• Title/Summary/Keyword: Finite difference sensitivity

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Form-finding analysis of suspension bridges using an explicit Iterative approach

  • Cao, Hongyou;Zhou, Yun-Lai;Chen, Zhijun;Wahab, Magd Abdel
    • Structural Engineering and Mechanics
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    • v.62 no.1
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    • pp.85-95
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    • 2017
  • This paper presents an explicit analytical iteration method for form-finding analysis of suspension bridges. By extending the conventional analytical form-finding method predicated on the elastic catenary theory, two nonlinear governing equations are derived for calculating the accurate unstrained lengths of the entire cable systems both the main cable and the hangers. And for the gradient-based iteration method, the derivation of explicit calculation for the Jacobian matrix while solving the nonlinear governing equation enhances the computational efficiency. The results from sensitivity analysis show well performance of the explicit Jacobian matrix compared with the traditional finite difference method. According to two numerical examples of long span suspension bridges studied, the proposed method is also compared with those reported approaches or the fundamental criterions in suspension bridge structural analysis, which eventually confirms the accuracy and efficiency of the proposed approach.

The Study for Reduction of Stress Concentration at the Stepped Shaft According to Two Types of External Force (하중 종류에 따른 다단축의 응력 집중 완화에 대한 연구)

  • Park, I.S.;Shim, J.J.
    • Journal of Power System Engineering
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    • v.14 no.1
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    • pp.47-52
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    • 2010
  • In this study, Finite Element Analysis have been adopted to analyze reducing stress effect and used to induce the sensitivity of design parameter on various techniques which was used for reducing stress. And so it can be utilized as a data to design on similar model. The effect of reducing stress with respect to change of relief groove radius can be increased by 27.3~18.2 % more than radius of fillet. And if a shoulder fillet radius is larger, additional reducing stress by relief groove radius is not obtained. And there was only little effect on reducing stress by changing the center point of groove radius along horizontal direction. In the case that undercut radius is 1.5mm, Max. Equivalent stress is reduced by 5.71% under bending force and 11.11% under torsion. The best effect of reducing stress at undercut model was yielded when the undercut radius is a forth of difference of stepped shaft radius.

Development of DS/FDM-a Robust CAD-based Optimal Design System and Its Application to Engineering Structures (CAD 기반 최적설계 시스템인 DS/FDM의 개발과 공학 구조물에 대한 적용)

  • Han, Jeong-Sam;Uphaus, Frank;Kim, Yeong-Ryeol;Kwak, Byung-Man
    • Proceedings of the KSME Conference
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    • 2000.04a
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    • pp.720-724
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    • 2000
  • In this paper, we introduce a seamlessly integrated CAD-based design system (DS) for CAD modeling, engineering analysis, and optimal design which has been developed in CCED at KAIST, The key points of this integrating philosophy are to make full use of a parametric CAD program as the platform of integration and to adopt finite difference method for design sensitivity analysis in optimization process to get robustness and versatility. Design variables are directly selected by clicking CAD model parameters and all the analysis and design activities are menu-driven. This integrated program, named as DS/FDM, runs on Windows NT or Unix and FE analyses are performed at a remote Unix-workstation for multiple users. Application examples include shape optimal design of a belt clip that fits onto a portable electronic device and a bracket to show performance of DS/FDM with shell and tetra solid elements. This software is found efficient and effective fur shape design and size design of engineering structures.

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Study on the Applications of Automatic Differentiation in Engineering Computation (자동 미분의 공학 계산 적용 연구)

  • Lee, Jae-Hun;Im, Dong-Kyun;Kwon, Jang-Hyuk
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.36 no.7
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    • pp.634-641
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    • 2008
  • Automatic Differentiation(AD) is a tool for generating sensitivities, such as gradient or Jacobian, automatically. AD tools provide mathematically exact sensitivities for the given source code. In this paper applications of automatic differentiation are studied. Derivative codes are generated with AD tools for structural analysis code and flow analysis code. How to apply AD tools is explained and the accuracy of sensitivities is compared with the finite difference. Sensitivities of generated derivative code accord well with finite difference, but the calculation time of derivative code increases. It was found that the calculation time can be decreased by additional modification of derivative code.

Bearing capacity at the pile tip embedded in rock depending on the shape factor and the flow

  • Ana S. Alencar;Ruben A. Galindo;Miguel A. Millan
    • Computers and Concrete
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    • v.31 no.5
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    • pp.443-455
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    • 2023
  • This is a research analyses on the bearing capacity at a pile tip embedded in rock. The aim is to propose a shape coefficient for an analytical solution and to investigate the influence of the plastic flow law on the problem. For this purpose, the finite difference method is used to analyze the bearing capacity of various types and states of rock masses, assuming the Hoek & Brown failure criterion, by considering both plane strain and an axisymmetric model. Different geometrical configurations were adopted for this analysis. First, the axisymmetric numerical results were compared with those obtained from the plane strain analytical solution. Then the pile shape influence on the bearing capacity was studied. A shape factor is now proposed. Furthermore, an evaluation was done on the influence of the plastic flow law on the pile tip bearing capacity. Associative flow and non-associative flow with null dilatancy were considered, resulting in a proposed correlation. A total of 324 cases were simulated, performing a sensitivity analysis on the results and using the graphic output of vertical displacement and maximum principal stress to understand how the failure mechanism occurs in the numerical model.

Development of an Electrical Capacitance Tomography Code for Analysis of Two-Phase Flow in the Rectangular Pipe (사각관 이상유동 분석을 위한 전기적 캐패시턴스 토모그라피 코드 개발)

  • Lee, Kyoung-Hwang;Lee, Jae-Young
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.29 no.1 s.232
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    • pp.87-94
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    • 2005
  • A computer code for Electrical Capacitance Tomography (ECT) is developed to sense the cross sectional phase distribution of two-phase flow in the rectangular pipe in which the tomography sensor furnished by the insulated wall, electrodes, and electric field screen. The computer code had two steps for the image reconstruction. In the forward projection step, the sensitivity matrix was constructed based on the electric field calculated by the finite difference method. In the backward projection step, the sensitivity matrix and the measured capacitances were used to reconstruct the cross sectional image. Several algorithms including LBP, TR, ITR, and PLI were employed to find the proper one for the two-phase flow analysis. Since the dielectric constant of the water in two-phase flow is sensitive to the thermal parameter such as, temperature and pressure, the developed code was evaluated to find their accuracy, speed of calculation, and sensitivity to the variation of the dielectric constant. It was found that the iterative methods are superior to the direct methods for the image reconstruction, and the PLI method was the best in the variation of the dielectric constants.

Covered Microlens Structure for Quad Color Filter Array of CMOS Image Sensor

  • Jae-Hyeok Hwang;Yunkyung Kim
    • Current Optics and Photonics
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    • v.7 no.5
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    • pp.485-495
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    • 2023
  • The pixel size in high-resolution complementary metal-oxide-semiconductor (CMOS) image sensors continues to shrink due to chip size limitations. However, the pixel pitch's miniaturization causes deterioration of optical performance. As one solution, a quad color filter (CF) array with pixel binning has been developed to enhance sensitivity. For high sensitivity, the microlens structure also needs to be optimized as the CF arrays change. In this paper, the covered microlens, which consist of four microlenses covered by one large microlens, are proposed for the quad CF array in the backside illumination pixel structure. To evaluate the optical performance, the suggested microlens structure was simulated from 0.5 ㎛ to 1.0 ㎛ pixels at the center and edge of the sensors. Moreover, all pixel structures were compared with and without in-pixel deep trench isolation (DTI), which works to distribute incident light uniformly into each photodiode. The suggested structure was evaluated with an optical simulation using the finite-difference time-domain method for numerical analysis of the optical characteristics. Compared to the conventional microlens, the suggested microlens show 29.1% and 33.9% maximum enhancement of sensitivity at the center and edge of the sensor, respectively. Therefore, the covered microlens demonstrated the highly sensitive image sensor with a quad CF array.

Modelling the rheological behaviour of fresh concrete: An elasto-viscoplastic finite element approach

  • Chidiac, S.E.;Habibbeigi, F.
    • Computers and Concrete
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    • v.2 no.2
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    • pp.97-110
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    • 2005
  • Rheological behaviour of fresh concrete is an important factor in controlling concrete quality. It is recognized that the measurement of the slump is not a sufficient test method to adequately characterize the rheology of fresh concrete. To further understand the slump measurement and its relationship to the rheological properties, an elasto-viscoplastic, 2-D axisymmetric finite element (FE) model is developed. The FE model employs the Bingham material model to simulate the flow of a slump test. An experimental program is carried out using the Slump Rate Machine (SLRM_II) to evaluate the finite element simulation results. The simulated slump-versus-time curves are found to be in good agreement with the measured data. A sensitivity study is performed to evaluate the effects of yield stress, plastic viscosity and cone withdrawal rate on the measured flow curve using the FE model. The results demonstrate that the computed yield stress compares well with reported experimental data. The flow behaviour is shown to be influenced by the yield stress, plastic viscosity and the cone withdrawal rate. Further, it is found that the value of the apparent plastic viscosity is different from the true viscosity, with the difference depending on the cone withdrawal rate. It is also confirmed that the value of the final slump is most influenced by the yield stress.

Design and Sensitivity Analysis of Design Factors for Induction Heating System (수치해석을 통한 유도가열 코일의 설계 및 설계인자의 민감도 해석)

  • Oh, Dong-Wook;Kim, Tae Hoon;Do, Kyu Hyung;Park, Jang Min;Lee, Jungho
    • Journal of the Korean Society for Heat Treatment
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    • v.26 no.5
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    • pp.233-240
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    • 2013
  • Rapid and homogeneous heating in heat treatment has been a challenging engineering issue throughout a heating temperature over $1,000^{\circ}C$. Induction heating has been widely used in field of heat treatment compared with conventional heating system. Advantages in homogeneous heating, simple fabrication, and repeatable use can be efficiently made with the induction heater. In this paper, numerical analysis of an induction coil system for heat flux gauge heating is performed. The effect of configuration on the heating performance was considered in various cases of the coil radius, distance between the winding, relative height difference between the heat flux gauge and the coil, and the applied current frequency. Temperature distribution within the heat flux gauge at frequency-steady state was calculated with a finite element method. Sensitivity analysis was also performed and the relative importance of 2 key parameters; coil radius, distance between the winding, were taken as main contributors for induction heating.

Isogeometric Shape Design Optimization of Structures Subjected to Design-dependent Loads (설계 의존형 하중 조건을 갖는 구조물의 아이소-지오메트릭 형상 최적설계)

  • Yoon, Min-Ho;Koo, Bon-Yong;Ha, Seung-Hyun;Cho, Seon-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.24 no.1
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    • pp.1-7
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    • 2011
  • In this paper, based on an isogeometric approach, we have developed a shape design optimization method for plane elasticity problems subjected to design-dependent loads. The conventional shape optimization using the finite element method has some difficulties in the parameterization of geometry. In an isogeometric analysis, however, the geometric properties are already embedded in the B-spline basis functions and control points so that it has potential capability to overcome the aforementioned difficulties. The solution space for the response analysis can be represented in terms of the same NURBS basis functions to represent the geometry, which yields a precise analysis model that exactly represents the normal and curvature depending on the applied loads. A continuum-based isogeometric adjoint sensitivity is extensively derived for the plane elasticity problems under the design-dependent loads. Through some numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.