• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.391-397
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• 2017

In this note we extend our previous result about the structure of the dual of a crossed product $C^*$-algebra $A{\rtimes}_{\sigma}G$, when G is a finite group. We consider the space $\tilde{\Gamma}$ which consists of pairs of irreducible representations of A and irreducible projective representations of subgroups of G. Our goal is to endow $\tilde{\Gamma}$ with a topology so that the orbit space e $G{\backslash}{\tilde{\Gamma}}$ is homeomorphic to the dual of $A{\rtimes}_{\sigma}G$. In particular, we will show that if $\widehat{A}$ is Hausdorff then $G{\backslash}{\tilde{\Gamma}}$ is homeomorphic to $\widehat{A{\rtimes}_{\sigma}G}$.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.7 s.238
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• pp.990-997
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• 2005

The objective of this paper is to present the element connectivity parameterization (ECP) fur three dimensional problems. In the ECP method, a continuum structure is viewed as discretized finite elements connected by zero-length elastic links whose stiffness values control the degree of inter-element connectivity. The ECP method can effectively avoid the formation of the low-density unstable elements. These elements appear when the standard element density method is used for geometrical nonlinear problems. In this paper, this ECP method developed fur two-dimensional problems is expanded to the design of three-dimensional geometrical nonlinear structures. Among others, the automatic procedure converting standard finite element models to the models suitable for the ECP approach is developed and applied for optimization problems defined on general three-dimensional design domains.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1265-1283
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• 2019

We develop a framework to construct geometric representations of finite groups G through the correspondence between real toric spaces $X^{\mathbb{R}}$ and simplicial complexes with characteristic matrices. We give a combinatorial description of the G-module structure of the homology of $X^{\mathbb{R}}$. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type A and B, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representation geometrically as the homology of real toric varieties.

• Journal of Power Electronics
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• v.19 no.3
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• pp.625-636
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• 2019

This paper proposes an active leakage magnetic field (LMF) suppression scheme, which uses the dual-transmitter (DT) topology, for EV wireless charging systems (EVWCS). The two transmitter coils are coplanar, concentric and driven by separate inverters. The LMF components generated by the three coils cancel each other out to reduce the total field strength. This paper gives a detailed theoretical analysis on the operating principles of the proposed scheme. Finite element analysis is used to simulate the LMF distribution patterns. Experimental results show that when there is no coil misalignment, 97% of the LMF strength can be suppressed in a 1kW prototype. These results also show that the impact on efficiency is small. The trade-off between LMF suppression and efficiency is revealed, and a control strategy to balance these two objectives is presented.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.2 s.107
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• pp.115-123
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• 2006

A feasibility of using the topology optimization method for structural damage identification is investigated for the first time. The frequency response functions (FRFs) are assumed to be constructed by the finite element models of damaged and undamaged structures. In addition to commonly used resonances, antiresonances are employed as the damage identifying modal parameters. For the topology optimization formulation, the modal parameters of the undamaged structure are made to approach those of the damaged structure by means of the constraint equations, while the objective function is an explicit penalty function requiring clear black-and-white images. The developed formulation is especially suitable for damage identification problems dealing with many modal parameters. Although relatively simple numerical problems were considered in this investigation, the possibility of using the topology optimization method for structural damage identification is suggested through this research.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1015-1018
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• 2006

In this paper, new topology optimization technique is proposed. It mainly uses the strain energy distributions induced by the mode shapes associated with natural frequencies of the structure and so we can implicitly consider the dynamic characteristics of the structure in the topology optimization process. The strain energy to be minimized is employed as the objective function and the initial volume of structures is adopted as the constraint function. The resizing algorithm devised from the optimality criteria method is used to update the hole size of the cell existing in each finite element. The cantilever beam problem is adopted to test the proposed techniques. From numerical test, it is found to be that the optimum topology of the cantilever produced by the proposed technique has a hugh increase of natural frequency value and the technique is very effective to maximize the fundamental frequency of the structure.

• Structural Engineering and Mechanics
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• v.45 no.6
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• pp.759-777
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• 2013

In this paper, a topology optimization method based on the element independent nodal density (EIND) is developed for continuum solids with multiple load cases and multiple constraints. The optimization problem is formulated ad minimizing the volume subject to displacement constraints. Nodal densities of the finite element mesh are used a the design variable. The nodal densities are interpolated into any point in the design domain by the Shepard interpolation scheme and the Heaviside function. Without using additional constraints (such ad the filtering technique), mesh-independent, checkerboard-free, distinct optimal topology can be obtained. Adopting the rational approximation for material properties (RAMP), the topology optimization procedure is implemented using a solid isotropic material with penalization (SIMP) method and a dual programming optimization algorithm. The computational efficiency is greatly improved by multithread parallel computing with OpenMP to run parallel programs for the shared-memory model of parallel computation. Finally, several examples are presented to demonstrate the effectiveness of the developed techniques.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.12
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• pp.1401-1409
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• 2009

All the forces in the real world act dynamically on structures. Design and analysis should be performed based on the dynamic loads for the safety of structures. Dynamic (transient or vibrational) responses have many peaks in the time domain. Topology optimization, which gives an excellent conceptual design, mainly has been performed with static loads. In topology optimization, the number of design variables is quite large and considering the peaks is fairly costly. Topology optimization in the frequency domain has been performed to consider the dynamic effects; however, it is not sufficient to fully include the dynamic characteristics. In this research, linear dynamic response topology optimization is performed in the time domain. First, the necessity of topology optimization to directly consider the dynamic loads is verified by identifying the relationship between the natural frequency of a structure and the excitation frequency. When the natural frequency of a structure is low, the dynamic characteristics (inertia effect) should be considered. The equivalent static loads (ESLs) method is proposed for linear dynamic response topology optimization. ESLs are made to generate the same response field as that from dynamic loads at each time step of dynamic response analysis. The method was originally developed for size and shape optimizations. The original method is expanded to topology optimization under dynamic loads. At each time step of dynamic analysis, ESLs are calculated and ESLs are used as the external loads in static response topology optimization. The results of topology optimization are used to update the design variables (density of finite elements) and the updated design variables are used in dynamic analysis in a cyclic manner until the convergence criteria are satisfied. The updating rules and convergence criteria in the ESLs method are newly proposed for linear dynamic response topology optimization. The proposed updating rules are the artificial material method and the element elimination method. The artificial material method updates the material property for dynamic analysis at the next cycle using the results of topology optimization. The element elimination method is proposed to remove the element which has low density when static topology optimization is finished. These proposed methods are applied to some examples. The results are discussed in comparison with conventional linear static response topology optimization.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1234-1239
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• 2003

In the product design process computer-aided engineering and optimization tools are widely utilized in order to reduce the total development time and cost. Since several simulation tools are involved in the process, information losses, omissions, or errors are common and the importance of seamless information exchange among the tools has been increased. In this study ISO STEP standards are adopted to represent the neutral format for CAE/CAO information exchange. The schema of AP209 is used to define the information of finite element analysis and the new schema is proposed to describe the information of structural optimization based on the STEP methodology. The schema is implemented by EXPRESS, information modeling language, and ST-Developer is employed to generate C++ classes and STEP Rose Library by using the schema denoted. To substantiate the proposed approach, the information access interfaces of the finite element modeling software (FEMAP), structural optimization software (GENESIS) and in-house topology optimization program are developed. Examples of the size optimization of a three-bar truss and topology optimization of a MBB beam are shown to validate the information exchange of finite element analysis and structural optimization using STEP standards.

• The Journal of Korean Academy of Prosthodontics
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• v.42 no.2
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• pp.125-132
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• 2004

Statements of problem: All ceramic fixed partial denture cores can be made by the slip casting method and the advanced alumina tape method. The fracture resistance of these core connector areas is relatively low. Purpose: The purpose of this study is to standardize the appropriate volumetric figure and location of the connectors in the alumina core fabricated in alumina tape to be used in fixed partial dentures by way of topology optimization. Material and method: A maxillary anterior three-unit bridge alumina core with teeth form and surrounding periodontal apparatus model was used to ultimately design the most structurally rigid form of the connector. Loadings from a $0^{\circ}$, $45^{\circ}$ and $60^{\circ}$ to the axis of each tooth were applied and analyzed with the 3-D finite element analysis method. Using the results from these experiments, the topology optimization was applied and the optimal reinforcement layout of connector was obtained and the detail shape in the fixed partial denture core was designed. Results: The modified prosthesis with the form of a bulk in the lower lingual surface of the connector in the event, reduced the stress concentration up to 20% in the 3-D FEA. Conclusion: The formation of a bulk in the lower lingual connector area of an alumina core for a fixed partial denture decreases the stress to a clinically favorable measure but does not harm the esthetic point of view. This result illustrates the possibility of clinical application of the modified form designed by the topology optimization method.