• Structural Engineering and Mechanics
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• v.85 no.2
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• pp.147-161
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• 2023

Based on the ideas of variational differential quadrature (VDQ) and finite element method (FEM), a numerical approach named as VDQFEM is applied herein to study the large deformations of plate-type structures under static loading with arbitrary shape hole made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) in the context of higher-order shear deformation theory (HSDT). The material properties of composite are approximated based upon the modified Halpin-Tsai model and rule of mixture. Furthermore, various FG distribution patterns are considered along the thickness direction of plate for GPLs. Using novel vector/matrix relations, the governing equations are derived through a variational approach. The matricized formulation can be efficiently employed in the coding process of numerical methods. In VDQFEM, the space domain of structure is first transformed into a number of finite elements. Then, the VDQ discretization technique is implemented within each element. As the last step, the assemblage procedure is performed to derive the set of governing equations which is solved via the pseudo arc-length continuation algorithm. Also, since HSDT is used herein, the mixed formulation approach is proposed to accommodate the continuity of first-order derivatives on the common boundaries of elements. Rectangular and circular plates under various boundary conditions with circular/rectangular/elliptical cutout are selected to generate the numerical results. In the numerical examples, the effects of geometrical properties and reinforcement with GPL on the nonlinear maximum deflection-transverse load amplitude curve are studied.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.3
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• pp.249-257
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• 2011

In this paper, an systematic approach is presented, in which the mixed variational theorem is employed to incorporate independent transverse shear stresses into a classical higher-order shear deformation theory(HSDT). The HSDT displacement field is taken to amplify the benefits of using a classical shear deformation theory such as simple and straightforward calculation and numerical efficiency. Those independent transverse shear stresses are taken from the fifth-order polynomial-based zig-zag theory where the fourth-order transverse shear strains can be obtained. The classical displacement field and independent transverse shear stresses are systematically blended via the mixed variational theorem. Resulting strain energy expressions are named as an enhanced higher-order shear deformation theory via mixed variational theorem(EHSDTM). The EHSDTM possess the same computational advantage as the classical HSDT while allowing for improved through-the-thickness stress and displacement variations via the post-processing procedure. Displacement and stress distributions obtained herein are compared to those of the classical HSDT, three-dimensional elasticity, and available data in literature.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.40 no.2
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• pp.233-238
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• 2020

Most deep learning (DL) approaches for bridge damage localization based on a structural health monitoring system commonly use supervised learning-based DL models. The supervised learning-based DL model requires the response data obtained from sensors on the bridge and also the label which indicates the damaged state of the bridge. However, it is impractical to accurately obtain the label data in fields, thus, the supervised learning-based DL model has a limitation in that it is not easily applicable in practice. On the other hand, an unsupervised learning-based DL model has the merit of being able to train without label data. Considering this advantage, this study aims to propose and theoretically validate a damage localization approach for bridges using a variational autoencoder, a representative unsupervised learning-based DL network: as a result, this study indicated the feasibility of VAE for damage localization.

• The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
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• v.3 no.1
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• pp.33-41
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• 1992

In this paper the propagation problems of waves nomally incident upon an anisotropic medium with arbitrary permittivity tensors are analyzed through the variational finite element method. First, a variational equation is derived from the new approach basd on the induction theorm, reactions, and reciprocity. Next, by using the finite element method, the propagation problems are solved from the obtained functional. Specially, the reflection and transmission coefficient and axis ratio are obtained on the case of normally incident upon a homogeneous and inhomogeneous anisotropic medium such as cold mgnetoplasma slab and showed agreement with those of the previous method.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.48 no.5
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• pp.10-15
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• 2011

Histogram equalization is an effective method to enhance the contrast of the image. However, it can result in unwanted artifacts such as excessive contrast enhancement and noise amplification. These artifacts can be reduced by modifying an intensity mapping function which is generated by histogram equalization. In this paper, we present a variational approach to the modification of the intensity mapping function. We define a functional whose minimization produces a modified intensity mapping function. Experimental results show that the intensity mapping function obtained by the proposed method can enhance the contrast of the image without visual artifacts.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.497-520
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• 2023

Numerous problems in science and engineering defined by nonlinear functional equations can be solved by reducing them to an equivalent fixed point problem. Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization problems, equilibrium problems, complementarity problems, selection and matching problems, and problems of proving the existence of solution of integral and differential equations.The theory of fixed is known to find its applications in many fields of science and technology. For instance, the whole world has been profoundly impacted by the novel Coronavirus since 2019 and it is imperative to depict the spread of the coronavirus. Panda et al. [24] applied fractional derivatives to improve the 2019-nCoV/SARS-CoV-2 models, and by means of fixed point theory, existence and uniqueness of solutions of the models were proved. For more information on applications of fixed point theory to real life problems, authors should (see [6, 13, 24] and the references contained in).

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.3
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• pp.91-97
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• 2023

Recent research shows that latent directions can be used to image process towards certain attributes. However, controlling the generation process of generative model is very difficult. Though the latent directions are used to image process for certain attributes, many restrictions are required to enhance the attributes received the latent vectors according to certain text and prompts and other attributes largely unaffected. This study presents a generative model having certain restriction to the latent vectors for image generation and manipulation. The suggested method requires only few minutes per manipulation, and the simulation results through Tensorflow Variational Auto-encoder show the effectiveness of the suggested approach with extensive results.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.131-164
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• 2024

In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite family of τ-demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertial extrapolation steps and adaptive non-monotonic step sizes. Under some appropriate conditions that are imposed on the parameters, the weak and linear convergence results of the proposed iterative scheme are established. Furthermore, we present some numerical examples and application of our proposed methods in comparison with other existing iterative methods. In order to show the practical applicability of our method to real word problems, we show that our algorithm has better restoration efficiency than many well known methods in image restoration problem. Our proposed iterative method generalizes and extends many existing methods in the literature.

• Honam Mathematical Journal
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• v.16 no.1
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• pp.103-109
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• 1994

Piezoceramic patches as collocated actuator and sensors are widely used in mechanical control systems. An approximation scheme for computing feedback gains arising in heat flux stabilization problem with such control mechanism is introduced. The scheme is based on a finite element method and a variational approach.

• East Asian mathematical journal
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• v.34 no.5
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• pp.549-570
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• 2018

We establish existence and bifurcation of global positive solutions for parametrized nonhomogeneous elliptic equations involving critical Sobolev-Hardy exponents and Hardy terms. The main approach to the problem is the variational method.