• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.20 no.1
• /
• pp.19-28
• /
• 2007

Discrete topology optimization processes of structures start from an initial design domain which is described by the topology of constant material densities. During optimization procedures, the structural topology changes in order to satisfy optimization problems in the fixed design domain, and finally, the optimization produces material density distributions with optimal topology. An introduction of initial holes in a design domain presented by Eschenauer et at. has been utilized in order to improve the optimization convergence of boundary-based shape optimization methods by generating finite changes of design variables. This means that an optimal topology depends on an initial topology with respect to topology optimization problems. In this study, it is investigated that various optimal topologies can be yielded under constraints of usable material, when partial solid phases are deposited in an initial design domain and thus initial topology is finitely changed. As a numerical application, structural topology optimization of a simple MBB-Beam is carried out, applying partial circular solid phases with varying sizes to an initial design domain.

• Structural Engineering and Mechanics
• /
• v.5 no.2
• /
• pp.209-220
• /
• 1997

The dynamic equations for an arbitrary cluster comprising rigid spheres or assemblies of spheres (subclusters) encountered in granular-type systems are considered. The system is treated within the framework of multibody dynamics. It is shown that for an arbitrary cluster topology the governing equations can be given in an explicit scalar from. The derivation is based on the D'Alembert principle, on inertial coordinate system for each body and direct utilization of the path matrix describing the topology. The scalar form of the equations is important in computer simulations of flow of granular-type materials. An illustrative example of a three-body system is given.

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

• Steel and Composite Structures
• /
• v.39 no.5
• /
• pp.511-528
• /
• 2021

There are recently some advances in solving numerically topology optimization problems for large-scaled trusses based on ground structure approach. A disadvantage of this approach is that the final design usually includes many bars, which is difficult to be produced in practice. One of efficient tools is a so-called filter scheme for the ground structure to reduce this difficulty and determine several distinct bars. In detail, this technique is valuable for practical uses because unnecessary bars are filtered out from the ground structure to obtain a well-defined structure during the topology optimization process, while it still guarantees the global equilibrium condition. This process, however, leads to a singular system of equilibrium equations. In this case, the minimization of least squares with Tikhonov regularization is adopted. In this paper, a proposed algorithm in controlling optimal Tikhonov parameter is considered in combination with the filter scheme due to its crucial role in obtaining solution to remove numerical singularity and saving computational time by using sparse matrix, which means that the discrete optimal topology solutions depend on choosing the Tikhonov parameter efficiently. Several numerical examples are investigated to demonstrate the efficiency of the filter parameter control algorithm in terms of the large-scaled optimal topology designs.

• Proceedings of the KIEE Conference
• /
• 2006.07b
• /
• pp.651-652
• /
• 2006

This research presents a topology optimization for manipulating the main heat flow in coupled magneto-thermal systems. The heat generated by eddy currents is considered in the design domain assuming an adiabatic boundary. For a practical optimization, the convection condition is considered in the topological process of the thermal field. Topology design sensitivity is derived by employing the discrete system equations combined with the adjoint variable method. As numerical examples, a simple iron and a C-core design heated-up by eddy currents demonstrate the strength of the proposed approach to solve the coupled problem.

• Journal of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.381-402
• /
• 1999

Let {Rn($\chi$)}{{{{ { } atop {n=0} }}}} be a discrete Sobolev orthogonal polynomials (DSOPS) relative to a symmetric bilinear form (p,q)={{{{ INT _{ } }}}} pqd$\mu$0 +{{{{ INT _{ } }}}} p qd$\mu$1, where d$\mu$0 and d$\mu$1 are signed Borel measures on . We find necessary and sufficient conditions for {Rn($\chi$)}{{{{ { } atop {n=0} }}}} to satisfy a second order difference equation 2($\chi$) y($\chi$)+ 1($\chi$) y($\chi$)= ny($\chi$) and classify all such {Rn($\chi$)}{{{{ { } atop {n=0} }}}}. Here, and are forward and backward difference operators defined by f($\chi$) = f($\chi$+1) - f($\chi$) and f($\chi$) = f($\chi$) - f($\chi$-1).

• Proceedings of the KIPE Conference
• /
• 2002.07a
• /
• pp.589-592
• /
• 2002

The CCM (Continuous Conduction Mode) boost topology is generally used in the PFC (Power Factor Correction) regulator of household air-conditioning systems. There are three kinds of power devices-bridge rectifier diodes, FRDs (Fast Recovery Diodes), and IGBTs (or MOSFETs) - used In a boost PFC regulator. Selecting the appropriate device is very cumbersome work, specially, in the case of FRDs and IGBTs, because there are several considerations as described below: 1) High frequency leakage current regulation (conducted and radiated EMI regulation) 2) Power losses and thermal design 3) Device cost. It should be noted that there are trade-offs between the power loss characteristic of 2) and the other characteristics of 1) and 3). This paper presents a detailed evaluation by using several types of power devices, which can be unintentionally used, to show that optimal selection can be achieved. Based on the given thermal resistances, thermal analysis and design procedures are also described from a practical viewpoint.

• Proceedings of the KIPE Conference
• /
• 2007.07a
• /
• pp.135-137
• /
• 2007

A phase shifted full-bridge PWM converter (PSFBC) has been used as the most popular topology for many applications. But, for the reasons of the cost and performance, the control circuits for the PSFBC have generally been implemented using analog circuits. The studies on the digital control of the PSFBC were recently presented. However, they considered only the digital implementation of the analog controller. This paper presents the modeling and design of the digital controller for the PSFBC in the discrete time domain. The discretized PSFBC model is first derived considering the sampling effect. Based on this model, the digital controller is directly designed in discrete time domain. The simulation and experimental results are provided to verify the proposed modeling and controller design.

• Journal of Korea Multimedia Society
• /
• v.22 no.1
• /
• pp.18-26
• /
• 2019

In this paper we propose how to detect circular objects in the gray scale image and segment them using the discrete Morse theory, which makes it possible to analyze the topology of a digital image, when it is transformed into the data structure of some combinatorial complex. It is possible to get meaningful information about how many connected components and topologically circular shapes are in the image by computing the persistent homology of the filtration using the Morse complex. We obtain a Morse complex by modeling an image as a cubical cellular complex. Each cell in the Morse complex is the critical point at which the topological structure changes in the filtration consisting of the level sets of the image. In this paper, we implement the proposed algorithm of segmenting the circularly shaped objects with a long persistence of homology as well as computing persistent homology along the filtration of the input image and displaying in the form of a persistence diagram.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.31 no.12
• /
• pp.1180-1187
• /
• 2007

In the present work, topology optimization method using adaptive inner-front level set method is presented. In the conventional level set based topology optimization method, there exists an incapability for inner-front creation during optimization process. In this regard, as a new attempt to avoid and to overcome the limitation, an inner-front creation algorithm is proposed. In the inner-front creation algorithm, the strain energy density of a structure along with volume constraint is considered. Especially, to facilitate the inner-front creation process during the optimization process, the inner-front creation map which corresponds to the discrete valued function of strain energy density is constructed. In the evolution of the level set function during the optimization process, the least-squares finite element method (LSFEM) is employed. As an application to shell structures, the lightweight design of doubly curved shell and segmented mirror is carried out.