• 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.

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.33-40
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• 1996

A convergence structure defined by Kent [4] is a correspondence between the filters on a given set X and the subsets of X which specifies which filters converge to points of X. This concept is defined to include types of convergence which are more general than that defined by specifying a topology on X. Thus, a convergence structure may be regarded as a generalization of a topology. With a given convergence structure q on a set X, Kent [4] introduced associated convergence structures which are called a topological modification and a pretopological modification. (omitted)

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.10 s.253
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• pp.1187-1193
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• 2006

Traditionally, the continuum-based topology optimization methods employing the SIMP technique have been used to design compliant mechanisms. Although they have been successful, the optimized mechanisms by the methods are usually difficult to manufacture because of their geometrical complexities. The objective of this study is to develop a topology optimization method that can produce easy-to-fabricate mechanism structure. The proposed method is a ground beam method where beam connectivity is controlled by the beam joint stiffness. In this approach, beam joint stiffness determines the mechanism configuration. Because b the ground structure beams have uniform thicknesses varying only discretely, the resulting mechanism topologies become easily manufacturable.

• Journal of the Architectural Institute of Korea Structure & Construction
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• v.34 no.6
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• pp.11-18
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• 2018

Isogeometric concept is introduced to find out the optimum layout of plane structure under free vibration. Eigenvalue problem is formulated and numerically solved in order to obtain natural frequencies and mode shapes of plane structures. For the exact geometric expression of the structure, the Non-Uniform Rational B-spline Surface (NURBS) basis functions is employed and it is also used to define the material density functions. A node-wise design variables is adopted to deal with the updating of material density in topology optimization (TO). The definition of modal strain energy is employed to achieve the maximization of fundamental frequency through its minimization. The verification of the proposed TO technique is performed by a series of benchmark test for plane structures.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.16 no.1
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• pp.47-52
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• 2007

A material mixing method to obtain an optimal topology for a structure in a thermal environment was suggested. This method is based on Evolutionary Structural Optimization(ESO). The proposed material mixing method extends the ESO method to a mixing several materials for a structure in the multicriteria optimization of thermal flux and thermal stress. To do this, the multiobjective optimization technique was implemented. The overall efficiency of material usage was measured in terms of the combination of thermal stress levels and heat flux densities by using a combination strategy with weighting factors. Also, a smoothing scheme was implemented to suppress the checkerboard pattern in the procedure of topology optimization. It is concluded that ESO method with a smoothing scheme is effectively applied to topology optimization. Optimal topologies having multiple thermal criteria for a printed circuit board(PCB) substrate were presented to illustrate validity of the suggested material mixing method. It was found that the suggested method works very well for the multicriteria topology optimization.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.157-162
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• 2007

A new level set based topology optimization employing inner-front creation algorithm is presented. In the conventional level set based topology optimization, the optimum topology strongly depends on the initial level set distribution due to the incapability of inner-front creation during optimization process. In the present work, in this regard, an inner-front creation algorithm is proposed. in which the sizes. shapes. positions, and number of new inner-fronts during the optimization process can be globally and consistently identified by considering both the value of a given criterion for inner-front creation and the occupied volume (area) of material domain. To facilitate the inner-front creation process, the inner-front creation map which corresponds to the discrete valued criterion of inner-front creation is applied to the level set function. In order to regularize the design domain during the optimization process, the edge smoothing is carried out by solving the edge smoothing partial differential equation (PDE). Updating the level set function during the optimization process, in the present work, the least-squares finite element method (LSFEM) is employed. As demonstrative examples for the flexibility and usefulness of the proposed method. the level set based topology optimization considering lightweight design of 3D shell structure is carried out.

• Structural Engineering and Mechanics
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• v.81 no.3
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• pp.267-280
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• 2022

Multiscale structure has attracted significant interest due to its high stiffness/strength to weight ratios and multifunctional performance. However, most of the existing concurrent topology optimization works are carried out under deterministic load conditions. Hence, this paper proposes a robust concurrent topology optimization method based on the bidirectional evolutionary structural optimization (BESO) method for the design of structures composed of periodic microstructures subjected to uncertain dynamic loads. The robust objective function is defined as the weighted sum of the mean and standard deviation of the module of dynamic structural compliance with constraints are imposed to both macro- and microscale structure volume fractions. The polynomial chaos expansion (PCE) method is used to quantify and propagate load uncertainty to evaluate the objective function. The effective properties of microstructure is evaluated by the numerical homogenization method. To release the computation burden, the decoupled sensitivity analysis method is proposed for microscale design variables. The proposed method is a non-intrusive method, and it can be conveniently extended to many topology optimization problems with other distributions. Several numerical examples are used to validate the effectiveness of the proposed robust concurrent topology optimization method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.3
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• pp.281-290
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• 2003

Co Evolutionary Structural Design(CESD) Framework is presented, which can deal with the load design and structural topology design simultaneously. The load design here is the exploration algorithm that finds the critical load patterns of the given structure. In general, the load pattern is a crucial factor in determining the structural topology and being selected from the experts어 intuition and experience. However, if any of the critical load patterns would be excluded during the process of problem formation, the solution structure might show inadequate performance under the load pattern. Otherwise if some reinforcement method such as safety factor method would be utilized, the solution structure could result in inefficient conservativeness. On the other hand, the CESD has the ability of automatically finding the most critical load patterns and can help the structural solution evolve into the robust design. The CESD is made up of a load design discipline and a structural topology design discipline both of which have the fully coupled relation each other. This coupling is resolved iteratively until the resultant solution can resist against all the possible load patterns and both disciplines evolve into the solution structure with the mutual help or competition. To verify the usefulness of this approach, the 10 bar truss and the jacket type offshore structure are presented. SORA(Sequential Optimization & Reliability Assessment) is adopted in CESD as a probabilistic optimization methodology, and its usefulness in decreasing the computational cost is verified also.

• 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 for History of Mathematics
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• v.10 no.2
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• pp.11-23
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• 1997

Category theory gives a convenient language for the study of mathematical structures besides its own study. In this paper, we investigate how the abstract structure theory emerged in 1930s affects the study in Topology and eventually becomes a rudiment for the category theory. Moreover, various extensions and universal mapping problems were put in their proper perspective as reflections by the category theory and by its duality principle, coreflections become an interesting subject in Topology, both of which give rise to a new discipline of the categorical topology.