• 제목/요약/키워드: singular solutions.

검색결과 177건 처리시간 0.024초

Analytical solution of a contact problem and comparison with the results from FEM

  • Oner, Erdal;Yaylaci, Murat;Birinci, Ahmet
    • Structural Engineering and Mechanics
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    • 제54권4호
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    • pp.607-622
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    • 2015
  • This paper presents a comparative study of analytical method and finite element method (FEM) for analysis of a continuous contact problem. The problem consists of two elastic layers loaded by means of a rigid circular punch and resting on semi-infinite plane. It is assumed that all surfaces are frictionless and only compressive normal tractions can be transmitted through the contact areas. Firstly, analytical solution of the problem is obtained by using theory of elasticity and integral transform techniques. Then, finite element model of the problem is constituted using ANSYS software and the two dimensional analysis of the problem is carried out. The contact stresses under rigid circular punch, the contact areas, normal stresses along the axis of symmetry are obtained for both solutions. The results show that contact stresses and the normal stresses obtained from finite element method (FEM) provide boundary conditions of the problem as well as analytical results. Also, the contact areas obtained from finite element method are very close to results obtained from analytical method; disagree by 0.03-1.61%. Finally, it can be said that there is a good agreement between two methods.

Large-scaled truss topology optimization with filter and iterative parameter control algorithm of Tikhonov regularization

  • Nguyen, Vi T.;Lee, Dongkyu
    • Steel and Composite Structures
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    • 제39권5호
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    • pp.511-528
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    • 2021
  • There are recently some advances in solving numerically topology optimization problems for large-scaled trusses based on ground structure approach. A disadvantage of this approach is that the final design usually includes many bars, which is difficult to be produced in practice. One of efficient tools is a so-called filter scheme for the ground structure to reduce this difficulty and determine several distinct bars. In detail, this technique is valuable for practical uses because unnecessary bars are filtered out from the ground structure to obtain a well-defined structure during the topology optimization process, while it still guarantees the global equilibrium condition. This process, however, leads to a singular system of equilibrium equations. In this case, the minimization of least squares with Tikhonov regularization is adopted. In this paper, a proposed algorithm in controlling optimal Tikhonov parameter is considered in combination with the filter scheme due to its crucial role in obtaining solution to remove numerical singularity and saving computational time by using sparse matrix, which means that the discrete optimal topology solutions depend on choosing the Tikhonov parameter efficiently. Several numerical examples are investigated to demonstrate the efficiency of the filter parameter control algorithm in terms of the large-scaled optimal topology designs.

Multiple unequal cracks between an FGM orthotropic layer and an orthotropic substrate under mixed mode concentrated loads

  • M. Hassani;M.M. Monfared;A. Salarvand
    • Structural Engineering and Mechanics
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    • 제86권4호
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    • pp.535-546
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    • 2023
  • In the present paper, multiple interface cracks between a functionally graded orthotropic coating and an orthotropic half-plane substrate under concentrated loading are considered by means of the distribution dislocation technique (DDT). With the use of integration of Fourier transform the problem is reduced to a system of Cauchy-type singular integral equations which are solved numerically to compute the dislocation density on the surfaces of the cracks. The distribution dislocation is a powerful method to calculate accurate solutions to plane crack problems, especially this method is very good to find SIFs for multiple unequal cracks located at the interface. Hence this technique allows considering any number of interface cracks. The primary objective of this paper is to investigate the effects of the interaction of multiple interface cracks, load location, material orthotropy, nonhomogeneity parameters and geometry parameters on the modes I and II SIFs. Numerical results show that modes I/II SIFs decrease with increasing the nonhomogeneity parameter and the highest magnitude of SIF occurs where distances between the load location and crack tips are minimal.

KNiFe(CN)6 전기화학적 이온교환체를 이용한 세슘 양이온의 분리에 관한 연구 (A Study on the Separation of Cesium Cations by Using Electrochemical Ion Exchanger of KNiFe(CN)6)

  • 황영기
    • 전기화학회지
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    • 제15권4호
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    • pp.256-263
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    • 2012
  • 본 연구에서는 전기화학적 이온교환체 중의 하나인 nickel hexacyanoferrate($KNiFe(CN)_6$) 막 전극을 사용하여 세슘 양이온을 분리하는 실험을 수행하였다. 1.0M $NaNO_3$와 1.0M $CsNO_3$의 단일성분계 및 이성분계 수용액에서 순환전위곡선을 측정하여 전극전위, 전류, 전기량의 변화 거동을 조사하였으며, 실험 전과 후에 $KNiFe(CN)_6$ 막의 구조 형태와 원자조성의 변화를 각각 SEM과 EDS 분석을 통하여 조사하였다. 또한 나트륨과 세슘 용액에서 교대로 이온교환 반응을 수행하여 측정한 순환전위곡선과 원자조성으로부터 $KNiFe(CN)_6$의 이온 선택성을 조사하였다. 본 연구의 실험 결과에 의하면, 전기를 인가한 $KNiFe(CN)_6$ 이온교환체는 화학적 유 무기물 이온교환체에 비해 약 40배 이상의 우수한 내구성을 가짐을 알 수 있었다. 또한 $KNiFe(CN)_6$ 이온교환체는 나트륨보다 세슘에 대해 보다 높은 선택도를 가짐을 확인할 수 있었다.

적합직교분해 기법에서의 효율적인 스냅샷 선정을 위한 고유값 분석 (ANALYSIS OF EIGEN VALUES FOR EFFECTIVE CHOICE OF SNAPSHOT DATA IN PROPER ORTHOGONAL DECOMPOSITION)

  • 강형민;전상욱;이관중
    • 한국전산유체공학회지
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    • 제22권1호
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    • pp.59-66
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    • 2017
  • The guideline of selecting the number of snapshot dataset, $N_s$ in proper orthogonal decomposition(POD) was presented via the analysis of Eigen values based on the singular value decomposition(SVD). In POD, snapshot datasets from the solutions of Euler or Navier-Stokes equations are utilized to SVD and a reduced order model(ROM) is constructed as the combination of Eigen vectors. The ROM is subsequently applied to reconstruct the flowfield data with new set of flow conditions, thereby enhancing the computational efficiency. The overall computational efficiency and accuracy of POD is dependent on the number of snapshot dataset; however, there is no reliable guideline of determining $N_s$. In order to resolve this problem, the order of maximum to minimum Eigen value ratio, O(R) from SVD was analyzed and presented for the decision of $N_s$; in case of steady flow, $N_s$ should be determined to make O(R) be $10^9$. For unsteady flow, $N_s$ should be increased to make O(R) be $10^{11\sim12}$. This strategy of selecting the snapshot dataset was applied to two dimensional NACA0012 airfoil and vortex flow problems including steady and unsteady cases and the numerical accuracies according to $N_s$ and O(R) were discussed.

시간의존 완경사방정식의 이론적 비교 (Analytical Comparison of Time-Dependent Mild-Slope Equations)

  • Lee, Chang-Hoon;James T. Kirby
    • 한국해안해양공학회지
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    • 제6권4호
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    • pp.389-396
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    • 1994
  • 현존하는 시간의존 완경사방정식으로 Smith와 Sprinks(1975)가 개발한 식(이와 대등한 정확도로 Radder와 Dingemans(1985)가 개발한 식)과 Kubo 등 (1992)이 개발한 식이 있다. 분산관계식과 에너지 전송의 관점에서 시간의존 완경사방정식을 분석하였다. 수평방향으로 1차원적으로 시간의존 완경사방정식의 진폭변조현상을 선형 Scrodinger식과 대비하여 비교하였다. 분산관계식과의 관점에서 보면, Smith와 Sprinks의 모형이 보다 얕은 수심(kh$\leq$0.2$\pi$)에서 더 정확하고 아주 얕은 수심(kh=0)에서는 선형 Scrodinger식을 만족시키는 반면 Kubo 등의 모형은 보다 깊은 수심(kh>0.2$\pi$)에서 더 정확하고 천이영역의 한 지점(kh=0.3$\pi$)에서 선형 Scrodinger식을 만족시킨다. 에너지 전송의 관점에서 보면 Kubo 등의 모형이 더 정확하지만 높은 주파수 영역에서 해가 발산하는 단점이 있다.

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BERT 기반 감성분석을 이용한 추천시스템 (Recommender system using BERT sentiment analysis)

  • 박호연;김경재
    • 지능정보연구
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    • 제27권2호
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    • pp.1-15
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    • 2021
  • 추천시스템은 사용자의 기호를 파악하여 물품 구매 결정을 도와주는 역할을 할 뿐만 아니라, 비즈니스 전략의 관점에서도 중요한 역할을 하기에 많은 기업과 기관에서 관심을 갖고 있다. 최근에는 다양한 추천시스템 연구 중에서도 NLP와 딥러닝 등을 결합한 하이브리드 추천시스템 연구가 증가하고 있다. NLP를 이용한 감성분석은 사용자 리뷰 데이터가 증가함에 따라 2000년대 중반부터 활용되기 시작하였지만, 기계학습 기반 텍스트 분류를 통해서는 텍스트의 특성을 완전히 고려하기 어렵기 때문에 리뷰의 정보를 식별하기 어려운 단점을 갖고 있다. 본 연구에서는 기계학습의 단점을 보완하기 위하여 BERT 기반 감성분석을 활용한 추천시스템을 제안하고자 한다. 비교 모형은 Naive-CF(collaborative filtering), SVD(singular value decomposition)-CF, MF(matrix factorization)-CF, BPR-MF(Bayesian personalized ranking matrix factorization)-CF, LSTM, CNN-LSTM, GRU(Gated Recurrent Units)를 기반으로 하는 추천 모형이며, 실제 데이터에 대한 분석 결과, BERT를 기반으로 하는 추천시스템의 성과가 가장 우수한 것으로 나타났다.