• Proceedings of the KSME Conference
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• 2004.04a
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• pp.468-473
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• 2004

New reliability-based topology optimization method is proposed by utilizing single-loop single vector approach, which approximate searching the most probable point in the probabilistic design domain analytically, to reduce the time cost and dealing with several constraints to handle practical design requirements. To examine uncertainties in the topology design of a structure, the modulus of elasticity of the material and applied loadings are considered as probabilistic design variables. The results of design examples show that the proposed method provides efficiency curtailing the time for the optimization process and accuracy satisfying the specified reliability.

• Proceedings of the KIEE Conference
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• 2003.07b
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• pp.741-743
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• 2003

A reliability-based topology optimization (RBTO) for electromagnetic systems using the finite element method is presented. Permeability and applied current density are considered as uncertain variable. In order to compute reliability constraints, performance measure approach is used. To find the reliability index, the limit state function is linearly approximated at each iteration. Numerical examples show the effectiveness of the proposed method.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.12
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• pp.3117-3132
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• 2012

The tree topology in multicast systems has high transmission efficiency, low latency, but poor resilience to node failures. In our work, some nodes are selected as backbone nodes to construct a tree-like core overlay. Backbone nodes are reliable enough and have strong upload capacity as well, which is helpful to overcome the shortcomings of tree topology. The core overlay is organized into a spanning tree while the whole overlay is of mesh-like topology. This paper focuses on improving the performance of the application-layer multicast overlay by optimizing the core overlay which is periodically adjusted with the proposed optimization algorithm. Our approach is to construct the overlay tree based on the out-degree weighted reliability where the reliability of a node is weighted by its upload bandwidth (out-degree). There is no illegal solution during the evolution which ensures the evolution efficiency. Simulation results show that the proposed approach greatly enhances the reliability of the tree-like core overlay systems and achieves shorter delay simultaneously. Its reliability performance is better than the reliability-first algorithm and its delay is very close to that of the degree-first algorithm. The complexity of the proposed algorithm is acceptable for application. Therefore the proposed approach is efficient for the topology optimization of a real multicast overlay.

• Steel and Composite Structures
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• v.47 no.5
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• pp.569-585
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• 2023

This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating popular radial basis functions (RBFs) into an implicit level set (ILS) method. Compared to traditional element density-based methods, a level set (LS) description of material boundaries produces a smoother boundary description of the design. The paper develops RBF implicit modeling with multiquadric (MQ) splines, thin-plate spline (TPS), exponential spline (ES), and Gaussians (GS) to define the ILS function with high accuracy and smoothness. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. A LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation (PDE) into a system of coupled non-linear ordinary differential equations (ODEs) over the entire design domain using a collocation formulation of the method of lines design variables. The paper presents detailed mathematical expressions for BiDFG beams topology optimization with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG). Several numerical examples are presented to verify the method's efficiency, reliability, and success in accuracy, convergence speed, and insensitivity to initial designs in the topology optimization of two-dimensional (2D) structures. Overall, the paper presents a novel and efficient approach to topology optimization that can handle bi-directional functionally graded structures with complex geometries.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.1
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• pp.37-43
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• 2010

In this paper, a reliability-based design optimization is developed for the topology design of linear structures using a performance measure approach. Spatial domain is discretized using three dimensional Reissner-Mindlin plate elements and design variable is taken as the material property of each element. A continuum based adjoint variable method is employed for the efficient computation of sensitivity with respect to the design and random variables. The performance measure approach of RBDO is employed to evaluate the probabilistic constraints. The topology optimizationproblem is formulated to have probabilistic displacement constraints. The uncertainties such as material property and external loads are considered. Numerical examples show that the developed topology optimization method could effectively yield a reliable design, comparing with the other methods such as deterministic, safety factor, and worst case approaches.

• Steel and Composite Structures
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• v.51 no.2
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• pp.203-223
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• 2024

This study shows functionally graded material structural topology optimization under buckling constraints. The SIMP (Solid Isotropic Material with Penalization) material model is used and a method of moving asymptotes is also employed to update topology design variables. In this study, the quadrilateral element is applied to compute buckling load factors. Instead of artificial density properties, functionally graded materials are newly assigned to distribute optimal topology materials depending on the buckling load factors in a given design domain. Buckling load factor formulations are derived and confirmed by the resistance of functionally graded material properties. However, buckling constraints for functionally graded material topology optimization have not been dealt with in single material. Therefore, this study aims to find the minimum compliance topology optimization and the buckling load factor in designing the structures under buckling constraints and generate the functionally graded material distribution with asymmetric stiffness properties that minimize the compliance. Numerical examples verify the superiority and reliability of the present method.

• Steel and Composite Structures
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• v.27 no.1
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• pp.27-33
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• 2018

In this study, a mixed-interpolated tensorial component 4 nodes method (MITC4) is treated as a numerical analysis model for topology optimization using multiple materials assigned within Reissner-Mindlin plates. Multi-material optimal topology and shape are produced as alternative plate retrofit designs to provide reasonable material assignments based on stress distributions. Element density distribution contours of mixing multiple material densities are linked to Solid Isotropic Material with Penalization (SIMP) as a design model. Mathematical formulation of multi-material topology optimization problem solving minimum compliance is an alternating active-phase algorithm with the Gauss-Seidel version as an optimization model of optimality criteria. Numerical examples illustrate the reliability and accuracy of the present design method for multi-material topology optimization with Reissner-Mindlin plates using MITC4 elements and steel materials.

• 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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.9 no.5
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• pp.1149-1160
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• 2005

Generally, the network topology design problem, which is difficult to solve with the classical method because it has exponentially increasing complexity with the augmented network size, is characterized as a kind of NP-hard combinatorial optimization problem. The problem of this research is to design the highly reliable network topology considering the connection cost and all-terminal network reliability, which can be defined as the probability that every pair of nodes can communicate with each other. In order to solve the highly reliable network topology design problem minimizing the construction cost subject to network reliability, we proposes an efficient two phase approach to design reliable network topology, i.e., the first phase employs, a genetic algorithm (GA) which uses $Pr\ddot{u}fer$ number for encoding method and backtracking Algorithm for network reliability calculation, to find the spanning tree; the second phase is a greedy method which searches the optimal network topology based on the spanning ree obtained in the first phase, with considering 2-connectivity. finally, we show some experiments to demonstrate the effectiveness and efficiency of our two phase approach.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1029-1034
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• 2004

Recent engineering process requires fast development and manufacturing of the products. This paper mainly discusses the process of rapid product development (RPD) from the reverse engineering to the optimal design. A laser scanning system scans a product and the efficient data processing method reduces the scanned point data. The reduced (scanned) points model is transformed to a finite element model without the construction of a CAD model. Since CAD modeling is a time-consuming work, skipping this step can save much time. This FE model is updated from the result based on the structural characteristics from modal test of the real model. For FE model updating, Response Surface Method is adopted. Finally, the updated FE model is optimized using the reliability-based topology optimization, which is developed recently. All these processes are applied to the design of an upper part model of a cellular phone.