• IE interfaces
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• v.7 no.3
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• pp.193-199
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• 1994

The purpose of this paper is to develop a method of the sensitivity analysis that can be applicable to a degenerate tree solution of the minimum cost flow problem. First, we introduce two types of sensitivity analysis. A sensitivity analysis of Type 1 is the well known method applicable to a spanning tree solution. However, this method have some difficulties in case of being applied to a degenerate tree solution. So we propose a sensitivity analysis of Type 2 that keeps solutions of upper bounds remaining at upper bounds, those of lower bounds at lower bounds, and those of intermediate values at intermediate values. For the cost coefficient, we present a method that the sensitivity analysis of Type 2 is solved by using the method of a sensitivity analysis of Type 1. Besides we also show that the results of sensitivity analysis of Type 2 are union set of those of Type 1 sensitivity analysis. For the right-hand side constant or the capacity, we present a simple method for the sensitivity analysis of Type 2 which uses arcs with intermediate values.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.492-497
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• 2004

Three methods for design sensitivity such as numerical differentiation, analytical method and semi-analytical method have been developed for the last three decades. Although analytical design sensitivity analysis is exact, it is hard to implement for practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable for most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate because its computational cost depends on the number of design variables and large numerical errors can be included especially in nonlinear design sensitivity analysis. Thus semi-analytical method is more suitable for complicated design problems. Moreover semi-analytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure for the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and computational technique is proposed, which evaluates the pseudo-load for design sensitivity analysis easily by using the design variation of corresponding internal nodal forces. Errors in semi-analytical design sensitivity analysis are examined and numerical examples are illustrated to confirm the reduction of numerical error considerably.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.10
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• pp.1590-1597
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• 2004

Three methods of design sensitivity analysis for structures such as numerical method, analytical method and semi-analytical method have been developed for the last three decades. Although analytical design sensitivity analysis can provide very exact result, it is difficult to implement into practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable fur most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate in nonlinear design sensitivity analysis because its computational cost depends on the number of design variables and large numerical errors can be included. Thus the semi-analytical method is more suitable for complicated design problems. Moreover, semi-analytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure fur the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and the computational technique is proposed for evaluating the partial differentiation of internal nodal force, so called pseudo-load. Numerical examples coupled with commercial finite element package are shown to verify usefulness of proposed semi-analytical sensitivity analysis procedure and computational technique for pseudo-load.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.119-126
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• 2004

A continuum-based design sensitivity analysis and topology optimization methods are developed for power flow analysis. Efficient adjoint sensitivity analysis method is employed and further extended to topology optimization problems. Young's moduli of all the finite elements are selected as design variables and parameterized using a bulk material density function. The objective function and constraint are an energy compliance of the system and an allowable volume fraction, respectively. A gradient-based optimization, the modified method of feasible direction, is used to obtain the optimal material layout. Through several numerical examples, we notice that the developed design sensitivity analysis method is very accurate and efficient compared with the finite difference sensitivity. Also, the topology optimization method provides physically meaningful results. The developed is design sensitivity analysis method is very useful to systematically predict the impact on the design variations. Furthermore, the topology optimization method can be utilized in the layout design of structural systems.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.3
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• pp.363-368
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• 2008

In this paper, the Resistive Companion Form(RCF) analysis method is applied to analyze small signal stability of power systems including thyristor controlled FACTS equipments such as SVC. The eigenvalue sensitivity analysis algorithm in discrete systems based on the RCF analysis method is presented and applied to the power system including SVC. As a result of simulation, the RCF analysis method is proved very effective to precisely calculate the variations of eigenvalues or newly generated unstable oscillation modes after periodic switching operations of SVC. Also the eigenvalue sensitivity analysis method based on the RCF analysis method enabled to precisely calculate eigenvalue sensitivity coefficients of controller parameters about the dominant oscillation mode after periodic switching operations in discrete systems. These simulation results are different from those of the conventional continuous system analysis method such as the state space equation and proved that the RCF analysis method is very effective to analyze the discrete power systems including periodically operated switching equipments such as SVC.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.1
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• pp.1-10
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• 1995

The purpose of this paper is to develop a method of the sensitivity analysis that can be applied to a non-tree solution of the minimum cost flow problem. First, we introduce two types of sensitivity analysis. A sensitivity analysis of Type 1a is the well known method applicable to a tree solution. However this method can not be applied to a non-tree solution. So we propose a sensitivity analysis of Type 2 that keeps solutions of upper bounds at upper bounds, those of lower bounds at lower bounds, and those of intermediate values at intermediate values. For the cost coefficient we present a method that the sensitivity analysis of Type 2 is solved by finding the shortest path. Besides we also show that the results of Type 2 and Type 1 are the same in a spanning tree solution. For the right-hand side constant or the capacity, the sensitivity analysis of Type 2 is solved by a simple calculation using arcs with intermediate values.

• Journal of Welding and Joining
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• v.19 no.2
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• pp.228-234
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• 2001

A methodology is developed and used to evaluate the response sensitivity of the thermal systems to variations in their design parameters. Technique for computing the sensitivity of temperature distributions to changes in processing parameters needed to decide the more effective laser input parameters for laser surface hardening treatment is considered. In this study, a state equation governing the heat flow in laser surface treatment is analyzed using a three-dimensional finite element method and sensitivity data of the processing parameter obtained using a direct differentiation method is applied to the sensitivity analysis. The interesting processing parameters are taken as the laser scan velocity and laser beam radius ( $r_{ b}$), and the sensitivities of the temperature T versus v and $r_{b}$ are analyzed. These sensitivity results are obtained with another parameters fixed. To verify the numerical analysis results, hardened layer dimensions (width and depth) of the numerical analysis are compared with the experimental ones.nes.

• Advances in Computational Design
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• v.4 no.1
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• pp.15-32
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• 2019

One of the efficient and useful tools to achieve the optimal design of structures is employing the sensitivity analysis in the finite element model. In the numerical optimization process, often the semi-analytical method is used for estimation of derivatives of the objective function with respect to design variables. Numerical methods for calculation of sensitivities are susceptible to the step size in design parameters perturbation and this is one of the great disadvantages of these methods. This article uses complex variables method to calculate the sensitivity analysis and combine it with discrete sensitivity analysis. Finally, it provides a new method to obtain the sensitivity analysis for linear structures. The use of complex variables method for sensitivity analysis has several advantages compared to other numerical methods. Implementing the finite element to calculate first derivatives of sensitivity using this method has no complexity and only requires the change in finite element meshing in the imaginary axis. This means that the real value of coordinates does not change. Second, this method has the lower dependency on the step size. In this research, the process of sensitivity analysis calculation using a finite element model based on complex variables is explained for linear problems, and some examples that have known analytical solution are solved. Results obtained by using the presented method in comparison with exact solution and also finite difference method indicate the excellent efficiency of the proposed method, and it can predict the sustainable and accurate results with the several different step sizes, despite low dependence on step size.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.9 s.240
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• pp.1209-1216
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• 2005

Three methods for design sensitivity such as numerical differentiation, analytical method and semi-analytical method have been developed for the last three decades. Although analytical design sensitivity analysis is exact, it is hard to implement for practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable for most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate because its computational cost depends on the number of design variables and large numerical errors can be included especially in nonlinear design sensitivity analysis. Thus semi-analytical method is more suitable for complicated design problems. Moreover semi-analytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure for the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and computational technique is proposed, which evaluates the pseudo-load for design sensitivity analysis easily by using the design variation of corresponding internal nodal forces. Errors in semi-analytical design sensitivity analysis are examined and numerical examples are illustrated to confirm the reduction of numerical error considerably.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.8
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• pp.175-184
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• 2003

A method of the shape design sensitivity analysis based on the boundary integral equation formulation is presented for two-dimensional inhomogeneous thermal conducting solids with multiple domains. Shape variation of the external and interface boundary is considered. A sensitivity formula of a general performance functional is derived by taking the material derivative to the boundary integral identity and by introducing an adjoint system. In numerical analysis, state variables of the primal and adjoint systems are solved by the boundary element method using quadratic elements. Two numerical examples of a compound cylinder and a thermal diffuser are taken to show implementation of the shape design sensitivity analysis. Accuracy of the present method is verified by comparing analyzed sensitivities with those by the finite difference. As application to the shape optimization, an optimal shape of the thermal diffuser is found by incorporating the sensitivity analysis algorithm in an optimization program.