• 제목/요약/키워드: modified direct iteration method

검색결과 3건 처리시간 0.018초

Numerical model for local corrosion of steel reinforcement in reinforced concrete structure

  • Chen, Xuandong;Zhang, Qing;Chen, Ping;Liang, Qiuqun
    • Computers and Concrete
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    • 제27권4호
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    • pp.385-393
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    • 2021
  • Reinforcement corrosion is the main cause of the durability failure of reinforced concrete (RC) structure. In this paper, a three-dimensional (3D) numerical model of macro-cell corrosion is established to reveal the corrosion mechanisms of steel reinforcement in RC structure. Modified Direct Iteration Method (MDIM) is employed to solve the system of partial differential equations for reinforcement corrosion. Through the sensitivity analysis of electrochemical parameters, it is found that the average corrosion current density is more sensitive to the change of cathodic Tafel slope and anodic equilibrium potential, compared with the other electrochemical parameters. Furthermore, both the anode-to-cathode (A/C) ratio and the anodic length have significant influences on the average corrosion current density, especially when A/C ratio is less than 0.5 and anodic length is less than 35 mm. More importantly, it is demonstrated that the corrosion rate of semi-circumferential corrosion is much larger than that of circumferential corrosion for the same A/C ratio value. The simulation results can give a unique insight into understanding the detailed electrochemical corrosion processes of steel reinforcement in RC structure for application in service life prediction of RC structures in actual civil engineer.

6절점 2차원 Isoparametric요소의 가우스적분점 수정에 관하여 -선형, 비선형의 정적 및 동적 굽힘해석- (On the Modification of Gauss Integral Point of 6 Node Two Dimensional Isoparametric Element -Linear and Nonlinear Static and Dynamic Bending Analyses-)

  • 김정운;정래훈;권영두
    • 대한기계학회논문집
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    • 제17권12호
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    • pp.3007-3019
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    • 1993
  • For the same configuration, the stiffness of 6-node two dimensional isoparametric is stiffer than that of 8-node two dimensional isoparametric element. This phenomenon may be called 'Relative Stiffness Stiffening Phenomenon.' In this paper, the relative stiffness stiffening phenomenon was studied, and could be corrected by modifying the position of Gauss integral points used in the numerical integration of the stiffness matrix. For the same deformation (bending) energy of 6-node and 8-node two dimensional isoparametric elements, Gauss integral points of 6-node element have to move closer, in comparison with those of 8-node element, in the case of numerical integration along the thickness direction.

Nonlinear free vibration and post-buckling of FG-CNTRC beams on nonlinear foundation

  • Shafiei, Hamed;Setoodeh, Ali Reza
    • Steel and Composite Structures
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    • 제24권1호
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    • pp.65-77
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    • 2017
  • The purpose of this research is to study the nonlinear free vibration and post-buckling analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams resting on a nonlinear elastic foundation. Uniformly and functionally graded distributions of single walled carbon nanotubes as reinforcing phase are considered in the polymeric matrix. The modified form of rule of mixture is used to estimate the material properties of CNTRC beams. The governing equations are derived employing Euler-Bernoulli beam theory along with energy method and Hamilton's principle. Applying von $K\acute{a}rm\acute{a}n's$ strain-displacement assumptions, the geometric nonlinearity is taken into consideration. The developed governing equations with quadratic and cubic nonlinearities are solved using variational iteration method (VIM) and the analytical expressions and numerical results are obtained for vibration and stability analysis of nanocomposite beams. The presented comparative results are indicative for the reliability, accuracy and fast convergence rate of the solution. Eventually, the effects of different parameters, such as foundation stiffness, volume fraction and distributions of carbon nanotubes, slenderness ratio, vibration amplitude, coefficients of elastic foundation and boundary conditions on the nonlinear frequencies, vibration response and post-buckling loads of FG-CNTRC beams are examined. The developed analytical solution provides direct insight into parametric studies of particular parameters of the problem.