• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.1
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• pp.19-26
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• 2023

Because of the development of computational resources, an entire structure in which many components are combined can be analyzed. To do so, the calculation time and number of data points are increased. In many practical industry structures, there are many parts with repeated patterns. To analyze the repetitive structures effectively, a homogenization method is usually employed. In a homogenization module, including commercial programs, it is generally assumed that a unit cell is repeated in all directions. However, the practical industry structures usually have complicated, repeated patterns or structures. Complicated patterns are difficult to address using the conventional homogenization method. Therefore, in this study, a multilevel homogenization method was devised to consider complex regularities. The proposed homogenization method divides the structure into several areas and performs multiple homogenizations, resulting in a more accurate analysis than that provided by the previous method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.7
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• pp.1210-1216
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• 2003

Topology optimization is applied to determine the layout of a structural component with a specified frequency by minimizing the difference between the specified structural frequency and a given frequency. The homogenization design method is employed and the topology design problem is solved by the optimality criteria method. The value of a weighting factor in the optimality criteria plays an important role in this topology design problem. The modified optimality criteria method approximated by using the binomial expansion is suggested to determine the suitable value of the weighting factor, which makes convergence stable. If a given frequency is set as an excited frequency, it is possible to avoid resonance by moving away the specified structural frequency from the given frequency. The results of several test problems are compared with previous works and show the validity of the proposed algorithm.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.183-190
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• 2001

Topology optimization. has been evolved into a very efficient conceptual design tool and has been utilized into design engineering processes in many industrial parts. In recent years, topology optimization has become the focus of structural optimization design and has been researched and widely applied both in academy and industry. Traditional topology optimization has been using homogenization method and optimality criteria method. Homogenization method provides relationship equation between structure which includes many holes and stiffness matrix in FEM. Optimality criteria method is used to update design variables while maintaining that volume fraction is uniform. Traditional topology optimization has advantage of good convergence but has disadvantage of too much convergency time and additive checkerboard prevention algorithm is needed. In one way to solve this problem, element remove method is presented. Then, it is applied to many examples. From the results, it is verified that the time of convergence is very improved and optimal designed results is obtained very similar to the results of traditional topology using 8 nodes per element.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.10
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• pp.1613-1620
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• 2001

This study is focused on the application of the homogenization design method (HDM) to reduce the vibration level of a structure excited by magnetic harmonic farces. This is accomplished by obtaining the optimal material distribution in a design domain to minimize the frequency response caused by the magnetic harmonic excitation. The Maxwell stress method is used to compute the magnetic force and the HDM is applied leer the optimization. The developed method is applied to a simple pole model that is excited by the harmonic bending farce caused by the current around an adjacent stator. Results shows that the HDM is valid to minimize the frequency response.

• Transactions of the Korean Society of Automotive Engineers
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• v.12 no.5
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• pp.85-93
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• 2004

Electric vehicle body has to be subjected to uniform load and requires auxiliary equipment such as air pipe and electric wire pipe. Especially, the cross beam supports the weight of passenger and electrical equipments. This need to use adaptive design in initial design stage to gain economy through interchangeability between many kinds of components. This study performs the topology optimization by the concept of homogenization based on optimality criteria method which is efficient for the problem with a number of boundary condition and design variable. Therefore this provides the method to determine the optimum position and the shape of circular hole in the cross beam and then can achieve the weight minimization of electric vehicle body.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.392-397
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• 2001

Topology optimization is applied to determine the layout of a structure whose eigenfrequency coincides with a specified frequency. The topology optimization problem is formulated to minimize the difference between the structural frequency and a given frequency using the homogenization method and the modified optimality criteria method. It turns out that the value of a weighting factor in the updating scheme plays an important role to achieve both a suitable speed and a stable convergence of an algorithm. Unlike a constant weighting factor in previous works, it is suggested that a weight factor is varied during the iteration to control the amount of the frequency change. To substantiate the proposed approach two-dimensional structural design problems are presented and the resulted topology layouts for the specified eigenfrequency are compared to layouts for maximizing the corresponding eigenfrequency.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.2 s.245
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• pp.164-170
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• 2006

To prevent the numerical instabilities in topology optimization, continuous approximation of material distribution (CAMD) is proposed to the homogenization design method (HDM) and the simple isotropic material with penalization (SIMP) method. The continuous FE approximation of design variables including high order elements is applied to the formulation of SIMP method. Numerical examples are presented to compare the efficiency of CAMD both in HDM and SIMP.

• Nuclear Engineering and Technology
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• v.44 no.1
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• pp.43-52
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• 2012

To compute a permeability coefficient along a rough fracture that takes into account the fracture geometry, this study performed detailed measurements of fracture roughness using a confocal laser scanning microscope, a quantitative analysis of roughness using a spectral analysis, and a homogenization analysis to calculate the permeability coefficient on the microand macro-scale. The homogenization analysis is a type of perturbation theory that characterizes the behavior of microscopically inhomogeneous material with a periodic boundary condition in the microstructure. Therefore, it is possible to analyze accurate permeability characteristics that are represented by the local effect of the facture geometry. The Cpermeability coefficients that are calculated using the homogenization analysis for each rough fracture model exhibit an irregular distribution and do not follow the relationship of the cubic law. This distribution suggests that the permeability characteristics strongly depend on the geometric conditions of the fractures, such as the roughness and the aperture variation. The homogenization analysis may allow us to produce more accurate results than are possible with the preexisting equations for calculating permeability.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.376.2-376
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• 2002

In this study, the shape of suspension load beam for NFR(Near Field Recording) was proposed, which was designed using Topology optimization based on Homogenization method. Lens and Micro-mirror are attached to the end of the suspension load beam for collection and control the light, which increasing the system mass. Increment of the system mass cause to decrease the tracking stiffness mode frequency. (omitted)

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.4
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• pp.293-299
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• 2016

In this paper, a projection method is introduced which is used in topology design optimization. In the projection method, each active design variable is projected onto the design domain depending on the shape and size of the projection functions, and the finite element under this projection receives a solid material. Furthermore, the size of the projection function defines the minimum length scale of the structural members. Therefore, a designer can easily apply design constraints without complicated post-processing procedure. In addition, the projection method can be combined with the homogenization theory, and applied to material design problem for composite materials. Topology design optimization for the unit-cell of the periodic structures can maximize the effective material properties, which yields the optimal material distribution with maximum bulk or shear moduli under a given volume fraction.