• Title, Summary, Keyword: Shape design sensitivity

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Optimum Design of the Process Parameter in Sheet Metal Forming with Design Sensitivity Analysis using the Direct Differentiation Approach (II) -Optimum Process Design- (직접미분 설계민감도 해석을 이용한 박판금속성형 공정변수 최적화 (II) -공정 변수 최적화-)

  • Kim, Se-Ho;Huh, Hoon
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.26 no.11
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    • pp.2262-2269
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    • 2002
  • Process optimization is carried out to determine process parameters which satisfy the given design requirement and constraint conditions in sheet metal forming processes. Sensitivity -based-approach is utilized for the optimum searching of process parameters in sheet metal forming precesses. The scheme incorporates an elasto-plastic finite element method with shell elements . Sensitivities of state variables are calculated from the direct differentiation of the governing equation for the finite element analysis. The algorithm developed is applied to design of the variablc blank holding force in deep drawing processes. Results show that determination of process parameters is well performed to control the major strain for preventing fracture by tearing or to decrease the amount of springback for improving the shape accuracy. Results demonstrate that design of process parameters with the present approach is applicable to real sheet metal forming processes.

Isogeometric Shape Design Optimization of Structures Subjected to Design-dependent Loads (설계 의존형 하중 조건을 갖는 구조물의 아이소-지오메트릭 형상 최적설계)

  • Yoon, Min-Ho;Koo, Bon-Yong;Ha, Seung-Hyun;Cho, Seon-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.24 no.1
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    • pp.1-7
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    • 2011
  • In this paper, based on an isogeometric approach, we have developed a shape design optimization method for plane elasticity problems subjected to design-dependent loads. The conventional shape optimization using the finite element method has some difficulties in the parameterization of geometry. In an 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. The solution space for the response analysis can be represented in terms of the same NURBS basis functions to represent the geometry, which yields a precise analysis model that exactly represents the normal and curvature depending on the applied loads. A continuum-based isogeometric adjoint sensitivity is extensively derived for the plane elasticity problems under the design-dependent loads. Through some numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.

Development of a Structural Optimal Design Code Using Response Surface Method Implemented on a CAD Platform (반응표면법을 이용한 구조물 최적설계 프로그램의 개발)

  • Yeom, Kee-Sun;Huh, Jae-Sung;Kwak, Byung-Man
    • Proceedings of the KSME Conference
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    • pp.580-585
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    • 2001
  • A response surface method(RSM) is utilized for structural optimization and implemented on a parametric CAD platform. Once an approximation of the performance function is made, no formal design sensitivity analysis is necessary. The approximation gives the designer the sensitivity information and furthermore intuition on the performance functions. The scheme for the design of experiment chosen for the RSM has a large influence on the accuracy of converged solutions and the amount of computation. The D-optimal design criterion as implemented in this paper is found efficient for the structural optimization. The program is developed on a parametric CAD platform and tested using several shape design problems of such as a torque arm and a belt clip. It is observed that the RSM used provides a faster convergence than other approximation methods for design sensitivity.

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Development of Optimal Blank Shape Design Program Using the Initial Velocity of Boundary Nodes (초기 속도법을 이용한 최적 블랭크 설계 프로그램의 개발)

  • 심현보;이상헌;손기찬
    • Proceedings of the Korean Society for Technology of Plasticity Conference
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    • pp.77-81
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    • 2002
  • A new method of optimal blank shape design using the initial nodal velocity (INOV) has been proposed for the drawings of arbitrary shaped cups. With the given information of tool shape and the final product shape, corresponding initial blank shape has been found from the motion of boundary nodes. Although the sensitivity method, the past work of Hynbo Shim and Kichan Son, has been proved to be excellent method to find optimal blank shapes, the method has a problem that a couple of deformation analysis is required at each design step and it also exhibits an abnormal behaviors in the rigid body rotation prevailing region. In the present method INOV, only a single deformation analysis per each design stage is required. Drawings of practical products as well as oil-pan have been chosen as the examples. At every case the optimal blank shapes have been obtained only after a few times of modification without predetermined deformation path. The deformed shape with predicted optimal blank almost coincides with the target shape at every case. Through the investigation the INOV is found to be very effective in the arbitrary shaped drawing process design.

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Development of Optimal Blank Shape Design Program Using the Initial Velocity of Boundary Nodes (초기 속도법을 이용한 최적 블랭크 설계 프로그램의 개발)

  • 심현보;이상헌;손기찬
    • Transactions of Materials Processing
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    • v.11 no.6
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    • pp.487-494
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    • 2002
  • A new method of optimal blank shape design using the initial nodal velocity (INOV) has been proposed for the drawings of arbitrary shaped cups. With the given information of tool shape and the final product shape, corresponding initial blank shape has been found from the motion of boundary nodes. Although the sensitivity method, the past work of the present authors, has been proved to be excellent method to find optimal blank shapes, the method has a problem that a couple of deformation analysis is required at each design step and it also exhibits an abnormal behaviors in the rigid body rotation prevailing region. In the present method INOV, only a single deformation analysis per each design stage is required. Drawings of practical products as well as oil-pan, have been chosen as the examples. At every case the optimal blank shapes have been obtained only after a few times of modification without predetermined deformation path. The deformed shape with predicted optimal blank almost coincides with the target shape at every case. Through the investigation the INOV is found to be very effective in the arbitrary shaped drawing process design.

Application of the Growth-Strain Method for Shape Optimal Design of a Flow System (유동 시스템의 형상 최적 설계를 위한 성장-변형률법의 적용)

  • Han, Seog-Young;Lee, Sang-Hwan;Kim, Jong-Pill;Maeng, Joo-Sung
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.26 no.7
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    • pp.945-950
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    • 2002
  • Shape optimization of a flow system is done to obtain the required effects, in the engineering fields. Most of these designs are accomplished by empirical or numerical analysis. In empirical analysis, it is difficult to obtain an optimal shape in the feasible design region. And, in numerical method, it usually needs much calculation expenses for shape optimization, because of design sensitivity analysis. In this study, we used the growth-strain method having only one distributed parameter such as a design variable. It optimizes a shape by making a distributed parameter such as dissipation energy uniform in a flow system, and then applied to two-flow systems. In order to overcome the stability occurred in numerical analysis performed by Azegami, the equation of volumic strain has been modified. Also, the shapes were compared with the known optimal shapes for the flow systems. Consequently, we confirm that the modified growth-strain method is very efficient and practical in shape optimization of the flow systems.

Sensitivity Error Analyses with Respect to Shape Variables in a Two-Dimensional Cantilever Beam (2차원 외팔보의 형상변수에 대한 민감도 오차해석)

  • 박경진
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.17 no.1
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    • pp.11-20
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    • 1993
  • Sensitivity information is required in the optimal design process. In structural optimization, sensitivity calculation is a bottleneck due to its complexities and expensiveness. Various schemes have been proposed for the calculation. Analytic and finite difference methods are the most popular at the present time. However, they have advantages and disadvantages in different ways. Semi-anayltic method has been suggested to overcome the difficulties. In spite of the excellency, the semi-analytic method has been found to possess numerical error quite much with respect to shape variables. In this research, the error from each method is evaluated and compared using a shape variable. A two-dimensional beam is selected for an example since it has mathematical solution. An efficient method is suggested for the structural optimization which utilizes finite element method.

Shape Design Sensitivity Analysis and Optimization of Axisymmetric Shell Structures (축대칭 쉘 구조물의 형상 설계민감도해석 및 최적설계)

  • 김인용;곽병만
    • Computational Structural Engineering
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    • v.7 no.2
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    • pp.147-153
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    • 1994
  • A method for shape design sensitivity analysis for axisymmetric shells of general shapes is developed. The basic approach is to divide the structures into many segments : For each of the segments, the formula for a shallow arch or shell can be applied and the results assembled. To interconnect those segments, the existing sensitivity formula, obtained for a variation only in the direction perpendicular to the plane on which the structure is mapped, has been extended to include a variation normal to the middle surface. The method follows the adjoint variable approach based on the material derivative concept as established in the literature. Numerical examples are taken to illustrate the method and the applicability to practical design problems.

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Topology Optimization of Electromagnetic Systems Using Material Sensitivity Analysis (매질 민감도해석을 이용한 전자기시스템의 위상 최적설계)

  • Byun Jin-Kyu;Choi Hong-Soon;Hahn Song-Yop;Park Il-Han
    • The Transactions of the Korean Institute of Electrical Engineers B
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    • v.54 no.4
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    • pp.163-173
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    • 2005
  • The conventional optimization study for electromagnetic systems has been mostly on the shape or size optimization. The goal for these optimization methods is to improve performance of electromagnetic systems by optimizing the interface shape of two different materials while their given layout or initial topology are held. The feasible topology can be diverse and an appropriate topology will give much better design results. In this paper we propose a theory and an algorithm for topology optimization of electromagnetic systems, which are based on the finite element method. The topology optimization technique employes a direct searching method of sensitivity analysis in which the information of material sensitivity is used. Two numerical examples of a switched reluctance motor and an electrostatic actuator of MEMS are tested and their design results show that the optimization method is valid and useful for the topology and basic layout design of electromagnetic systems.

DDM Rotordynamic Design Sensitivity Analysis of an APU Turbogenerator Having a Spline Shaft Connection

  • Lee, An-Sung;Ha, Jin-Woong
    • Journal of Mechanical Science and Technology
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    • v.17 no.1
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    • pp.57-63
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    • 2003
  • An eigenvalue design sensitivity formulation of a general nonsymmetric-matrix rotor-bearing system is devised. using the DDM (direct differential method). Then, investigations on the design sensitivities of critical speeds are carried out for an APU turbogenerator with a spline shaft connection. Results show that the dependence of the rate of change of the critical speed on the stiffness changes of bearing models of spline shaft connection points is negligible, and thereby their modeling uncertainty does not present any problem. And the passing critical speeds up to the 4th critical speed are not sensitive to the design stiffness coefficients of four main bearings. Further, the dependence of the rate of change of the critical speed on the shaft-element length changes shows quantitatively that the spline shaft has some limited influence on the 4th critical speed but no influence on the 1st to 3rd critical speeds. With no adverse effect from the spline shaft, the APU system achieves a critical speed separation margin of more than 40% at a rated speed of 60,000 rpm.