• Steel and Composite Structures
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• v.48 no.1
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• pp.73-88
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• 2023

This paper presents a novel implicit level set method for topology optimization of functionally graded (FG) structures with pre-existing discontinuities (pre-cracks) using radial basis functions (RBF). The mathematical formulation of the optimization problem is developed by incorporating RBF-based nodal densities as design variables and minimizing compliance as the objective function. To accurately capture crack-tip behavior, crack-tip enrichment functions are introduced, and an eXtended Finite Element Method (X-FEM) is employed for analyzing the mechanical response of FG structures with strong discontinuities. The enforcement of boundary conditions is achieved using the Hamilton-Jacobi method. The study provides detailed mathematical expressions for topology optimization of systems with defects using FG materials. Numerical examples are presented to demonstrate the efficiency and reliability of the proposed methodology.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.410-411
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• 2008

A topology optimization technique to develop extremely light trailer frame structure is performed due to the strong needs of the customers and makers owing to high level of oil price. First, the overall layout of the frame is derived using topology optimization and then, final specification is also derived utilizing DOE optimization technique for mass product.

• Journal of Integrative Natural Science
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• v.10 no.2
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• pp.115-118
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• 2017

We study a notion of $\mathcal{A}$-frequent hypercyclicity of linear maps between the Banach algebras consisting of operators on a separable infinite dimensional Banach space. We prove a sufficient condition for a linear map to satisfy the $\mathcal{A}$-frequent hypercyclicity in the strong operator topology.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.647-650
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• 2009

For a bounded operator T = $U{\mid}T{\mid}$ (polar decomposition), we consider a transform b $\widehat{T}$ = ${\mid}T{\mid}U$ and discuss the convergence of iterated transform of $\widehat{T}$ under the strong operator topology. We prove that such iteration of quasiaffine hyponormal operator converges to a normal operator under the strong operator topology.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1479-1503
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• 2007

In this paper, we study a strong k-deformation retract derived from a relative k-homotopy and investigate its properties in relation to both a k-homotopic thinning and the k-fundamental group. Moreover, we show that the k-fundamental group of a wedge product of closed k-curves not k-contractible is a free group by the use of some properties of both a strong k-deformation retract and a digital covering. Finally, we write an algorithm for calculating the k-fundamental group of a dosed k-curve by the use of a k-homotopic thinning.

• Steel and Composite Structures
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• v.21 no.6
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• pp.1389-1410
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• 2016

This paper proposes a hybrid of topological derivative-based level set method (LSM) and isogeometric analysis (IGA) for structural topology optimization. In topology optimization a significant drawback of the conventional LSM is that it cannot create new holes in the design domain. In this study, the topological derivative approach is used to create new holes in appropriate places of the design domain, and alleviate the strong dependency of the optimal topology on the initial design. Furthermore, the values of the gradient vector in Hamilton-Jacobi equation in the conventional LSM are replaced with a Delta function. In the topology optimization procedure IGA based on Non-Uniform Rational B-Spline (NURBS) functions is utilized to overcome the drawbacks in the conventional finite element method (FEM) based topology optimization approaches. Several numerical examples are provided to confirm the computational efficiency and robustness of the proposed method in comparison with derivative-based LSM and FEM.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.591-603
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• 2006

For a set $X{\subset}{\mathbb{Z}}^n$ let $(X,\;T^n_X)$ be the subspace of the Khalimsky n-dimensional space $({\mathbb{Z}}^n,\;T^n)$, $n{\in}N$. Considering a k-adjacency of $(X,\;T^n_X)$, we use the notation $(X,\;k,\;T^n_X)$. In this paper for a map $$f:(X,\;k,\;T^n_X){\rightarrow}(Y,\;2\;T_Y)$$, we find the condition that weak (k, 2)-continuity of the map f implies strong (k, 2)-continuity of f.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.99-107
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• 2010

This paper is a study about the relationships among topologies and intuitionistic fuzzy topology induced, respectively, by approximation operators and an intuitionistic fuzzy approximation operator associated with an approximation space (X, R), when the relation R on X is precisely reflexive and transitive. In particular, we consider an intuitionistic fuzzy approximation operator on an approximation space X (i.e., a set X with a reflexive and transitive relation on it), which turns out to be an intuitionistic fuzzy closure operator. This intuitionistic fuzzy closure operator gives rise to two saturated fuzzy topologies on X and it turns out that all the level topologies of one of the fuzzy topology coincide and equal to the topology analogously induced on X by a crisp approximation operator. These observations are then applied to intuitionistic fuzzy automata.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.11-17
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• 2011

We study some properties of quasi-topological spaces. Also we introduce the concept of Q-continuity and investigate several types of quasi-topology on an SGNS.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.1
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• pp.66-76
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• 2012

In this paper, we introduce the concept of ordinary smooth topology on a set X by considering the gradation of openness of ordinary subsets of X. And we obtain the result [Corollary 2.13] : An ordinary smooth topology is fully determined its decomposition in classical topologies. Also we introduce the notion of ordinary smooth [resp. strong and weak] continuity and study some its properties. Also we introduce the concepts of a base and a subbase in an ordinary smooth topological space and study their properties. Finally, we investigate some properties of an ordinary smooth subspace.