• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.593-600
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• 2003

Structural optimization often requires the evaluation of design sensitivities. The Semi Analytic Method(SAM) fur computing sensitivity is popular in shape optimization because this method has several advantages. But when relatively large rigid body motions are identified for individual elements. the SAM shows severe inaccuracy. In this study, the improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes. Moreover. the error of the SAM caused by numerical difference scheme is alleviated by using a series approximation for the sensitivity derivatives and considering the higher order terms. Finally the present study shows that the refined SAM including the iterative method improves the results of sensitivity analysis in dynamic problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.2 s.72
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• pp.213-219
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• 2006

Topology optimization problem requires numerous repeated evaluations of objective function and design sensitivity for elements within design domain with various density distributions. The recently proposed two-level condensation scheme(TLCS) is very promising for the construction of reduced system and for an accurate and efficient analysis concerned about eigenvalue and dynamic problems. We used the two-level dynamic condensation scheme for the analysis and sensitivity computation part in the structural topology optimization problem. The results of the topology optimization for the reduced system show the TLCS provides high accuracy and computation efficiency compared to the full scale system within engineering accuracy.

• Composites Research
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• v.12 no.1
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• pp.1-10
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• 1999

In order to predict the dynamic behavior of composite laminated plate accurately, the parametric identification is performed using its mechanical properties- $E_1,\;E_2,\;V_{12},\;G_{12}$ as design parameters. After natural frequencies are measured through simple vibration test, the objective function consists of the sum of errors between experimental and numerical frequencies of a structure. As optimization algorithm, conjugate gradient method is used to minimize the objective function. Sensitivity Analysis is performed to update design parameters during this process and can explain the result of parametric identification. In order to check the propriety of result, mode shapes are compared before and after identification. The improved prediction of natural frequencies of composite laminated plate is obtained with updated properties. For the application of result, updated properties is applied to the composite laminated plate that has different stacking sequence.

• Journal of KSNVE
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• v.10 no.5
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• pp.783-791
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• 2000

This describes a study on the support location optimizations of the beams using the genetic algorithm and the sensitivity analysis. The genetic algorithm is a probabilistic method searching the optimum at several points simultaneously and requiring only the values of the object and constraint functions. It has therefore more chances to find the global solution and can be applied to the various problems. Nevertheless, it has such a shortcoming that it takes too many calculations, because it is ineffective in local search. While the traditional method using sensitivity analysis is of great advantage in searching the near optimum. thus the combination of the two techniques will make use of the individual advantages, that is, the superiority in global searching form the genetic algorithm and that in local searching form the sensitivity analysis. In this thesis, for the practical applications, the analysis is conducted by FEB ; and as the shapes of structures are taken as the design variation, it requires re-meshing for every analysis. So if it is not properly controlled, the result of the analysis is affected and the optimized solution amy not be the real one. the method is efficiently applied to the problems which the traditional methods are not working properly.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.11 s.242
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• pp.1527-1533
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• 2005

Three methods for design sensitivity analysis such as finite difference method(FDM), direct differentiation method(DDM) and adjoint variable method(AVM) are well known. FDM and DDM for design sensitivity analysis cost too much when the number of design variables is too large. An AVM is required to compute adjoint variables from the simultaneous linear system equation, the so-called adjoint equation. Because the adjoint equation is independent of the number of design variables, an AVM is efficient for when number of design variables is too large. In this study, AVM has been extended to the eigenproblem of damped systems whose eigenvlaues and eigenvectors are complex numbers. Moreover, this method is implemented into a commercial finite element analysis program by means of the semi-analytical method to show applicability of the developed method into practical structural problems. The proposed_method is compared with FDM and verified its accuracy for analytical and practical cases.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.10
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• pp.4411-4417
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• 2012

The present study proposes the optimization of wing structure base on reduced model which assures the solution accuracy and computational efficiency. Well-constructed reduced model assures the accurate result in the eigenvalue problem, dynamic analysis or sensitivity of design optimization. Reduced system is classified into the reduce-order model based on structural modes and the reduced system based on degrees of freedom. Because this study uses the reduced system based on degrees of freedom, it is important to select the dominant degrees of freedom properly. For this work, robust selection method, two-level selection scheme, is employed and IRS(Improved Reduced System) is applied to construct the final reduced system. In the optimization process based on the reduced system, all of the equivalent stress, eigenvalue and design sensitivities are calculated from the reduced system. Through a numerical example, it is shown that the present optimization methodology based on the reduction method can provide an optimal results for objective function satisfying constraint condition.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.4
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• pp.15-25
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• 1993

In order to promote the efficient use of composite materials, effort is currently being directed at the development of design criteria for composite structures. Insofar as design against buckling is concerned, it is well known that, for metal shells, a key step is the definition of 'knockdown' factors on the elastic critical buckling stress accounting mainly for the influence of initial geometric imperfections. At present, the imperfection sensitivity of composite shells has not been explored in detail. Due to the large number of parameters influencing buckling response (considerably larger than for isotropic shells), a very large number of tests would be needed to quantify imperfection sensitivity experimentally. An alternative approach is to use validated numerical models for this task. Thus, the objective of this paper is to outline the underlying theory used in developing a composite shell element and to present results from a validation exercise and subsequently from a parametric study on axially loaded glass fibre-reinforced plastic (GFRP) curved panels using finite element modelling. Both eigenvalue and incremental analyses are performed, the latter including the effect of initial geometric imperfection shape and amplitude, and the results are used to estimate 'knockdown' factors for such panels.

• Journal of the Earthquake Engineering Society of Korea
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• v.16 no.4
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• pp.19-26
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• 2012

For a seismic design or performance evaluation of a structure, an experimental investigation on a scale model of the structure or numerical analysis based on the finite element model is considered. Regarding the numerical analysis, a three-dimensional finite element analysis is performed if a high accuracy of the results is required, while a sensitivity or fragility analysis which uses huge seismic ground motions leads to the use of a lumped-mass stick model. The conventional modeling technique to build the lumped-mass stick model calculates the amount of the lumped mass by considering the geometric shape of the structure, like a tributary area. However, the eigenvalues of the conventional model obtained through such a calculation are normally not the same as those of the actual structure. In order to overcome such a deficiency, in this study, a new lumped mass stick model is proposed. The model is named the "frequency adaptive-lumped-mass stick model." It provides the same eigenvalues and similar dynamic responses as the actual structure. A non-prismatic column is considered as an example, and its natural frequencies as well as the dynamic performance of the new lumped model are compared to those of the full-finite element model. To investigate the damping effect on the new model, 1% to 5% of the critical damping ratio is applied to the model and the corresponding results are also compared to those of the finite element model.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.159-166
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• 2001

Structural optimization often requires the evaluation of design sensitivities. The Semi Aanalytic method(SAM) for computing sensitivity is popular in shape optimization because this method has several advantages. But when relatively large rigid body motions are identified for individual elements, the SA method shows severe inaccuracy. In this paper, the improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes. Moreover, the error of the SA method caused by numerical difference scheme is alleviated by using a series approximation for the sensitivity derivatives and considering the higher order terms. Finally, this paper shows that the refined SA method including the iterative method improves the results of sensitivity analysis in dynamic problems.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.5
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• pp.707-718
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• 1997

This paper presents an efficient numerical method for the computation of eigenpair derivatives for a real symmetric eigenvalue problem with distinct and multiple eigenvalues. The method has a very simple algorithm and gives an exact solution. Furthermore, it saves computer sotrage and CPU time. The algorithm preserves not only the symmetricity but also the band width of the matrices, allowing efficient computer storage and solution techniques. Results from the proposed method for calculating the eigenpair derivatives are compared with those from Rudisill and Chu's method and Nelson's method which is known efficient one in the case of distinct natural frequencies. As an example to demonstrate the efficiency of the proposed method in the case of distinct eigenvalues, a cantilever plate is considered. The design parameter of the cantilever plate is its thickness. For the eigenvalue problem with multiple natural frequencies, the adjacent eigenvectors are used in the algebraic equation as side conditions, lying adjacent to the multiplicity of multiple natural frequency distinct eigenvalues, which appear when design parameter varies. A cantilever beam is used to demonstrate the efficiency of the proposed method in the case of multiple natural frequencies. Results form the proposed method for calculating the eigenpair derivatives are compared with those from Dailey's method(an amendation of Ojalvo's work) which finds the exact eigenvector derivatives. The design parameter of the cantilever beam is its height. Data is presented showing the amount of CPU time used to compute the first ten eigenpair derivatives by each method. It is important to note that the numerical stability of the proposed method is proved.