• 제목/요약/키워드: rational curves

검색결과 98건 처리시간 0.031초

Influence of end fixity on post-yield behaviors of a tubular member

  • Cho, Kyu Nam
    • Structural Engineering and Mechanics
    • /
    • 제13권5호
    • /
    • pp.557-568
    • /
    • 2002
  • For the evaluation of the capability of a tubular member of an offshore structure to absorb the collision energy, a simple method can be employed for the collision analysis without performing the detailed analysis. The most common simple method is the rigid-plastic method. However, in this method any characteristics for horizontal movement and rotation at the ends of the corresponding tubular member are not included. In a real structural system of an offshore structure, tubular members sustain a certain degree of elastic support from the adjacent structure. End fixity has influences in the behaviors of a tubular member. Three-dimensional FEM analysis can include the effect of end fixity fully, however in viewpoints of the inherent computational complexities of the 3-D approach, this is not the recommendable analysis at the initial design stage. In this paper, influence of end fixity on the behaviors of a tubular member is investigated, through a new approach and other approaches. A new analysis approach that includes the flexibility of the boundary points of the member is developed here. The flexibility at the ends of a tubular element is extracted using the rational reduction of the modeling characteristics. The property reduction is based on the static condensation of the related global stiffness matrix of a model to end nodal points of the tubular element. The load-displacement relation at the collision point of the tubular member with and without the end flexibility is obtained and compared. The new method lies between the rigid-plastic method and the 3-demensional analysis. It is self-evident that the rigid-plastic method gives high strengthening membrane effect of the member during global deformation, resulting in a steeper slope than the present method. On the while, full 3-D analysis gives less strengthening membrane effect on the member, resulting in a slow going load-displacement curve. Comparison of the load-displacement curves by the new approach with those by conventional methods gives the figures of the influence of end fixity on post-yielding behaviors of the relevant tubular member. One of the main contributions of this investigation is the development of an analytical rational procedure to figure out the post-yielding behaviors of a tubular member in offshore structures.

지반-1차지보재-2차라이닝의 상호작용을 고려한 터널 2차라이닝 해석모델 (An Analysis Model of the Secondary Tunnel Lining Considering Ground-Primary Support-Secondary Lining Interaction)

  • 서성호;장석부;이상덕
    • 터널과지하공간
    • /
    • 제12권2호
    • /
    • pp.107-114
    • /
    • 2002
  • 터널 2차라이닝은 지반하중의 합리적인 산정기준의 부재와 보수적 경향의 지반이완하중법이 적용되고 있기 때문에 과다한 경향으로 보강되고 있는 실정이다. 2차라이닝에 고려되는 주요하중으로는 지반이완하중과 수압을 들 수 있으며, 배수터널의 경우에는 지반하중이 가장 큰 하중이 된다. 터널 주변 지반에 별도의 외력이 작용하지 않는다면, 2차라이닝에 작용하는 하중의 직접적인 원인은 1차지보재의 지지력 저하이다. 따라서, 2차라이닝의 설계시에는 지반과 1차지보재와의 상호작용을 고려한 합리적인 해석방법이 요구된다. 본 논문에서는 단순한 질량-스프링 모델을 통하여 지반-1차지보재-2차라이닝의 상호작용을 개념적 모델로 설명하였으며, 이를 원형터널에 대한 이론해석을 통하여 지반-1차지보재-2차라이닝 의 상호작용에 대한 하중전이 특성을 입증하였다. 그리고, 복잡한 터널해석조건에 대한 본 모델의 적용성을 검토하기 위하여 수치해석법의 적용성을 검증하였다.

Prediction of post fire load deflection response of RC flexural members using simplistic numerical approach

  • Lakhani, Hitesh;Singh, Tarvinder;Sharma, Akanshu;Reddy, G.R.;Singh, R.K.
    • Structural Engineering and Mechanics
    • /
    • 제50권6호
    • /
    • pp.755-772
    • /
    • 2014
  • A simplistic approach towards evaluation of complete load deflection response of Reinforced Concrete (RC) flexural members under post fire (residual) scenario is presented in this paper. The cross-section of the RC flexural member is divided into a number of sectors. Thermal analysis is performed to determine the temperature distribution across the section, for given fire duration. Temperature-dependent stress-strain curves for concrete and steel are then utilized to perform a moment-curvature analysis. The moment-curvature relationships are obtained for beams exposed to different fire durations. These are then utilized to obtain the load-deflection plots following pushover analysis. Moreover one of the important issues of modeling the initial stiffness giving due consideration to stiffness degradation due to material degradation and thermal cracking has also been addressed in a rational manner. The approach is straightforward and can be easily programmed in spreadsheets. The presented approach has been validated against the experiments, available in literature, on RC beam subjected to different fire durations viz. 1hr, 1.5hrs and 2hrs. Complete load-deflection curves have been obtained and compared with experimentally reported counterparts. The results also show a good match with the results obtained using more complicated approaches such as those involving Finite element (FE) modeling and conducting a transient thermal stress analysis. Further evaluation of the beams during fire (at elevated temperatures) was performed and a comparison of the mechanical behavior of RC beams under post fire and during fire scenarios is made. Detailed formulations, assumptions and step by step approach are reported in the paper. Due to the simplicity and ease of implementation, this approach can be used for evaluation of global performance of fire affected structures.

A complete S-shape feed rate scheduling approach for NURBS interpolator

  • Du, Xu;Huang, Jie;Zhu, Li-Min
    • Journal of Computational Design and Engineering
    • /
    • 제2권4호
    • /
    • pp.206-217
    • /
    • 2015
  • This paper presents a complete S-shape feed rate scheduling approach (CSFA) with confined jerk, acceleration and command feed rate for parametric tool path. For a Non-Uniform Rational B-Spline (NURBS) tool path, the critical points of the tool path where the radius of curvature reaches extreme values are found firstly. Then, the NURBS curve is split into several NURBS sub-curves or blocks by the critical points. A bidirectional scanning strategy with the limitations of chord error, normal/tangential acceleration/jerk and command feed rate is employed to make the feed rate at the junctions between different NURBS blocks continuous. To improve the efficiency of the feed rate scheduling, the NURBS block is classified into three types: short block, medium block and long block. The feed rate profile corresponding to each NURBS block is generated according to the start/end feed rates and the arc length of the block and the limitations of tangential acceleration/jerk. In addition, two compensation strategies are proposed to make the feed rate more continuous and the arc increment more precise. Once the feed rate profile is determined, a second-order Taylor's expansion interpolation method is applied to generate the position commands. Finally, experiments with two free-form NURBS curves are conducted to verify the applicability and accuracy of the proposed method.

Estimation for Primary Tunnel Lining Loads

  • 김학준
    • 한국지반공학회:학술대회논문집
    • /
    • 한국지반공학회 1998년도 터널.암반역학위원회 박사학위 논문집
    • /
    • pp.153-204
    • /
    • 1998
  • Prediction of lining loads due to tunnelling is one of the major issues to be addressed in the design of a tunnel. The objective of this study is to investigate rational and realistic design loads on tunnel linings. factors influencing the lining load are summarized and discussed. The instruments for measuring the lining loads are reviewed and discussed because field measurements are often necessary to verify the design methods. Tunnel construction in the City of Edmonton has been very active for storm and sanitary purposes. Since the early 1970's, the city has also been developing an underground Light Rail Transit system. The load measurements obtained from these tunnels are compared with the results from the existing design methods. However, none of the existing methods are totally satisfactory, Therefore, there is some room for improvement in the prediction of lining loads. The convergence-confinement method is reviewed and applied to a case history of a tunnel in Edmonton. The convergence curves are obtained from 2-D finite element analyses using three different material models and theoretical equations. The limitation of the convergence-confinement method is discussed by comparing these curves with the field measurements. Three-dimensional finite element analyses are performed to gain a better understanding of stress and displacement behaviour near the tunnel face. An improved design method is proposed based on the review of existing design methods and the performance of numerical analyses. A specific method or combination of two different methods is suggested for the estimation of lining loads for different conditions of tunnelling. A method to determine the stress reduction factor is described. Typical values of dimensionless load factors nD/H for tunnels in Edmonton are obtained from parametric analyses. Finally, the loads calculated using the proposed method are compared with field measurements collected from various tunnels in terms of soil types and construction methods to verify the method. The proposed method gives a reasonable approximation of the lining loads. The proposed method is recommended as an approximate guideline for the design of tunnels, but the results should be confirmed by field measurements due to the uncertainties of the ground and lining properties and the construction procedures, This is the reason that in-situ monitoring should be an integral part of the design procedure.

  • PDF

Damage states of yielding and collapse for elevated water tanks supported on RC frame staging

  • Lakhade, Suraj O.;Kumar, Ratnesh;Jaiswal, mprakash R.
    • Structural Engineering and Mechanics
    • /
    • 제67권6호
    • /
    • pp.587-601
    • /
    • 2018
  • Elevated water tanks are inverted pendulum type structures where drift limit is an important criterion for seismic design and performance evaluation. Explicit drift criteria for elevated water tanks are not available in the literature. In this study, probabilistic approach is used to determine maximum drift limit for damage state of yielding and damage state of collapse for the elevated water tanks supported on RC frame staging. The two damage states are defined using results of incremental dynamic analysis wherein a total of 2160 nonlinear time history analyses are performed using twelve artificial spectrum compatible ground motions. Analytical fragility curves are developed using two-parameter lognormal distribution. The maximum allowable drifts corresponding to yield and collapse level requirements are estimated for different tank capacities. Finally, a single fragility curve is developed which provides maximum drift values for the different probability of damage. Further, for rational consideration of the uncertainties in design, three confidence levels are selected and corresponding drift limits for damage states of yielding and collapse are proposed. These values of maximum drift can be used in performance-based seismic design for a particular damage state depending on the level of confidence.

ON THE MODULAR FUNCTION $j_4$ OF LEVEL 4

  • Kim, Chang-Heon;Koo, Ja-Kyung
    • 대한수학회지
    • /
    • 제35권4호
    • /
    • pp.903-931
    • /
    • 1998
  • Since the modular curves X(N) = $\Gamma$(N)\(equation omitted)* (N =1,2,3) have genus 0, we have field isomorphisms K(X(l))(equation omitted)C(J), K(X(2))(equation omitted)(λ) and K(X(3))(equation omitted)( $j_3$) where J, λ are the classical modular functions of level 1 and 2, and $j_3$ can be represented as the quotient of reduced Eisenstein series. When N = 4, we see from the genus formula that the curve X(4) is of genus 0 too. Thus the field K(X(4)) is a rational function field over C. We find such a field generator $j_4$(z) = x(z)/y(z) (x(z) = $\theta$$_3$((equation omitted)), y(z) = $\theta$$_4$((equation omitted)) Jacobi theta functions). We also investigate the structures of the spaces $M_{k}$($\Gamma$(4)), $S_{k}$($\Gamma$(4)), M(equation omitted)((equation omitted)(4)) and S(equation omitted)((equation omitted)(4)) in terms of x(z) and y(z). As its application, we apply the above results to quadratic forms.rms.

  • PDF

기존 철근콘크리트 골조의 반복거동 예측을 위한 이력모델 (Hysteresis Model for the Cyclic Response of Existing Reinforced Concrete Frames)

  • 손주기;이창환
    • 한국공간구조학회논문집
    • /
    • 제20권3호
    • /
    • pp.81-89
    • /
    • 2020
  • As the damage caused by earthquakes gradually increases, seismic retrofitting for existing public facilities has been implemented in Korea. Several types of structural analysis methods can be used to evaluate the seismic performance of structures. Among them, for nonlinear dynamic analysis, the hysteresis model must be carefully applied because it can significantly affect the behavior. In order to find a hysteresis model that predicts rational behavior, this study compared the experimental results and analysis results of the existing non-seismic reinforced concrete frames. For energy dissipation, the results were close to the experimental values in the order of Pivot, Concrete, Degrading, and Takeda models. The Concrete model underestimated the energy dissipation due to excessive pinching. In contrast, the other ones except the Pivot model showed the opposite results with relatively little pinching. In the load-displacement curves, the experimental and analysis results tended to be more similar when the column axial force was applied to columns.

A Comparative Study of Twist Property in KSS Curves of Embedding Degree 16 and 18 from the Implementation Perspective

  • Khandaker, Md. Al-Amin;Park, Taehwan;Nogami, Yasuyuki;Kim, Howon
    • Journal of information and communication convergence engineering
    • /
    • 제15권2호
    • /
    • pp.97-103
    • /
    • 2017
  • Implementation of faster pairing calculation is the basis of efficient pairing-based cryptographic protocol implementation. Generally, pairing is a costly operation carried out over the extension field of degree $k{\geq}12$. But the twist property of the pairing friendly curve allows us to calculate pairing over the sub-field twisted curve, where the extension degree becomes k/d and twist degree d = 2, 3, 4, 6. The calculation cost is reduced substantially by twisting but it makes the discrete logarithm problem easier if the curve parameters are not carefully chosen. Therefore, this paper considers the most recent parameters setting presented by Barbulescu and Duquesne [1] for pairing-based cryptography; that are secure enough for 128-bit security level; to explicitly show the quartic twist (d = 4) and sextic twist (d = 6) mapping between the isomorphic rational point groups for KSS (Kachisa-Schaefer-Scott) curve of embedding degree k = 16 and k = 18, receptively. This paper also evaluates the performance enhancement of the obtained twisted mapping by comparing the elliptic curve scalar multiplications.

가상 공간 디자인을 위한 3차원 목표곡선을 이용한 곡면 변형 (Surface Deformation by using 3D Target Curve for Virtual Spatial Design)

  • 권정훈;이정인;채영호
    • 한국정보과학회논문지:소프트웨어및응용
    • /
    • 제33권10호
    • /
    • pp.868-876
    • /
    • 2006
  • 2차원 평면 입력을 통한 모델링에서는 입력 값을 3차원 데이타로 바꾸기 위한 기능과 메뉴들이 필요하지만 가상공간 디자인을 위한 3차원 입력 시스템은 입력 값을 곧바로 3차원 데이타로 변환될 수 있다. 하지만 3차원 입력시스템에서 효율적인 곡면 모델링 방법, 특히 곡면 변형 방법은 제안되지 않고 있다. 본 논문에서는 기존의 변형방법이 3차원 입력시스템에서 적용되었을 때 발생할 수 있는 문제점을 제시한다. 그리고 디자이너가 접근하기 쉬운 목표곡선을 이용한 변형을 제안한다. 이와 같은 3차원 목표곡선을 이용한 변형을 통해 디자이너가 보다 쉽게 3차원 입력시스템에 접근하여 가상공간 스케칭 및 디자인을 구현할 수 있다.