• 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 the Society of Naval Architects of Korea
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• v.32 no.4
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• pp.64-72
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• 1995

Sizing design sensitivity analysis of structures subjected to the harmonic vibration is performed using adjoint variable method. Constraint is the stress and sizing design variables are thickness, bending moment of inertia, and cross-sectional area of structures. Accurate sensitivities are computed and plotted sensitivity can be used as a design guidance tool. The accuracy of sensitivities is verified by the finite difference values. Also, optimal design of three-bar structure is performed using the computed sensitivity and feasible direction method while satisfying constraints and obtaining the minimum weight.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.7
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• pp.821-827
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• 2010

This paper proposes a density method based topology optimization of a perpendicular magnetic recording system design in which the saturation effect is taken into account. During the topology optimization process in magnetic fields, the magnetic reluctivity is updated in accordance with the changes in element density determined by a sensitivity analysis. The magnetic reluctivity is determined from a B-H curve and is used to represent nonlinear material property, i.e., the saturation effect. The sensitivity for a generalized response functional is formulated using the adjoint variable method in which the nonlinear property is taken into account and the objective function is set such that the magnetic energy in the media is maximized. Effects due to the nonlinear property can be observed from a numerical study in which the linear and the nonlinear topology optimization results are compared.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.1
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• pp.9-18
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• 2015

In this paper, we verify the optimal topology design for heat conduction problems in steady stated which is obtained numerically using the adjoint design sensitivity analysis(DSA) method. In adjoint variable method(AVM), the already factorized system matrix is utilized to obtain the adjoint solution so that its computation cost is trivial for the sensitivity. For the topology optimization, the design variables are parameterized into normalized bulk material densities. The objective function and constraint are the thermal compliance of the structure and the allowable volume, respectively. For the experimental validation of the optimal topology design, we compare the results with those that have identical volume but designed intuitively using a thermal imaging camera. To manufacture the optimal design, we apply a simple numerical method to convert it into point cloud data and perform CAD modeling using commercial reverse engineering software. Based on the CAD model, we manufacture the optimal topology design by CNC.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.34 no.3
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• pp.328-338
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• 1998

It is main objective of this approach to present a method to analyse stochastic design sensitivity for problems of structural dynamics with randomness in design parameters. A combination of the adjoint variable approach and the second oder perturbation method is used in the finite element approach. An alternative form of the constant functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The terminal problem of the adjoint system is solved using equivalent homogeneous equations excited by initial velocities. The numerical procedures are shown to be much more efficient when based on the fold superposition method : the generalized co-ordinates are normalized and the correlated random variables are transformed to uncorrelated variables, where as the secularities are eliminated by the fast Fourier transform of complex valued sequences. Numerical algorithms have been worked out and proved to be accurate and efficient : they codes whose element derivative matrices can be explicitly generated. The numerical results of two cases - 2-dimensional portal frame and 3/4-cylindrical shell structure - for the deterministic and stochastic sensitivity analysis illustrates in this paper.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.2
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• pp.1-9
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• 1990

A variational approach with reference volume and adjoint structure concepts is applied for the structural design densitivity analysis of geometrically nonlinear structures. A general form of sensitivity equation is used and then nonlinear finite element procedure is implemented for the discretized structural model. Usability and effectiveness of the variational approach for the design sensitivity analysis of geometrically nonlinear structural responses are verified through a numerical example.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.32 no.2
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• pp.177-190
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• 1996

구조물의 동적 응답 해석 문제에 대해서, 확률 유한요소법을 논의코자, 기조의 유한요소 해석법에 수반 변수법(adjoint variable approach)과 2차 섭동법(second order perturbation method)을 적용한다. 동적 민감도의 시간 응답을 고려하기 위해서 모든 시간에 대해서 갖는 구속 조건의 범함수 형태를 취하고, 시간 적분에 있어서 중첩법(fold superposition technique)에 근거를 둔 수치 해석이 훨씬 더 효과적임을 보인다. 본 논문의 확률 유한요소 해석법은 기존의 유한요소 해석법은 기존의 유한요소 코드에 맞추어 쉽게 적용할 수 있는 이점이 있음을 보이며, 이의 검정을 위해서, 2차원과 3차원 프레임 구조물에 대한 수치 해석을 하고 그 결과를 검토해 보았다.

• Computational Structural Engineering
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• v.7 no.1
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• pp.91-98
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• 1994

Design sensitivity analysis method for the vibration of vehicle structure is developed using adjoint variable method. A variational approach with complex response method is used to derive sensitivity expression. To evaluate sensitivity, FEM analysis of ship deck and vehicle structure are performed using MSC/NASTRAN installed in the super computer CRAY2S, and sensitivity computation is performed by PC. The accuracy of sensitivity is verified by the results of finite difference method. When compared to structural analysis time on CRAY2S, sensitivity computation is remarkably economical. The sensitivity of vehicle frame can be used to reduce the vibration responses such as displacement and acceleration of vehicle.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.1
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• pp.12-23
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• 1994

This paper proposes an optimal design software for the open-chain dynamic systems whose governing equations are expressed as differential equation. In this software, an input module and an automatic creation module of the equation of motion are developed to contrive the user's convenience. To analyze the equation of motion of the dynamic systems, variable-order and variable-stepsize Adams-Bashforth-Moulton predictor-corrector method is used to improve the efficiency. For the optimization and the design sensitivity analysis, ALM(augmented lagrange multiplier)method and adjoint variable method are adopted respectively. An output module with which the user can compare and investigate the analysis and the optimization results through tables and graphs is also provided. The developed software is applied to three typical dynamic response optimization problems, and the results compare very well with those available in the literature, demonstrating its effectiveness.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.1
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• pp.82-87
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• 1987

In this study a method of shape optimization is applied to two dimensional heat transfer system. For this the optimization problem is defined in a functional form including cost, constraints and the system governing equation. Then the material derivative concept in continuum mechanics and the adjoint variable method are employed for the shape design sensitivity analysis. With the sensitivity analysis results, an optimum is sought with the gradient projection optimization algorithm. The two dimensional isoparametric finite elements are used for accurate analysis and sensitivity calculations. The above method is employed to find the boundary shape to achieve a desired temperature distribution along a segment of the boundary subject to the maximum area constraint.