有横缝高拱坝非线性地震响应动接触模型
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摘要
本文针对有横缝高拱坝的非线性动摩擦接触问题,提出一种新的动接触算法——有限元混合法。该方法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,并且当考虑坝体中有多条横缝的情况,可以保持关于接触力的柔度矩阵的带状性和稀疏性,大大提高了计算效率。文中首先给出了有横缝高拱坝的非线性动摩擦接触问题的力学模型,推导得出了相应的有限元柔度方程,然后详细给出了迭代求解的步骤。最后,用本文方法对地震作用下某高拱坝横缝的张开与闭合过程进行了算例分析。
A new algorithm for dynamic contact problem——mixed finite element method is proposed for nonlinear dynamic contact problems of high arch dams with contraction joints.Based on the characteristic of local nonlinearity for this problem,the system of forces acting on the contactor is divided into two parts: external forces and contact forces.The displacements of contactor are chosen as the basic variables and the nodal contact forces in possible contact region are chosen as the iterated variables,so that the nonlinear iteration process is only limited in the possible contact surface.In this way,the sophisticated contact nonlinearity is shown by the variety of the contact forces.Moreover,in the case of multi-joints contact problem,the flexibility matrix is symmetric and sparse.Thus the iteractive procedure becomes easily to be carried out and much more economical.Firstly,the mechanical model of three-dimensional dynamic contact problems with friction and initial gaps is presented,its finite element compliance equations are obtained and the iteration process is then given in detail.At last,the opening and closing of the joints of a high arch dam is analyzed as an example according to the proposed method.
A new algorithm for dynamic contact problem——mixed finite element method is proposed for nonlinear dynamic contact problems of high arch dams with contraction joints.Based on the characteristic of local nonlinearity for this problem,the system of forces acting on the contactor is divided into two parts: external forces and contact forces.The displacements of contactor are chosen as the basic variables and the nodal contact forces in possible contact region are chosen as the iterated variables,so that the nonlinear iteration process is only limited in the possible contact surface.In this way,the sophisticated contact nonlinearity is shown by the variety of the contact forces.Moreover,in the case of multi-joints contact problem,the flexibility matrix is symmetric and sparse.Thus the iteractive procedure becomes easily to be carried out and much more economical.Firstly,the mechanical model of three-dimensional dynamic contact problems with friction and initial gaps is presented,its finite element compliance equations are obtained and the iteration process is then given in detail.At last,the opening and closing of the joints of a high arch dam is analyzed as an example according to the proposed method.
引文
[1]宋战平,李宁,陈飞熊,等.拱坝有缝坝体-坝基系统的非线性抗震分析[J].水利学报,2004,(6):33～40.
[2]林皋,胡志强,陈健云.考虑横缝影响的拱坝动力分析[J].世界地震工程与工程震动,2004,24(6):45～52.
[3]王水林,邓建辉.葛修润.改进的拉氏乘子法在接触摩擦问题中的应用[J].岩土工程学报,1998,20(5):64～67.
[4]Peric D,Owen D R J.Computational Model for 3-D contact problems with friction based on the penalty method[J].International Journal for Numeical Methods in Engineering,1992,35:1289～1309.
[5]雷晓燕,Swobode G,杜庆华.接触摩擦单元的理论及其应用[J].岩土工程学报,1994,16(3):23～32.
[6]Haug D,Saxce G,Frictionless contact of elastic bodies by finite element method and mathematical programmingtechnique[J].Computer Structures,1980,11:55～67.
[7]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.
[8]王勖成.有限单元法[M].北京:清华大学出版社,2003:666～671.
[9]Katona M G,Zienkiewicz.A unified set of signle-step algorithms,Part 3:the beta-m method,a generalization of theNewmark scheme[J].International Journal for Numerical Methods in Engineering,1985,21:1345～1359.
[10]林皋,胡志强.拱坝横缝影响及有效抗震措施研究[J].世界地震工程,2004,20(3):1～8.
[11]徐艳杰,张楚汉,王光纶,等.小湾拱坝模拟实际横缝间距的非线性反应分析[J].水利学报,2001,(4):68～74.
[2]林皋,胡志强,陈健云.考虑横缝影响的拱坝动力分析[J].世界地震工程与工程震动,2004,24(6):45～52.
[3]王水林,邓建辉.葛修润.改进的拉氏乘子法在接触摩擦问题中的应用[J].岩土工程学报,1998,20(5):64～67.
[4]Peric D,Owen D R J.Computational Model for 3-D contact problems with friction based on the penalty method[J].International Journal for Numeical Methods in Engineering,1992,35:1289～1309.
[5]雷晓燕,Swobode G,杜庆华.接触摩擦单元的理论及其应用[J].岩土工程学报,1994,16(3):23～32.
[6]Haug D,Saxce G,Frictionless contact of elastic bodies by finite element method and mathematical programmingtechnique[J].Computer Structures,1980,11:55～67.
[7]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.
[8]王勖成.有限单元法[M].北京:清华大学出版社,2003:666～671.
[9]Katona M G,Zienkiewicz.A unified set of signle-step algorithms,Part 3:the beta-m method,a generalization of theNewmark scheme[J].International Journal for Numerical Methods in Engineering,1985,21:1345～1359.
[10]林皋,胡志强.拱坝横缝影响及有效抗震措施研究[J].世界地震工程,2004,20(3):1～8.
[11]徐艳杰,张楚汉,王光纶,等.小湾拱坝模拟实际横缝间距的非线性反应分析[J].水利学报,2001,(4):68～74.
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