考虑坝体与坝肩动力相互作用的坝肩稳定动接触降强算法
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摘要
针对拱坝坝体与坝肩动力相互作用的非线性动摩擦接触问题,提出了坝肩稳定分析的动接触降强算法。该方法在传统有限元动力时程降强法的基础上,将坝肩可能滑动块体、地基、坝体和库水作为一个统一体系进行动力分析计算,能更准确地考虑坝肩滑块体与坝体的动力相互作用,并且根据接触问题局部非线性的特点,将作用在接触体上的力系分解为外力和接触界面上的接触力,以接触体的位移为基本未知量,而以接触区域局部坐标系下的结点接触力为迭代变量,将非线性接触迭代收缩在可能接触面上进行,把复杂的摩擦接触非线性反映在接触力的变化上,使得迭代计算变得简单易行。
A new strength reduction method is proposed for reduction of the nonlinear dynamic contact strength under interaction between the body and abutments of arch dam.As an improvement over the traditional finite-element time-schedule strength reduction method,this new method integrates abutment sliding body,foundation,arch dam body and reservoir water into a single system,so that better accuracy of dynamic interaction can be obtained.To consider the local nonlinearity of contacts,the force on the contact surface is divided into an external part and a contact part,and the surface displacements are used as basic variables.Since the contact forces at nodes in the possible contact region are iterative variables,nonlinear iteration is limited to the possible contact surface.Thus the proposed method simplifies the sophisticated contact nonlinearity into a variety of contact forces,and makes the iteration easier and feasible.
A new strength reduction method is proposed for reduction of the nonlinear dynamic contact strength under interaction between the body and abutments of arch dam.As an improvement over the traditional finite-element time-schedule strength reduction method,this new method integrates abutment sliding body,foundation,arch dam body and reservoir water into a single system,so that better accuracy of dynamic interaction can be obtained.To consider the local nonlinearity of contacts,the force on the contact surface is divided into an external part and a contact part,and the surface displacements are used as basic variables.Since the contact forces at nodes in the possible contact region are iterative variables,nonlinear iteration is limited to the possible contact surface.Thus the proposed method simplifies the sophisticated contact nonlinearity into a variety of contact forces,and makes the iteration easier and feasible.
引文
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[2]李南生,周晶,林皋.有横缝高拱坝的动力接触模型及其数值解[J].水利学报,1999,(12):17～22.LI Nansheng,ZHOU Jing,LIN Gao.The dynamic contact model for high arch dams with ontraction joints and its numerical solution[J].Journal of Hydraulic Engineering,1999,(12):17～22.(in Chinese)
[3]赵兰浩.考虑坝体-库水-地基相互作用的有横缝拱坝地震响应分析[D].南京:河海大学,2006.ZHAO Lanhao.Seismic Analysis of Arch Dams with Contraction Joints and Dam-water-foundation Interaction[D].Nanjing:HohaiUniversity,2006.(in Chinese)
[4]赵兰浩,李同春,牛志伟.有横缝高拱坝非线性地震响应动接触模型[J].水力发电学报,2007,26(4):91～95.ZHAO Lanhao,LI Tongchun,NIU Zhiwei.The dynamic contact model of nonlinear seismic response of high arch dams withcontraction joints[J].Journal of Hydroelectric Engineering,2007,26(4):91～95.(in Chinese)
[5]Lysmer J,Kulemeyer R L.Finite Dynamic Model for Infinite Media[J].J.Engrg.Mech.Div,ASCE,1969,95:859～877.
[6]Clayton R,Engquist B.Absorbing Boundary Conditions for Acoustic and Elastic Wave Equations[J].Bull.Seism.Soc.Amer.,1977,76:1529～1540.
[7]Clayton R,Engquist B.Absorbing Boundary Conditions for Wave-Equation Migration[J].Geophysics,1980,45:895～904.
[8]廖振鹏,黄孔亮,杨柏坡.暂态波透射边界[J].中国科学(A辑),1984,26(6):50～56.LIAO Zhenpeng,HUANG Kongliang,YANG Baipo.Transient wave transmission boundary[J].China Science(A album),1984,26(6):50～56.(in Chinese)
[9]Deeks A J,Randolph M F.Axisymmetric Time-domain Transmitting Boundaries[J].Journal of Engineering Mechanics,1994,120(1):25～42.
[10]刘晶波,吕彦东.结构-地基动力相互作用问题分析的一种直接方法[J].土木工程学报,1998,31(3):55～64.LIU Jingbo,Lu Yandong.A Diect method for analysis of dynamic soil-structure interaction[J].China Civil Engineering Journal,1998,31(3):55～64.(in Chinese)
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