• 제목/요약/키워드: analytical solutions

검색결과 1,317건 처리시간 0.028초

Multi-material topology optimization for crack problems based on eXtended isogeometric analysis

  • Banh, Thanh T.;Lee, Jaehong;Kang, Joowon;Lee, Dongkyu
    • Steel and Composite Structures
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    • 제37권6호
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    • pp.663-678
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    • 2020
  • This paper proposes a novel topology optimization method generating multiple materials for external linear plane crack structures based on the combination of IsoGeometric Analysis (IGA) and eXtended Finite Element Method (X-FEM). A so-called eXtended IsoGeometric Analysis (X-IGA) is derived for a mechanical description of a strong discontinuity state's continuous boundaries through the inherited special properties of X-FEM. In X-IGA, control points and patches play the same role with nodes and sub-domains in the finite element method. While being similar to X-FEM, enrichment functions are added to finite element approximation without any mesh generation. The geometry of structures based on basic functions of Non-Uniform Rational B-Splines (NURBS) provides accurate and reliable results. Moreover, the basis function to define the geometry becomes a systematic p-refinement to control the field approximation order without altering the geometry or its parameterization. The accuracy of analytical solutions of X-IGA for the crack problem, which is superior to a conventional X-FEM, guarantees the reliability of the optimal multi-material retrofitting against external cracks through using topology optimization. Topology optimization is applied to the minimal compliance design of two-dimensional plane linear cracked structures retrofitted by multiple distinct materials to prevent the propagation of the present crack pattern. The alternating active-phase algorithm with optimality criteria-based algorithms is employed to update design variables of element densities. Numerical results under different lengths, positions, and angles of given cracks verify the proposed method's efficiency and feasibility in using X-IGA compared to a conventional X-FEM.

A novel coupled finite element method for hydroelastic analysis of FG-CNTRC floating plates under moving loads

  • Nguyen, Vu X.;Lieu, Qui X.;Le, Tuan A.;Nguyen, Thao D.;Suzuki, Takayuki;Luong, Van Hai
    • Steel and Composite Structures
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    • 제42권2호
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    • pp.243-256
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    • 2022
  • A coupled finite element method (FEM)-boundary element method (BEM) for analyzing the hydroelastic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) floating plates under moving loads is firstly introduced in this article. For that aim, the plate displacement field is described utilizing a generalized shear deformation theory (GSDT)-based FEM, meanwhile the linear water-wave theory (LWWT)-relied BEM is employed for the fluid hydrodynamic modeling. Both computational domains of the plate and fluid are coincidentally discretized into 4-node Hermite elements. Accordingly, the C1-continuous plate element model can be simply captured owing to the inherent feature of third-order Hermite polynomials. In addition, this model is also completely free from shear correction factors, although the shear deformation effects are still taken into account. While the fluid BEM can easily handle the free surface with a lower computational effort due to its boundary integral performance. Material properties through the plate thickness follow four specific CNT distributions. Outcomes gained by the present FEM-BEM are compared with those of previously released papers including analytical solutions and experimental data to validate its reliability. In addition, the influences of CNT volume fraction, different CNT configurations, water depth, and load speed on the hydroelastic behavior of FG-CNTRC plates are also examined.

Effect of the variable visco-Pasternak foundations on the bending and dynamic behaviors of FG plates using integral HSDT model

  • Hebali, Habib;Chikh, Abdelbaki;Bousahla, Abdelmoumen Anis;Bourada, Fouad;Tounsi, Abdeldjebbar;Benrahou, Kouider Halim;Hussain, Muzamal;Tounsi, Abdelouahed
    • Geomechanics and Engineering
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    • 제28권1호
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    • pp.49-64
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    • 2022
  • In this work, the bending and dynamic behaviors of advanced composite plates resting on variable visco-Pasternak foundations are studied using a simple shear deformation integral plate model. The research is carried out with a view to a three-parameter foundation including the influences of the variable Winkler coefficient, the constant Pasternak coefficient and the damping coefficient of the elastic medium. The present theory uses a displacement field with integral terms instead of derivative terms by including also the shear deformation effect without introducing the shear correction factors. The equations of motion for advanced composite plates are obtained using the Hamilton principle. Analytical solutions for the bending and dynamic analysis are deduced for simply supported plates resting on variable visco-Pasternak foundations. Some numerical results are presented to demonstrate the impact of material index, elastic foundation type, and damping coefficient of the foundation, on the bending and dynamic responses of advanced composite plates.

바닥의 움직임에 따른 선형파의 생성을 모의할 수 있는 간편 수치해석 기법 (A Simplified Numerical Method for Simulating the Generation of Linear Waves by a Moving Bottom)

  • 정재상
    • 한국해안·해양공학회논문집
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    • 제35권2호
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    • pp.41-48
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    • 2023
  • 본 연구에서는 바닥의 움직임에 따른 파랑의 생성 및 변화를 모의할 수 있는 간단한 선형 수치해석 기법을 소개한다. 연속방정식과 선형의 동역학적 및 운동학적 자유수면 경계조건, 선형의 운동학적 바닥 경계조건을 공간에 대해 푸리에 변환한 후 파수 영역에서 수치해석을 수행하며, 결과는 푸리에 역변환을 통해 공간영역에서 표현된다. 파수 영역에서 동역학적 자유수면 경계조건과 운동학적 자유수면 경계조건이 수치적으로 계산되며, 이 때 평균수면 (z = 0)에서의 속도포텐셜은 연속방정식과 운동학적 바닥 경계조건을 만족한다. 삼각형 및 사각형 형상의 바닥이 주기적으로 움직이는 경우의 파랑 생성 및 전파에 대해 검토하였다. 간편 수치해석 기법을 이용한 결과는 기존의 선형 해석해와 비교하였으며, 거의 일치하는 결과를 보였다. 계산 시간간격(Δt)과 계산 파수간격(Δk)에 따른 수치해석 결과의 안정성에 대해서도 검토하였다. 검토 결과 Δt ≤T(주기)/1000, Δk ≤ π/100 일 때 수치해석에 의한 결과가 적절하게 도출되는 것으로 나타났다.

Visco-elastic foundation effect on buckling response of exponentially graded sandwich plates under various boundary conditions

  • Mimoun Bennedjadi;Salem Mohammed Aldosari;Abdelbaki Chikh;Abdelhakim Kaci;Abdelmoumen Anis Bousahla;Fouad Bourada;Abdeldjebbar Tounsi;Kouider Halim Benrahou;Abdelouahed Tounsi
    • Geomechanics and Engineering
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    • 제32권2호
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    • pp.159-177
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    • 2023
  • In the present work, a simple and refined shear deformation theory is used to analyze the effect of visco-elastic foundation on the buckling response of exponentially-gradient sandwich plates under various boundary conditions. The proposed theory includes indeterminate integral variables kinematic with only four generalized parameters, in which no shear correction factor is used. The visco-Pasternak's foundation is taken into account by adding the influence of damping to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's foundation modulus. The four governing equations for FGM sandwich plates are derived by employing principle of virtual work. To solve the buckling problem, Galerkin's approach is utilized for FGM sandwich plates for various boundary conditions. The analytical solutions for critical buckling loads of several types of powerly graded sandwich plates resting on visco-Pasternak foundations under various boundary conditions are presented. Some numerical results are presented to indicate the effects of inhomogeneity parameter, elastic foundation type, and damping coefficient of the foundation, on the critical buckling loads.

Free vibration of deep and shallow curved FG nanobeam based on nonlocal elasticity

  • S.A.H., Hosseini;O., Rahmani;V., Refaeinejad;H., Golmohammadi;M., Montazeripour
    • Advances in aircraft and spacecraft science
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    • 제10권1호
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    • pp.51-65
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    • 2023
  • In this paper, the effect of deepness on in-plane free vibration behavior of a curved functionally graded (FG) nanobeam based on nonlocal elasticity theory has been investigated. Differential equations and boundary conditions have been developed based on Hamilton's principle. In order to figure out the size effect, nonlocal theory has been adopted. Properties of material vary in radial direction. By using Navier solution technique, the amount of natural frequencies has been obtained. Also, to take into account the deepness effect on vibrations, thickness to radius ratio has been considered. Differences percentage between results of cases in which deepness effect is included and excluded are obtained and influences of power-law exponent, nonlocal parameter and arc angle on these differences percentage are studied. Results show that arc angle and power law exponent parameters have the most influences on the amount of the differences percentage due to deepness effect. It has been observed that the inclusion of geometrical deep term and material distribution results in an increase in sensitivity of dimensionless natural frequency about variation of aforementioned parameters and a change in variation range of natural frequency. Finally, several numerical results of deep and shallow curved functionally graded nanobeams with different geometry dimensions are presented, which may serve as benchmark solutions for the future research in this field.

Free vibration investigation of functionally graded plates with temperature-dependent properties resting on a viscoelastic foundation

  • Abdeldjebbar Tounsi;Adda Hadj Mostefa;Amina Attia;Abdelmoumen Anis Bousahla;Fouad Bourada;Abdelouahed Tounsi;Mohammed A. Al-Osta
    • Structural Engineering and Mechanics
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    • 제86권1호
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    • pp.1-16
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    • 2023
  • The free vibration of temperature-dependent functionally graded plates (FGPs) resting on a viscoelastic foundation is investigated in this paper using a newly developed simple first-order shear deformation theory (FSDT). Unlike other first order shear deformation (FSDT) theories, the proposed model contains only four variables' unknowns in which the transverse shear stress and strain follow a parabolic distribution along the plates' thickness, and they vanish at the top and bottom surfaces of the plate by considering a new shape function. For this reason, the present theory requires no shear correction factor. Linear steady-state thermal loads and power-law material properties are supposed to be graded across the plate's thickness. Uniform, linear, non-linear, and sinusoidal thermal rises are applied at the two surfaces for simply supported FGP. Hamilton's principle and Navier's approach are utilized to develop motion equations and analytical solutions. The developed theory shows progress in predicting the frequencies of temperature-dependent FGP. Numerical research is conducted to explain the effect of the power law index, temperature fields, and damping coefficient on the dynamic behavior of temperature-dependent FGPs. It can be concluded that the equation and transformation of the proposed model are as simple as the FSDT.

기업의 윤리적 인공지능 기반 서비스 개발을 위한 정책수단 연구: AHP를 활용한 탐색적 분석 (A Study on Policy Instrument for the Development of Ethical AI-based Services for Enterprises: An Exploratory Analysis Using AHP)

  • 장창기;이민상;성욱준
    • 한국IT서비스학회지
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    • 제22권2호
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    • pp.23-40
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    • 2023
  • Despite the growing interest and normative discussions on AI ethics, there is a lack of discussion on policy instruments that are necessary for companies to develop AI-based services in compliance with ethical principles. Thus, the purpose of this study is to explore policy instruments that can encourage companies to voluntarily comply with and adopt AI ethical standards and self-checklists. The study reviews previous research and similar cases on AI ethics, conducts interviews with AI-related companies, and analyzes the data using AHP to derive action plans. In terms of desirability and feasibility, Research findings show that policy instruments that induce companies to ethically develop AI-based services should be prioritized, while regulatory instruments require a cautious approach. It was also found that a consulting support policy consisting of experts in various fields who can support the use of AI ethics, and support for the development of solutions that adhere to AI ethical standards are necessary as incentive policies. Additionally, the participation and agreement of various stakeholders in the process of establishing AI ethical standards are crucial, and policy instruments need to be continuously supplemented through implementation and feedback. This study is significant as it presents the necessary policy instruments for companies to develop ethical AI-based services through an analytical methodology, moving beyond discursive discussions on AI ethical principles. Further analysis on the effectiveness of policy instruments linked to AI ethical principles is necessary for establishing ethical AI-based service development.

정규압밀 점토지반에서 피에조콘관입 결과를 이용한 원위치 응력상태 평가 (Estimation of In-situ Stress State for NC Clays Using PCPT Results)

  • 조성환;서경범;장범수;이준환
    • 한국지반공학회논문집
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    • 제26권10호
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    • pp.15-25
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    • 2010
  • 본 연구에서는 정규압밀된 점토지반에서 피에조콘관입시험 (PCPT) 결과를 이용하여 원위치 응력상태를 평가할 수 있는 방법을 제안하였다. 이를 위해 다양한 현장시험과 실내시험 결과를 분석하였으며, 현장시험에서 구해진 PCPT 결과값과 실내시험에서 얻어진 결과를 토대로 이론식을 산정하였다. 제안된 방법에서는 기존 방법에 포함되어 있던 불교란 시료 채취과정과 단위중량 결정을 위한 별도의 실험과정이 요구되지 않으며, PCPT 시험결과를 통해 유효응력의 추정이 가능하기 때문에, 조사과정에서의 비용이나 소요시간을 최소화 할 수 있다. 제안된 방법의 적용성 평가를 위하여 국내의 다양한 점성토 지반에서 수행된 피에조콘관입시험 결과를 수집하였으며, 이를 토대로 제안된 방법에 의한 결과와 기존방법의 결과와의 비교분석을 실시하였다. 분석결과, 예측된 결과는 측정된 결과와 유사함을 확인할 수 있었다.

시험 방법에 따른 동결토의 인장강도 (A Comparative Study on the Tensile Strength of Frozen Soil according to Test Methods)

  • 서영교;강효섭
    • 한국지반공학회논문집
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    • 제24권4호
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    • pp.57-66
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    • 2008
  • 본 연구에서는 쪼갬 인장시험과 Fang, H. Y. and Fernandez(1981)에 의해 고안된 일축관입시험을 통한 동결토의 인장강도를 살펴보았다. 본 연구는 영하 15도의 환경 속에서 화강풍화토, 표준사와 카오리가 혼합된 사질 혼합토의 일축관입인장강도와 쪼갬 인장강도가 어떻게 변화하는지를 고찰하였다. 동결공시체는 함수비, 점토함량에 따라 다양하게 실험을 실시하였으며, 함수비와 점토함유량에 따라 일축관입인장강도와 쪼갬 인장강도간의 상호관계를 분석하였다. 결과를 요약하면, 평균적으로 쪼갬 인장강도는 일축관입인장강도에 비해서 4배정도 큰 강도를 나타내었다. 함수비가 증가함에 따라 두 인장강도간의 차이가 크게 나타났으며, 그리고 점토함량이 증가할수록 두 인장강도는 모두 감소하는 경향을 나타내었다.