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numerical characteristics of the full operator hybrid simulation method

Earthquake Engineering and Engineering Vibration 2011年第3期10卷 453-463页

作者： Chung-Chan Hung Yong-Song Chen Department of Civil Engineering Central University （NCU） Chinese Taipei Department of Mechanical Engineering Chung Cheng University （NCCU） Chinese Taipei

The full operator method （FOM） has been proposed to overcome some of the shortcomings of the commonly used operator splitting method （OSM）. In particular, the FOM is improved by increasing the accuracy of both the predictor and corrector using the estimated tangent stiffness of the tested structure. The numerical characteristics of the FOM, including stability and accuracy, are investigated in this study. It is shown that FOM is conditionally stable. The stability and accuracy characteristics are dependent on the accuracy of the estimated tangent stiffness and the parameters associated with the acceleration variation in the time-stepping integration method. Mass-spring systems with different types of nonlinearity, including hardening, stiffening, and softening behavior, are used to evaluate the performance of the FOM. It is found that the FOM can capture these types of nonlinearity with satisfactory accuracy. Using a prototype 12-story composite coupled wall system, the influences of the strong nonlinearity of the system as well as the displacement control errors from hydraulic actuators on the performance of the FOM are explored. The results show that the FOM is capable of generating reasonably accurate results despite the presence of strong structural nonlinearity and displacement control errors.

关键词： hybrid simulation tangent stiffness numerical characteristic composite coupled wall system collapse behavior nonlinear behavior

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Matrix description of differential relations of moment functions in structural reliability sensitivity analysis

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Applied Mathematics and Mechanics(English Edition) 2017年第1期38卷 57-72页

作者： Tianxiao ZHANG Department of Mechanical and Industrial Engineering University of Illinois at ChicagoIllinois 60607-7022U.S.A.

In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessary. Based on that, the structural system reliability is analyzed with a fourth-order moment method. The reliability sensitivity is required to conduct the differential operation of the numerical characteristic functions. A reliability sensitivity analysis formula is then derived in combination with the relation of the differential operation. Based on the matrix theory and Kronecker algebra, this paper systematically derives a matrix expression of the first four moments of the state functions, and establishes the matrix relation between the first four moments of the state functions and those of the basic random variables. On this basis, a differential operation formula of the first four moments of the state functions is further derived against the first four moments of the basic random variables. The vector relation between the state functions and the multidimensional basic random variables is described by means of the matrix operation to extend the operation method. Finally, a concise and intuitive formula is obtained to explore the inherent essential relation between the numerical characteristics of the state functions and those of the basic random variables, leading to a universal equation for the two kinds of numerical characteristics.

关键词： structural system reliability analysis state function numerical characteristic matrix description Kronecker product functional differential reliability sensitivity

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