Algorithms by Design: Part I—On the Hidden Point Collocation Within LMS Methods and Implications for Nonlinear Dynamics Applications

REFERENCES

• Masuri , S. , Hoitink , A. , Zhou , X. and Tamma , K. K. “ Algorithms by Design: Part II—A Novel Normalized Time Weighted Residual Methodology and Design Leading to a Family of Symplectic-Momentum Conserving Algorithms for Nonlinear Structural Dynamics ” . In International Journal for Computational Methods in Science and Engineering in press
   Google Scholar
• Masuri , S. , Hoitink , A. , Zhou , X. and Tamma , K. K. “ Algorithms by Design: Part III—A Novel Normalized Time Weighted Residual Methodology and Design of Optimal Symplectic-Momentum Based Controllable Numerical Dissipative Algorithms for Nonlinear Structural Dynamics ” . In International Journal for Computational Methods in Science and Engineering in press
   Google Scholar
• Zhou , X. and Tamma , K. K. 2004 . Design, Analysis, and Synthesis of Generalized Single Step Single Solve and Optimal Algorithms for Structural Dynamics . International Journal for Numerical Methods in Engineering , vol. 59 : 597 – 668 .
   Web of Science ®Google Scholar
• Zhou , X. and Tamma , K. K. 2006 . Algorithms by Design with Illustrations to Solid and Structural Mechanics/Dynamics . International Journal for Numerical Methods in Engineering , vol. 66 : 1738 – 1790 .
   Web of Science ®Google Scholar
• Zhou , X. and Tamma , K. K. 2004 . A New Unified Theory Underlying Time Dependent Linear First-Order Systems: A Prelude to Algorithms by Design . International Journal for Numerical Methods in Engineering , vol. 60 : 1699 – 1740 .
   Web of Science ®Google Scholar
• Newmark , N. M. 1959 . A Method of Computation for Structural Dynamics . Journal for American Society of Civil Engineers , vol. 1 : 67 – 94 .
   Google Scholar
• Tamma , K. K. and Namburu , R. R. 1990 . Applicability and Evaluation of An Implicit Self-Starting Unconditionally Stable Methodology for Dynamics of Structures . Computers and Structures , vol. 34 : 835 – 842 .
   Web of Science ®Google Scholar
• Hilber , H. M. 1977 . Analysis and Design of Numerical Integration Methods in Structural Dynamics , PhD thesis Berkeley , California : University of California at Berkeley, College of Engineering, University of California .
   Google Scholar
• Wood , W. L. , Bossak , M. and Zienkiewic , O. C. 1980 . An Alpha Modification of Newmark's Method . International Journal for Numerical Methods in Engineering , vol. 15 : 1562 – 1566 .
   Web of Science ®Google Scholar
• Shao , H. P. and Cai , C. W. The Direct Integration Three-Parameters Optimal Schemes for Structural Dynamics . Proceeding of the International Conference: Machine Dynamics and Engineering Applications . pp. C16 – C20 . Xi'an , , China : Xi'an Jiaotong University Press .
   Google Scholar
• Erlicher , S. , Bonaventura , L. and Bursi , O. S. 2002 . The Analysis of the Generalized-α Method for Nonlinear Dynamic Problems . Computational Mechanics , vol. 28 : 83 – 104 .
   Web of Science ®Google Scholar
• Hoitink , A. , Masuri , S. , Zhou , X. and Tamma , K. K. “ On the Precise Evaluation of Acceleration Computations for General Structural Dynamic Applications: Issues and Noteworthy Perspectives ” . In Communications in Numerical Methods in Engineering (In Review)
   Google Scholar
• Tamma , K. K. , Zhou , X. and Sha , D. 2000 . The Time Dimension: A Theory of Development/Evolution, Classification, Characterization and Design of Computational Algorithms for Transient/Dynamic Applications . Archives in Computational Mechanics , vol. 7 ( 2 ) : 67 – 290 .
   Web of Science ®Google Scholar
• Tamma , K. K. , Zhou , X. and Sha , D. 2001 . A Theory of Development and Design of Generalized Integration Operators for Computational Structural Dynamics . International Journal of Numerical Methods in Engineering , vol. 50 : 1619 – 1664 .
   Web of Science ®Google Scholar
• Hilber , H. M. , Hughes , T. J. R. and Taylor , R. L. 1977 . Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics . Earthquake Engineering and Structural Dynamics , vol. 5 : 283 – 292 .
   Web of Science ®Google Scholar
• Leontiev , V. A. 2007 . Extension of LMS formulations for L-Stable Optimal Integration Methods with U0-V0 Overshoot Properties in Structural Dynamics: The Level-Symmetric (LS) Integration Methods . International Journal for Numerical Methods in Engineering , vol. 71 : 1598 – 1632 .
   Web of Science ®Google Scholar
• Chung , J. and Hulbert , G. 1993 . A Time Integration Method for Structural Dynamics With Improved Numerical Dissipation: The Generalized α-Method . Journal of Applied Mechanics , vol. 30 : 371 – 375 .
   Google Scholar
• Masuri , S. , Hoitink , A. , Zhou , X. and Tamma , K. K. Algorithms by Design: A Novel Normalized Time Weighted Residual Methodology and Design Leading to a Family of Energy-Momentum Conserving Algorithms for Nonlinear Structural Dynamics . International Journal of Numerical Methods in Engineering , (In Review)
   Google Scholar
• Masuri , S. , Hoitink , A. , Zhou , X. and Tamma , K. K. Algorithms by Design: Optimal Energy-Momentum Based Controllable Numerical Dissipative Schemes in the Sense of Linear Multi-Step (LMS) Methods for Nonlinear Structural Dynamics . Computer Methods in Applied Mechanics and Engineering , (In Review)
   Google Scholar
• Kuhl , K. and Crisfield , M. 1999 . Energy-Conserving and Decaying Algorithms in Non-linear Structural Dynamics . International Journal for Numerical Methods in Engineering , vol. 45 : 569 – 599 .
   Web of Science ®Google Scholar