• Structural Engineering and Mechanics
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• v.7 no.1
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• pp.111-126
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• 1999

The work presented here focuses on the development of suitable discretised formulations, for large-displacement shape and non-shape design sensitivity analysis (DSA), which enable the straightforward incorporation of structural optimisation into established finite element analysis (FEA) codes. For the generalised displacement-based functional the design sensitivity vector has been expressed in terms of displacement sensitivity. The Total Lagrangian formulation is utilised for modelling of large deformation of truss structures. The variational formulation of the sensitivity analysis procedure is discretised by using "pseudo" - finite elements, Results are presented for the sensitivity analysis and optimisation of standard truss structures. For the purposes of this work, the analysis and optimisation procedures outlined below are incorporated into the FEA code ABAQUS.

• Proceedings of the KIEE Conference
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• 1992.07b
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• pp.567-569
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• 1992

Design sensitivity analysis is proposed for the optimal shape design of three dimensional magnetostatic problems. The direct differentiation method is introduced for design sensitivity analysis and the boundary element method with reduced magnetic scalar potential as the state variable is used to analyze the magnetic characteristics. In the direct differentiation method, the design sensitivity, defined as the total derivative of the objective function with respect to the design variables, is calculated based on the variation of the state variable with respect to the design variable. And the variation of He state variable is calculated by differentiating the both sides of the system matrix equation obtained by applying boundary element method. Through the numerical example with simple electromagnet, the usefullness is proved.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.41 no.8
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• pp.850-857
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• 1992

Design sensitivity analysis is proposed for the optimal shape design of three-dimensional magnetostatic problems. The direct differentiation method is introduced for design sensitivity analysis and the boundary element method with reduced magnetic scalar potential as the state variable is used to analyze the magnetic characteristics. In the direct differentiation method, the design sensitivity, defined as the total derivative of the objective function with respect to the design variables, is calculated based on the variation of the state variable with respect to the design variable. And the variation of the state variable is calculated by differetiating the both sides of the system matrix equation obtained by applying boundary element method. Through the numerical example with simple electromagnet, the usefulness is proved.

• Proceedings of the KIEE Conference
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• 1990.11a
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• pp.19-22
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• 1990

In this paper, in order to reduce the cogging torque in a permanent motor, a method to optimize the shape of permanent magnet and iron pole is presented. Because the cogging torque comes from the irregular system energy variation according to the rotor position, system energy variation is taken as object function and the object function is minimized to optimize the shape. The positions of permanent magnet surface and iron pole surface are chosen as design parameters and sensitivity of object function with respect to design parameter is calculated. The shape is changed according to sensitivity. Sensitivity can be generated by methods that exploit the FEM formulation. A numerical example shows that about 90% of the original cogging torque is reduced.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.705-709
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• 2002

The spacer grids in nuclear fuel assembly locate and align the fuel rods with respect to each other. They provide axial and lateral restraint against an excessive rod motion mainly caused by coolant flow. It is understood that each rod Is supported by multiple spacer grid. In such a case, it is important to determine spacer grid span so as to avoid resonance between the natural frequency of the fuel rods and excitation frequency. Actually dynamic characteristics of the fuel rods can be improved by assigning adequate spacer grid locations. When a dynamic performance of the structure is to be improved, design sensitivity analysis plays an important role as like many structural redesign problems. In this work, a shape design concept, different from conventional design, was applied to the problem. According to the theory shape can be a design parameter and optimal shape design can be found. This study concentrates on eigenvalue design sensitivity of the fuel rod supported by multiple spacer grids to determine optimal spacer grids positions.

• Journal of the Society of Naval Architects of Korea
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• v.44 no.2 s.152
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• pp.130-138
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• 2007

A coupled variational equation for fluid-structure interaction (FSI) problems is derived from a steady state Navier-Stokes equation for incompressible Newtonian fluid and an equilibrium equation for geometrically nonlinear structures. For a fully coupled FSI formulation, between fluid and structures, a traction continuity condition is considered at interfaces where a no-slip condition is imposed. Under total Lagrange formulation in the structural domain, finite rotations are well described by using the second Piola-Kirchhoff stress and Green-Lagrange strain tensors. An adjoint shape design sensitivity analysis (DSA) method based on material derivative approach is applied to the FSI problem to develop a shape design optimization method. Demonstrating some numerical examples, the accuracy and efficiency of the developed DSA method is verified in comparison with finite difference sensitivity. Also, for the FSI problems, a shape design optimization is performed to obtain a maximal stiffness structure satisfying an allowable volume constraint.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.10
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• pp.1936-1941
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• 2009

This paper deals with a new methodology for topology optimization in which the topology of the design domain may change during the shape optimization process. To achieve this, the concept of the topological gradient is introduced to compute the sensitivity of an objective function when a small hole is drilled in the domain. Based on shape and topological sensitivity values, the shape and topology of the design domain may be simultaneously changed during design iterations if necessary. To verify the advantages and also to facilitate understanding of the method itself, two electrostatic design problems have been tested by using 2D finite element analysis: the first is the inverse problem of a simple dielectric model and the second is the rotor design of a MEMS actuator.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.1
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• pp.141-152
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• 1993

A generalized method is presented for shape design sensitivity analysis of axisymmetric thermal conducting solids. The shape sensitivity formula of a general performance functional arising in shape optimal design problem is derived using the material derivative concept and the adjoint variable method. The method for deriving the formula is based on standard axisymmetric boundary integral equation formulation. It is then applied to obtain the sensitivity formulas for temperature and heat flux constraints imposed over a small segment of the boundary. To show the accuracy of the sensitivity analysis, numerical implementations are done for three examples. Sensitivities calculated by the presented method are compared with analytic sensitivities for two examples with analytic solutions, and compared with sensitivies by finite difference for a cooling fin example.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.3 s.174
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• pp.645-652
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• 2000

A method for shape design sensitivity analysis is proposed utilizing commercial software ANSYS for thermal conduction problems. While the sensitivity formula is derived analytically by introduing adjoint variable concept, sensitivity calculation in practice as well as the primal and adjoint solution of thermal conduction is performed using the ANSYS very easily. Since the formula always takes boundary integral form, sensitivity evaluation in ANSYS requires a little more addition of post-processing routine which involves evaluation of boundary variable from the obtained solution. Though the BEM has been used as a better tool for this purpose, the present study shows it can also be calculated using any kind of analysis code such as ANSYS since the formula is based on analytic nature. Therefore the present study provides a new and efficient way of optimization which was not possible before using commercial software. The usefulness of the method is illustrated via a weight minimization problem of thermal diffuser.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.3
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• pp.430-437
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• 2010

In this paper, we develop a shape design optimization method for thermo-elastoplasticity problems that is applicable to the welding or thermal deformation problems of ship structures. Shell elements and a programming language APDL in a commercial finite element analysis code, ANSYS, are employed in the shape optimization. The point of developed method is to determine the design parameters such that the deformed shape after welding fits very well to a desired design. The geometric parameters of surfaces are selected as the design parameters. The modified method of feasible direction (MMFD) and finite difference sensitivity are used for the optimization algorithm. Two numerical examples demonstrate that the developed shape design method is applicable to existing hull structures and effective for the structural design of ships.