모델차수축소법을 이용한 효율적 고유치 및 열탄성 해석

최진복(Jinbok Choi) 한국자동차공학회 2011 한국자동차공학회 부문종합 학술대회 Vol.2011 No.5

Although there has been a great advance in computing resources and power, the modal analysis is still very time consuming. A lot of reduction methods have been suggested to resolve this problem. Among of them, model order reduction(MOR) method has been recognized as one of the powerful methods because of its advantages such as simplicity of implementation and theoretical robustness. Especially, in this study, the MOR method applies to the thermo-mechanical problem which results in the quadratic eigenvalue problem(QEP). The QEP is not easy to solve directly so it is generally converted into the generalized eigenvalue problem(GEP). The doubled degrees of freedom during this procedure eventually increase the computation time and the coupling between mechanical and thermal part makes it difficult to apply the conventional reduction methods. But the MOR method can be successfully applied to this tightly coupled multi-physics problem and reduce the computing time dramatically.

구조 동특성 파라미터를 이용한 구조물 손상 탐색기법 비교 연구

최병민(Choi, Byoung-Min),우호길(Woo, Ho-Kil) 한국소음진동공학회 2007 한국소음진동공학회 논문집 Vol.17 No.3

Detection of structural damage is an inverse problem in structural engineering. There are three main questions in the damage detection: existence, location and extent of the damage. In concept, the natural frequency and mode shapes of any structure must satisfy an eigenvalue problem. But, if a potential damage exists in a structure, an error resulting from the substitution of the refined analytical finite element model and measured modal data into the structural eigenvalue equation will occur, which is called the residual modal forces, and can be used as an indicator of potential damage in a structure. In this study, a useful damage detection method is proposed and compared with other two methods. Two degree-of-freedom system and Cantilever beam are used to demonstrate the approach. And the results of three introduced method are compared.

2 단계 축소 기법을 이용한 구조 자유 진동의 위상 최적 설계

박수현(Soohyun Park),조맹효(Maenghyo Cho) 대한기계학회 2005 대한기계학회 춘추학술대회 Vol.2005 No.11

Topology optimization problem requires numerous repeated evaluation of objective function and design sensitivity for elements within design domain with various density distributions. In this work, a structural topology optimization of free vibration problem is developed by using finite element method. The recently proposed two-level condensation scheme is very promising for the construction of reduced system and for an accurate and efficient analysis concerned about eigenvalue and dynamic problems. Thus we use the two-level condensation scheme(TLCS) for the analysis and sensitivity computation part in the structural topology optimization problem.

축소시스템을 이용한 구조체의 고유치 해석 기법

한정삼(Jeong Sam Han) 대한기계학회 2006 대한기계학회 춘추학술대회 Vol.2006 No.11

This paper presents the Krylov-subspaces based model order reduction (MOR) for eigenvalue problems of large-scale mechanical systems. The eigenvalue analyses can be performed efficiently by the model order reduction which reduces the number of degrees of freedom of an original finite element model via the Arnoldi process. Eigenvalue problems of a HDD actuator/suspension and a wheel will be studied to demonstrate the advantages of the suggested approach.

단순지지 경계조건을 가진 임의 형상 평판의 효율적인 고유진동수 추출을 위한 NDIF법의 대수 고유치 문제로의 정식화

강상욱(Kang, S.W.),김진곤(Kim, J.G.) 한국소음진동공학회 2009 한국소음진동공학회 논문집 Vol.19 No.6

A new formulation of NDIF method to the algebraic eigenvalue problem is introduced to efficiently extract natural frequencies of arbitrarily shaped plates with the simply supported boundary condition. NDIF method, which was developed by the authors for the free vibration analysis of arbitrarily shaped membranes and plates, has the feature that it yields highly accurate natural frequencies compared with other analytical methods or numerical methods(FEM and BEM). However, NDIF method has the weak point that it needs the inefficient procedure of searching natural frequencies by plotting the values of the determinant of a system matrix in the frequency range of interest. A new formulation of NDIF method developed in the paper doesn't require the above inefficient procedure and natural frequencies can be efficiently obtained by solving the typical algebraic eigenvalue problem. Finally, the validity of the proposed method is shown in several case studies, which indicate that natural frequencies by the proposed method are very accurate compared to other exact, analytical, or numerical methods.

세 물체 간 마찰 완전 접촉 문제의 응력 특이성 거동

김형규 한국트라이볼로지학회 2019 한국윤활학회지(윤활학회지) Vol.35 No.4

This study investigates the stress singularity that occurs at the contact edge of three bodies in a frictional complete contact. We use the asymptotic analysis method, wherein we constitute an eigenvalue problem and observe the eigenvalue behavior, which we use to obtain the order of the stress singularity. For the present geometry of three bodies in contact, a contact between a cracked indenter and half plane is considered. This is a typical geometry of the PCMI problem of a nuclear fuel rod. Thus, this paper, specifically presents the characteristics of the PCMI problem from the perspective of stress singularity. Consequently, it is noted that the behavior of the stress singularity varies with the difference in the crack angle, coefficient of friction, and material dissimilarity, as is observed in a frictional complete contact of two bodies. In addition, we find that the stress singularity changes essentially linearly with respect to the coefficient of friction, regardless of the variation in the crack angle and material dissimilarity. Concurrently, we find the order of singularity to be 0.5 at a certain coefficient of friction, irrespective of the crack angle, which we also observe in the crack problem of a homogeneous and isotropic body. The order of singularity can also exceed 0.5 in the frictional complete contact problem of three bodies. This implies that the propensity for failure when three bodies are in frictional complete contact can be even worse than that in case of a failure induced by a crack.

연소시스템의 열음향 불안정 예측을 위한 Helmholtz Solver 개발

김성구(Seong-Ku Kim),최환석(Hwan Seok Choi),차동진(Dong Jin Cha) 한국항공우주학회 2010 韓國航空宇宙學會誌 Vol.38 No.5

본 연구에서는 실제 로켓엔진 및 가스터빈용 연소기 내부의 열음향 불안정을 효과적으로 예측하기 위하여, 헬름홀츠 방정식과 시간지연모델을 이용한 3차원 유한요소법 해석코드를 개발하였다. 연소응답항에 의해 수치적으로 야기되는 비선형성은 반복법으로 선형화하였으며, Arnoldi 방법을 사용하여 대용량 고유치 문제를 해석하였다. 해석결과인 복소 각주파수와 음향 압력장을 통해 각 음향모드의 공진주파수, 진폭의 증폭/감쇠 여부 그리고 모드 형태를 예측할 수 있다. 이론해가 존재하는 두 가지 문제를 통해 출구 임피던스와 예혼합 화염이 종 방향 음향장에 미치는 영향에 대한 예측 정확도를 평가하였으며, 배플 유무에 따른 횡 방향 음향 모드의 주파수 변이를 상온 음향시험 결과와 비교/검증하였다. In order to effectively predict thermo-acoustic instability within real combustors of rocket engines and gas turbines, in the present study, the Helmholtz equation in conjunction with the time lag hypothesis is discretized by the finite element method on three-dimensional hybrid unstructured mesh. Numerical nonlinearity caused by the combustion response term is linearized by an iterative method, and the large-scale eigenvalue problem is solved by the Arnoldi method available in the ARPACK. As a consequence, the final solution of complex valued eigenfrequency and acoustic pressure field can be interpreted as resonant frequency, growth rate, and modal shape for acoustic modes of interest. The predictive capabilities of the present method have been validated against two academic problems with complex impedance boundary and premixed flame, as well as an ambient acoustic test for liquid rocket combustion chamber with/without baffle.

대형 시스템의 고유치 해석을 위한 부구조화 기법과 연동한 시스템 축소 기법 연구

백승민(Sungmin Baek),김현기(Hyungi Kim),조맹효(Maenghyo Cho) 대한기계학회 2007 대한기계학회 춘추학술대회 Vol.2007 No.10

Eigenvalue reduction schemes approximate the lower eigenmodes that represent the global behavior of the structures. In the previous study, we proposed a two-level condensation scheme (TLCS) for the construction of a reduced system. And we improve previous TLCS with combination of the iterated improved reduced system method (IIRS) to increase accuracy of the higher modes intermediate range. In this study, we apply previous improved TLCS to multi-level sub-structuring scheme. In first step, the global system is recursively partitioned into a hierarchy of subdomain. And next, each uncoupled subdomains condensates by improved TLCS. Finally, Numerical examples demonstrate performance of proposed method.

대형 동적 구조 시스템에서의 향상된 다단계 부구조화 기법에 관한 연구

백승민(Sungmin Baek),조맹효(Maenghyo Cho) 대한기계학회 2011 대한기계학회 춘추학술대회 Vol.2011 No.10

The structural dynamic analysis of the large-scaled system requires a huge amount of computational resources and calculation time. The component mode synthesis (CMS) shows good performance to overcome the computational limitations. Based on the advantage of a multi-level sub-structuring scheme on several levels the method constructs reduced system of much smaller number of unknowns which still yields satisfactory accuracy over a wide frequency range of interest. We present new approach to enhance the multilevel sub-structuring scheme through the implementation of the dynamic constraint mode which represent the acceleration of the interface region. The proposed approach can be used to improve the accuracy of the calculated eigenproperties by utilizing the dynamic aspect of component modes but without re-analysis of the reduced system or calculation additional normal modes of the substructures. Finally, numerical studies demonstrated the efficiency of the proposed method.

효율적 동적 시스템 축소를 위한 주자유도 선정에 관한 연구

백승민(Sungmin Baek),조맹효(Meanghyo Cho) 대한기계학회 2009 대한기계학회 춘추학술대회 Vol.2009 No.5

Dynamic system condensation scheme provides efficient eigenvalue solutions that approximate the lower eigenmodes which represent the global behavior of the structures in large-scale problem. For the reliable reduction, the selection of primary degrees of freedom (PDOFs) has to be appropriate. In the previous study, we proposed an enhancement of the two-level condensation scheme (TLCS) with iterated improved reduced system (IIRS). After the selection of candidate region by element-wise energy estimation through Ritz vector calculation, the PDOFs are selected by the sequential elimination method. Additionally, the IIRS is applied to increase accuracy of the higher modes in the intermediate range. In this study, we propose the DOFs-wise energy estimator which select PDOFs through Rayleigh quotient type energy estimation. Finally, numerical examples demonstrate the performance of the proposed method, and efficiency and accuracy of various selection techniques of the PDOFs are compared.