• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.3
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• pp.339-345
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• 2007

In this paper, a variational formulation for plane elasticity problems is derived based on an isogeometric approach. The isogeometric analysis is an emerging methodology such that the basis functions for response analysis are generated directly from NURBS (Non-Uniform Rational B-Splines) geometry. Furthermore, the solution space for the response analysis can be represented in terms of the same functions to represent the geometry, which enables to provide a precise construction method of finite element model to exactly represent geometry using B-spline base functions in CAD geometric modeling and analyze arbitrarily shaped structures without re-meshing. In this paper, a continuum-based adjoint sensitivity analysis method using the isogeometric approach is extensively derived for the plane elasticity problems. The conventional shape optimization using the finite element method has some difficulties in the parameterization of geometry In the isogeometric analysis, however, the geometric properties are already embedded in the B-spline basis functions and control points so that it has potential capability to overcome the aforementioned difficulties. Through some numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.

• Journal of Korean Society of Steel Construction
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• v.9 no.3 s.32
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• pp.457-465
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• 1997

The Shape optimization makes it possible to reduce the weight of structure and cost then member sizing optimization. A vast amount of imprecise information is existed in constraints of the optimum design. It is very difficult and sometimes confusing to describe and to deal with the several criteria which contain fuzzy degrees of relatives importance. This paper proposed weighting strategies in the multiobjective shape optimization of fuzzy structural system by ${\alpha}$-cut approach. The algorithm in this research is numerically tested for 2-bar truss structure. The result show that. the user can choose the one optimum solution in practices as obtaining the optimum solutions according to the ${\alpha}$-cut approach, weight of volume and displacement.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.1
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• pp.1-8
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• 2014

Using the level set and the meshfree methods, we develop a topological shape optimization method applied to linear elasticity problems. Design gradients are computed using an efficient adjoint design sensitivity analysis(DSA) method. The boundaries are represented by an implicit moving boundary(IMB) embedded in the level set function obtainable from the "Hamilton-Jacobi type" equation with the "Up-wind scheme". Then, using the implicit function, explicit boundaries are generated to obtain the response and sensitivity of the structures. Global nodal shape function derived on a basis of the reproducing kernel(RK) method is employed to discretize the displacement field in the governing continuum equation. Thus, the material points can be located everywhere in the continuum domain, which enables to generate the explicit boundaries and leads to a precise design result. The developed method defines a Lagrangian functional for the constrained optimization. It minimizes the compliance, satisfying the constraint of allowable volume through the variations of boundary. During the optimization, the velocity to integrate the Hamilton-Jacobi equation is obtained from the optimality condition for the Lagrangian functional. Compared with the conventional shape optimization method, the developed one can easily represent the topological shape variations.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.1
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• pp.9-16
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• 2014

Using a level set method and topological derivatives, a topological shape optimization method that is independent of an initial design is developed for linearly elastic structures. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. The "Hamilton-Jacobi(H-J)" equation and computationally robust numerical technique of "up-wind scheme" lead the initial implicit boundary to an optimal one according to the normal velocity field while minimizing the objective function of compliance and satisfying the constraint of allowable volume. Based on the asymptotic regularization concept, the topological derivative is considered as the limit of shape derivative as the radius of hole approaches to zero. The required velocity field to update the H-J equation is determined from the descent direction of Lagrangian derived from optimality conditions. It turns out that the initial holes are not required to get the optimal result since the developed method can create holes whenever and wherever necessary using indicators obtained from the topological derivatives. It is demonstrated that the proper choice of control parameters for nucleation is crucial for efficient optimization process.

• 한국신재생에너지학회:학술대회논문집
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• 2009.11a
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• pp.427-430
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• 2009

풍력 터빈 블레이드용 익형의 경우 운용 조건에서 높은 양항비를 가지도록 설계되나 풍속, 풍향의 변동에 의해 운용조건에 변화가 발생할 경우 성능의 저하가 발생할 수 있다. 따라서 운용조건의 변동이 발생하더라도 공력 성능이 크게 변하지 않는 익형이 요구된다. 본 연구에서는 이러한 운용조건의 불확실성을 고려하여 풍력 터빈 블레이드용 익형의 신뢰성 기반 강건 최적 설계를 수행하였다. 익형 설계를 위해서 여러 익형 형상 변수들을 고려할 수 있는 익형 모델링 함수를 정의하였고 기저형상으로는 NREL에서 개발한 S809 익형을 사용하였다.

• Journal of Korean Society of Steel Construction
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• v.16 no.6 s.73
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• pp.819-832
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• 2004

This study describes an efficient and facile method for configuration optimum design of structures. One of the ways to achieve numerical shape representation and the selection of design variables is using the design element concept. Using this technique, the number of design variables could be drastically reduced. Isoparametric mapping was utilized to automatically generate the finite element mesh during the optimization process, and this made it possible to easily calculate the derivatives of the coordinates of generated finite element nodes w.r.t. the design variables. For the structural analysis, finite element analysis was adopted in the optimization procedure, and two different techniques(the deterministic method, a modified method of feasible direction; and the stochastic method, a genetic algorithms) were applied to obtain the minimum volumes and section areas for an efficient configuration optimization procedure. Futhermore, spline interpolation was introduced to present a realistic optimum configuration that meet the manufacturing requirements. According to the results of several numerical examples(steel structures), the two techniques suggested in this study simplified the process of configuration optimum design of structures, and yielded improved objective function values with a robust convergence rate. This study's applicability and capability have therefore been demonstrated.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.7
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• pp.729-736
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• 2011

The technique for order preference by similarity to ideal solution (TOPSIS) is regarded as a classical method of multiple attribute decision making (MADM), often used to solve various decision-making or selection problems. It is based on the concept that the chosen alternative should have the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution. The TOPSIS can be applied to a design process for carrying out multi-objective shape optimization wherein the best and worst alternatives are to be decided. In this paper, multi-objective shape optimization using the TOPSIS and Rational Bezier curve was applied to the funnel of a cathode-ray tube (CRT). In order to minimize the weight and first principal stress, a new multi-objective shape optimization methodology is proposed, wherein the relative-closeness coefficients of the TOPSIS are defined as the performance indices of a multi-objective function and evaluated by response surface models. This methodology enables the designer to decide on the best solution from a number of design specification groups by examining the various conflicts between the weight and the first principal stress.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.10
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• pp.1223-1228
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• 2011

A moving-coil type linear actuator has been widely used in the system reciprocating short stroke because of its several advantages, such as the structural simplicity, low weight and a fast control response speed. This paper presents a design approach for improving the actuating performance with a clear expression of optimal configuration represented by a level set function. The optimization problem is formulated to minimize the variation of magnetic force at every moving displacement of the mover for fast and easy control. To consider the manufacturability of actuator, the concept of phase-field model is incorporated to control the complexity of structural boundaries. To verify the usefulness of the proposed method, the core design example of cylindrical linear actuator is performed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.2
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• pp.159-171
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• 2001

평면 아치 구조물에 대해 선형 탄성 변분방정식에 기반을 둔 설계민감도 해석을 위한 일반적 이론을 개발하였다. 아치 구조물내의 임의 마디에 정의된 응력범함수를 고려하였고 이에 대한 설계민감도 공식을 유도하기 위해 전미분(material derivative) 개념과 보조(adjoint) 변수 방법을 도입하였다. 얻어진 민감도 공식은 구조해석 결과를 얻고 나면 이들로부터 단순 대수연산을 통해 계산이 되므로 적용이 간편할 뿐 아니라 해의 정확도가 높은 잇점이 있다. 본 방법은 아치의 형상을 매개변수를 통해 표현하므로 얕은 아치에 국한하지 않고 어떠한 형상도 고려가 가능하며, 나아가서 아치의 형상변화를 형상에 대해 수직뿐 아니라 접선방향도 포함하여 일반적으로 고려하므로 다양한 형상설계가 가능하다. 몇 가지 예제에서 민감도 계산을 수행함으로써 본 방법의 정확도와 효율성을 입증하였으며, 두 가지의 설계최적화 문제를 대상으로 실제로 두께 및 형상최적설계를 수행하였다.

• Journal of Korean Society of Steel Construction
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• v.17 no.4 s.77
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• pp.385-394
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• 2005

In this paper, a discrete optimum design program was developed using the refined fuzzy-genetic algorithms based on the genetic algorithms and the fuzzy theory. The optimum design in this study can perform section and shape optimization simultaneously for planar and spatial steel structures. In this paper, the objective function is the weight of steel structures and the constraints are the design limits defined by the design and buckling strengths, displacements, and thicknesses of the member sections. The design variables are the dimensions and coordinates of the steel sections. Design examples are given to show the applicability of the discrete optimum design using the improved fuzzy-genetic algorithms in this study.