A time integral formulation and algorithm for structural dynamics with nonlinear stiffness

被引:4
作者
Yu, Kaiping [1 ]
Zhao, Jie [1 ]
机构
[1] Harbin Inst Technol, Dept Astronaut Sci & Mech, Harbin 150001, Peoples R China
关键词
nonlinear structural dynamics; numerical algorithm; stability; overshoot;
D O I
10.1007/s10409-006-0025-6
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
A newly-developed numerical algorithm, which is called the new Generalized-a (G-a) method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-a method has undesired overshoot properties as for a class of alpha-method. In the present work, seven independent parameters are introduced into the single-step three-stage algorithmic formulations and the nonlinear internal force at every time interval is approximated by means of the generalized trapezoidal rule, and then the algorithm is implemented based on the finite difference theory. An analysis on the stability, accuracy, energy and overshoot properties of the proposed scheme is performed in the nonlinear regime. The values or the ranges of values of the seven independent parameters are determined in the analysis process. The computational results obtained by the new algorithm show that the displacement accuracy is of order two, and the acceleration can also be improved to a second order accuracy by a suitable choice of parameters. Obviously, the present algorithm is zero-stable, and the energy conservation or energy decay can be realized in the high-frequency range, which can be regarded as stable in an energy sense. The algorithmic overshoot can be completely avoided by using the new algorithm without any constraints with respect to the damping force and initial conditions.
引用
收藏
页码:479 / 485
页数:7
相关论文
共 20 条
[1]  
[Anonymous], AM SOC CIV ENG P 1
[2]  
Bathe KJ., 1976, NUMERICAL METHOD FIN
[3]   A TIME INTEGRATION ALGORITHM FOR STRUCTURAL DYNAMICS WITH IMPROVED NUMERICAL DISSIPATION - THE GENERALIZED-ALPHA METHOD [J].
CHUNG, J ;
HULBERT, GM .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1993, 60 (02) :371-375
[4]   A FAMILY OF SINGLE-STEP HOUBOLT TIME INTEGRATION ALGORITHMS FOR STRUCTURAL DYNAMICS [J].
CHUNG, JT ;
HULBERT, GM .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1994, 118 (1-2) :1-11
[5]   The analysis of the Generalized-α method for non-linear dynamic problems [J].
Erlicher, S ;
Bonaventura, L ;
Bursi, OS .
COMPUTATIONAL MECHANICS, 2002, 28 (02) :83-104
[6]   COLLOCATION, DISSIPATION AND OVERSHOOT FOR TIME INTEGRATION SCHEMES IN STRUCTURAL DYNAMICS [J].
HILBER, HM ;
HUGHES, TJR .
EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, 1978, 6 (01) :99-117
[7]   IMPROVED NUMERICAL DISSIPATION FOR TIME INTEGRATION ALGORITHMS IN STRUCTURAL DYNAMICS [J].
HILBER, HM ;
HUGHES, TJR ;
TAYLOR, RL .
EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, 1977, 5 (03) :283-292
[8]   PRACTICAL PERFORMANCE OF THE THETA-1-METHOD AND COMPARISON WITH OTHER DISSIPATIVE ALGORITHMS IN STRUCTURAL DYNAMICS [J].
HOFF, C ;
PAHL, PJ .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1988, 67 (01) :87-110
[9]   DEVELOPMENT OF AN IMPLICIT METHOD WITH NUMERICAL DISSIPATION FROM A GENERALIZED SINGLE-STEP ALGORITHM FOR STRUCTURAL DYNAMICS [J].
HOFF, C ;
PAHL, PJ .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1988, 67 (03) :367-385
[10]  
Hughes T. J. R., 1976, Computers and Structures, V6, P313, DOI 10.1016/0045-7949(76)90007-9