Based on Hertz contact theory, a method to determine the parameters of Kelvin impact model for seismic pounding analysis of bridges is proposed. The impact stiffness of Kelvin model is determined by the ratio of maxim...Based on Hertz contact theory, a method to determine the parameters of Kelvin impact model for seismic pounding analysis of bridges is proposed. The impact stiffness of Kelvin model is determined by the ratio of maximum impact force to maximum contact deformation, which is calculated based on Hertz contact theory with considering the vibration effect. The restitution coefficient which has great influence on the damping coefficient of Kelvin impact model is investigated by numerical analysis. Numerical results indicate that the impact stiffness of Kelvin impact model increases with the increment of the Hertz contact stiffness, approaching velocity or the length ratio of short to long girders. Vibration effect has remarkable influence on the impact stiffness and cannot be neglected. The restitution coefficient decreases when approaching velocity increases or the length ratio of short girder to long girder decreasing. The practical ranges of impact stiffness and restitution coefficient are obtained as 3 × 10^8--6 × 10^8 N/m and 0.6-3.95 respectively.展开更多
Contact detection between interacting blocks is of great importance to discontinuity-based numerical methods, such as DDA, DEM, and NMM. A rigorous contact theory is a prerequisite to describing the interactions of mu...Contact detection between interacting blocks is of great importance to discontinuity-based numerical methods, such as DDA, DEM, and NMM. A rigorous contact theory is a prerequisite to describing the interactions of multiple blocks. Currently, the penalty method, in which mathematical springs with high stiffness values are employed, is always used to calculate the contact forces. High stiffness values may cause numerical oscillations and limit the time step. Furthermore, their values are difficult to identify. The intention of this study is to present a two-scale contact model for the calculation of forces between colliding blocks. In this new model, a calculation step taken from the moment of contact will be divided into two time stages: the free motion time stage and the contact time stage. Actually, these two time stages correspond to two real physical processes. Based on this, we present a new numerical model that is intended to be more precise and useful in calculating the contact forces without mathematical springs. The propagation of the elastic wave during collision is of a characteristic length, which determines the volume of material involved in the contact force calculation. In conventional contact models, this range is always regarded as the length of one element, which may lead to an inaccurate calculation of contact forces. In fact, the real scale of this range is smaller than the length of a single element, and subdivided elements, which are refined according to the characteristic length and are presented in the new contact model.展开更多
基金Supported by National Natural Science Foundation of China (No. 50578109)Tianjin Municipal Natural Science Foundation of China(No. 05YFGMGC10900)
文摘Based on Hertz contact theory, a method to determine the parameters of Kelvin impact model for seismic pounding analysis of bridges is proposed. The impact stiffness of Kelvin model is determined by the ratio of maximum impact force to maximum contact deformation, which is calculated based on Hertz contact theory with considering the vibration effect. The restitution coefficient which has great influence on the damping coefficient of Kelvin impact model is investigated by numerical analysis. Numerical results indicate that the impact stiffness of Kelvin impact model increases with the increment of the Hertz contact stiffness, approaching velocity or the length ratio of short to long girders. Vibration effect has remarkable influence on the impact stiffness and cannot be neglected. The restitution coefficient decreases when approaching velocity increases or the length ratio of short girder to long girder decreasing. The practical ranges of impact stiffness and restitution coefficient are obtained as 3 × 10^8--6 × 10^8 N/m and 0.6-3.95 respectively.
基金supported by the National Basic Research Program of China("973"Project)(Grant No.2015CB250903)the CAS Strategic Priority Research Program(B)(Grant No.XDB10030303)+1 种基金the National Key Technology Research and Development Program of the Ministry of Science and Technology of China(Grant No.2012BAK10B01)the Youth Science Fund of the National Natural Science Foundation of China(Grant No.11302230)
文摘Contact detection between interacting blocks is of great importance to discontinuity-based numerical methods, such as DDA, DEM, and NMM. A rigorous contact theory is a prerequisite to describing the interactions of multiple blocks. Currently, the penalty method, in which mathematical springs with high stiffness values are employed, is always used to calculate the contact forces. High stiffness values may cause numerical oscillations and limit the time step. Furthermore, their values are difficult to identify. The intention of this study is to present a two-scale contact model for the calculation of forces between colliding blocks. In this new model, a calculation step taken from the moment of contact will be divided into two time stages: the free motion time stage and the contact time stage. Actually, these two time stages correspond to two real physical processes. Based on this, we present a new numerical model that is intended to be more precise and useful in calculating the contact forces without mathematical springs. The propagation of the elastic wave during collision is of a characteristic length, which determines the volume of material involved in the contact force calculation. In conventional contact models, this range is always regarded as the length of one element, which may lead to an inaccurate calculation of contact forces. In fact, the real scale of this range is smaller than the length of a single element, and subdivided elements, which are refined according to the characteristic length and are presented in the new contact model.
