposed to investigate the in-plane flexural vibration behavior of arches depending on the curvature, aspect ratio and boundary conditions, etc. The proposed element including the effect of shear deformation is based on the Hellinger-Reissner variational principle, and employs the quadratic displacement functions and consistent linear stress functions. The stress parameters are then eliminated from the stationary condition of the variational principle so that the standard stiffness equations are obtained. Several numerical examples confirm the accuracy of the proposed finite element and also show the dynamic behavior of arches with various shapes.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.1
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• pp.163-171
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• 1996

For the effective analysis of two dimensional plane problems, Treffiz finite elements and cavity elements have been proposed. These element matrix equaitons were formulated on the basis of hybrid variational principle and Treffiz function sets derived consitstently from the complex theoy of plane elasticity. In order to suggest the accuracy chatacteristics of the proposed Treffiz elements typical plane problems were analyzed and these results were compared with ones obtained by using the conveintional displacement type elements. The accuracy of the proposed elements is less sensitive to the element size and shape than the conventional displacement type elements. These elements, being able to be formed with multi-nodes, give the convenient modeling of an analytic domain. The cavity elements give the comparatively exact values of stress concentration factors of stress intensity factors and can be effectively used for the analysis of mechanical stuctures containing various cavities.

• International journal of advanced smart convergence
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• v.12 no.4
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• pp.142-146
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• 2023

We present a method for generating 3D structures and rendering objects by combining VAE (Variational Autoencoder) and GAN (Generative Adversarial Network). This approach focuses on generating and rendering 3D models with improved quality using residual learning as the learning method for the encoder. We deep stack the encoder layers to accurately reflect the features of the image and apply residual blocks to solve the problems of deep layers to improve the encoder performance. This solves the problems of gradient vanishing and exploding, which are problems when constructing a deep neural network, and creates a 3D model of improved quality. To accurately extract image features, we construct deep layers of the encoder model and apply the residual function to learning to model with more detailed information. The generated model has more detailed voxels for more accurate representation, is rendered by adding materials and lighting, and is finally converted into a mesh model. 3D models have excellent visual quality and accuracy, making them useful in various fields such as virtual reality, game development, and metaverse.