Numerical Integration of Second Order Differential—Algebraic Systems in Flexible Mechanism Dynamics

This paper studies second order accurate methods to numerically time-integrate the equations of motion for flexible mechanism dynamics. The aspects of stability, accuracy, conditioning of equations and time step control are discussed for the implicit scheme of Hilber, Hughes and Taylor (HHT).

[1]  Nathan M. Newmark,et al.  A Method of Computation for Structural Dynamics , 1959 .

[2]  J. Baumgarte Stabilization of constraints and integrals of motion in dynamical systems , 1972 .

[3]  L. Shampine,et al.  Computer solution of ordinary differential equations : the initial value problem , 1975 .

[4]  J. Z. Zhu,et al.  The finite element method , 1977 .

[5]  Thomas J. R. Hughes,et al.  Improved numerical dissipation for time integration algorithms in structural dynamics , 1977 .

[6]  T. Hughes,et al.  Collocation, dissipation and [overshoot] for time integration schemes in structural dynamics , 1978 .

[7]  O. C. Zienkiewicz,et al.  An alpha modification of Newmark's method , 1980 .

[8]  D. Arnold,et al.  Computer Solution of Ordinary Differential Equations. , 1981 .

[9]  W. L. Wood,et al.  A unified set of single step algorithms. Part 1: General formulation and applications , 1984 .

[10]  C. W. Gear,et al.  Differential-Algebraic Equations , 1984 .

[11]  C. W. Gear,et al.  ODE METHODS FOR THE SOLUTION OF DIFFERENTIAL/ALGEBRAIC SYSTEMS , 1984 .

[12]  E. Haug Computer Aided Analysis and Optimization of Mechanical System Dynamics , 1984 .

[13]  F. R. Gantmakher The Theory of Matrices , 1984 .

[14]  Per Lötstedt,et al.  Numerical solution of nonlinear differential equations with algebraic constraints I: Convergence results for backward differentiation formulas , 1986 .

[15]  Per Lötstedt,et al.  Numerical solution of nonlinear differential equations with algebraic contraints II: practical implications , 1986 .

[16]  I. Gladwell,et al.  Variable-order variable-step algorithms for second-order systems. Part 2: The codes , 1988 .

[17]  P. J. Pahl,et al.  Development of an implicit method with numerical dissipation from a generalized ingle-step algorithm for structural dynamics , 1988 .

[18]  Sang H. Lee,et al.  Expedient implicit integration with adaptive time stepping algorithm for nonlinear transient analysis , 1990 .

[19]  Yi Min Xie,et al.  A simple error estimator and adaptive time stepping procedure for dynamic analysis , 1991 .

[20]  J. C. Simo,et al.  Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum , 1991 .

[21]  J. C. Simo,et al.  Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics , 1992 .

[22]  A. Cardona,et al.  Integrador temporal de paso variable para análisis dinámico de estructuras y mecanismos , 1992 .

[23]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.