• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.739-742
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• 2011

일반적으로 고층건물이나 교량 등의 지진하중 하에서의 내진 성능 향상을 위해서는 과도지진해석을 수행하는 것이 필요하다. 본 논문에서는 이러한 지진해석을 수행하는데 Krylov 부공간 축소기법을 이용하는 것을 제안하고 기존의 모드중첩법을 이용한 축소기법과 비교하였다. 해석에서 지진하중은 El Centro Earthquake (1940)의 데이터를 이용하였으며 고층건물 모델을 이용하여 두 방법을 정확성과 효율성 측면에서 비교한 수치결과를 제시하였다.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2009.04a
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• pp.131-134
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• 2009

Krylov 부공간 모델차수축소법은 초기 유한요소모델과 축소모델의 전달함수의 계수인 모멘트를 일치시키는 방법을 이용하는 축소기법으로 이미 대형 유한요소모델의 주파수응답 해석의 효율적인 계산에 많이 사용되고 있는 방법 중의 하나이다. 본 논문에서는 Krylov 부공간 축소기법을 이용한 관심 주파수영역에 대한 주파수응답 해석 및 이를 통하여 계산된 주파수응답의 여러 가지 설계변수에 대한 설계민감도 해석방법을 제안하였다. 일반적으로 구조물의 주파수응답을 고려한 최적설계를 위해서는 설계변수에 대한 관심 주파수영역에서의 주파수응답 및 그의 민감도 정보가 요구되므로, 고려하는 유한요소모델이 대형일 경우에 관심 주파수영역에서의 반복적인 해석으로 인한 계산비용의 문제가 대두된다. 본 논문에서는 축소모델을 이용하여 주파수응답과 주파수응답의 설계민감도 해석을 수행하여 계산의 효율성을 극대화하였다. 민감도 계산에는 시간측면과 구현의 용이성 측면에서 장점이 있는 준해석적 방법을 이용하였다. 수치 예제를 통하여 축소기법을 이용한 주파수응답의 설계민감도 해석 결과를 유한차분법에 근거한 민감도 결과와 비교하였다. 본 논문에서 제안된 방법을 이용하는 경우, 주파수응답을 고려한 최적설계를 계산비용 측면에서 매우 효율적으로 수행할 수 있을 것이다.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.436-441
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• 2008

One of important factors in designing array-type MEMS resonators is obtaining a desired frequency response function (FRF) within a specific range. In this paper Krylov subspace-based model order reduction using moment-matching with non-zero expansion points is represented to calculate the FRF of array-type resonators. By matching moments at a frequency around a specific range of the array-type resonators, required FRFs can be efficiently calculated with significantly reduced systems regardless of their operating frequencies. In addition, because of the characteristics of moment-matching method, a minimal order of reduced system with a specified accuracy can be determined through an error indicator using successive reduced models, which is very useful to automate the order reduction process and FRF calculation for structural optimization iterations.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.2
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• pp.101-111
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• 2021

In general, several computational resources are required to perform multiple-loading transient response analyses. In this paper, we present the procedure for multiple-loading transient response analysis using the Krylov subspace model order reduction and Newmark's time integration scheme. We utilized ANSYS MAPDL, Python, and ANSYS ACT to automate the transient response analysis procedure in the ANSYS Workbench environment and studied several engineering numerical examples to demonstrate the feasibility and efficiency of the proposed approach.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.38 no.9
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• pp.933-941
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• 2014

This paper provides a comparison between the Krylov subspace method (KSM) and modal truncation method (MTM), which are typical projection-based model order reduction methods. The frequency responses are compared to determine the numerical accuracies and efficiencies. In order to compare the numerical accuracies of the KSM and MTM, the frequency responses and relative errors according to the order of the reduced model and frequency of interest are studied. Subsequently, a numerical examination shows whether a reduced order can be determined automatically with the help of an error convergence indicator. As for the numerical efficiency, the computation time needed to generate the projection matrix and the solution time to perform a frequency response analysis are compared according to the reduced order. A finite element model for a car suspension is considered as an application example of the numerical comparison.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.2
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• pp.153-163
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• 2010

In this paper a frequency response analysis using Krylov subspace-based model reduction and its design sensitivity analysis with respect to design variables are presented. Since the frequency response and its design sensitivity information are necessary for a gradient-based optimization, problems of high computational cost and resource may occur in the case that frequency response of a large sized finite element model is involved in the optimization iterations. In the suggested method model order reduction of finite element models are used to calculate both frequency response and frequency response sensitivity, therefore one can maximize the speed of numerical computation for the frequency response and its design sensitivity. As numerical examples, a semi-monocoque shell and an array-type $4{\times}4$ MEMS resonator are adopted to show the accuracy and efficiency of the suggested approach in calculating the FRF and its design sensitivity. The frequency response sensitivity through the model reduction shows a great time reduction in numerical computation and a good agreement with that from the initial full finite element model.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.10
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• pp.1211-1222
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• 2011

It is necessary to use prestressed modal analysis to calculate the modal frequencies and mode shapes of a prestressed structure such as a spinning blade, a preloaded structure, or a thermally deformed pipe, because the prestress effect sometimes causes significant changes in the frequencies and mode shapes. When the finite element model under consideration has a very large number of degrees of freedom, repeated prestressed modal analyses for investigating the prestress effects might become too computationally expensive to finish within a reasonable design-process time. To alleviate these computational difficulties, a Krylov subspace-based model order reduction, which reduces the number of degrees of freedom of the original finite element model and speeds up the necessary prestressed modal analysis with the reduced order models (ROMs), is presented. The numerical process for the moment-matching model reduction is performed directly on the full order models (FOMs) (modeled in ANSYS) by the Arnoldi process. To demonstrate the advantages of this approach for performing prestressed modal analysis, the prestressed wheel and the compressor impeller under their high-speed rotation are considered as examples.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.5
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• pp.541-549
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• 2007

In the case of control for mechanical systems, it is highly useful to be able to provide a compact model of the mechanical system to control engineers using the smallest number of state variables, while still providing an accurate model. The reduced mechanical model can then be inserted into the complete system models and used for extended system-level dynamic simulation. In this paper, moment-matching based model order reductions (MOR) using Krylov subspaces, which reduce the number of degrees of freedom of an original finite element model via the Arnoldi process, are presented to study the eigenvalue and frequency response problems of a HDD actuator and suspension system.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.3 s.246
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• pp.310-317
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• 2006

Currently most practical vibration and structural problems in automotive suspensions require the use of the finite element method to obtain their structural responses. When the finite element model has a very large number of degrees of freedom the harmonic and dynamic analyses are computationally too expensive to repeat within a feasible design process time. To alleviate the computational difficulty, this paper presents a moment-matching based model order reduction (MOR) which reduces the number of degrees of freedom of the original finite element model and speeds up the necessary simulations with the reduced-size models. The moment-matching model reduction via the Arnoldi process is performed directly to ANSYS finite element models by software mor4ansys. Among automotive suspension components, a knuckle is taken as an example to demonstrate the advantages of this approach for vibration simulation. The frequency and transient dynamic responses by the MOR are compared with those by the mode superposition method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.9
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• pp.878-885
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• 2009

One of important factors in designing MEMS resonators for RF filters is obtaining a desired frequency response function (FRF) within a specific frequency range of interest. Because various array-type MEMS resonators have been recently introduced to improve the filter characteristics such as bandwidth, pass-band, and shape factor, the degrees of freedom (DOF) of finite elements for their FRF calculation dramatically increases and therefore raises computational difficulties. In this paper the Krylov subspace-based model order reduction using moment-matching with non-zero expansion points is represented as a numerical solution to perform the frequency response analyses of those array-type MEMS resonators in an efficient way. By matching moments at a frequency around the specific operation range of the array-type resonators, the required FRF can be efficiently calculated regardless of their operating frequency from significantly reduced systems. In addition, because of the characteristics of the moment-matching method, a minimal order of reduced system with a prearranged accuracy can be determined through an error indicator using successive reduced models, which is very useful to automate the order reduction process and FRF calculation for structural optimization iterations. We also found out that the presented method could obtain the FRF of a $6\times6$ array-type resonator within a seventieth of the computational time necessary for the direct method and in addition FRF calculation by the mode superposition method could not even be completed because of a data overflow with a half after calculation of 9,722 eigenmodes.