New Practical Approach to Nonlinear Dynamic Analysis of Structures: Refinement of Newmark’s and Wilson’s Classical Methods
Publication: Practice Periodical on Structural Design and Construction
Volume 17, Issue 1
Abstract
This paper presents a new method for direct time integration of nonlinear structural dynamic problems. In the proposed method, the order of time integration scheme is higher than the conventional Newmark’s family of methods. This method assumes second-order variation of the acceleration at each time step. Two variable parameters are used to increase the stability and accuracy of the method. The result obtained from this new higher-order method is compared with two implicit methods, namely the Wilson- and the Newmark’s average acceleration methods. The proposed method is an alternative quick method that can be written using matrix laboratory (MATLAB) for checking results from a more refined analysis or for a quick calculation with adequate accuracy.
Get full access to this article
View all available purchase options and get full access to this article.
References
Bathe, K. J. (1996). Finite element procedures, Prentice-Hall, Englewood Cliffs, NJ.
Belytschko, T., Liu, W. K., and Moran, B. (2000). Nonlinear finite elements for continua and structures, 3rd Ed., Wiley, Chichester, U.K.
Bert, C. W., and Striklin, J. D. (1988). “Comparative evaluation of six different numerical integration methods for non-linear dynamic systems.” J. Sound Vib., 127(2), 221–229.
Chen, S., Hansen, J., and Tortorelli, D. (2000). “Unconditionally energy stable implicit time integration: Application to multibody system analysis and design.” Int. J. Numer. Methods Eng., 48(6), 791–822.
Chopra, A. (2007). Dynamics of structures: Theory and applications to earthquake engineering, 3rd Ed., Prentice-Hall, Upper Saddle River, NJ.
Clough, R. W., and Penzien, J. (1983). Dynamics of structures, McGraw Hill, New York.
Crisfield, M. A. (1997). Non-linear finite element analysis of solids and structures, Vol. 2, Wiley, New York.
Hughes, T. J. R., and Belytschko, T. (1983). “A précis of developments in computational methods for transient analysis.” J. Appl. Mech., 50(4b), 1033–1041.
Humar, J. L. (1990). Dynamics of structures, Prentice-Hall, Englewood Cliffs, NJ.
Newmark, N. M. (1959). “A method of computation for structural dynamics.” J. Engrg. Mech. Div., 85(3), 67–94.
Park, K. C. (1977). “Practical aspects of numerical time integration.” Comput. Struct., 7(3), 343–353.
Paz, M. (1997). Structural dynamics: Theory and computation, 4th Ed., Chapman & Hall, New York.
Subbaraj, K., and Dokainish, M. A. (1989). “A survey of direct time integration methods in computational structural dynamics. II: Implicit methods.” Comput. Struct., 32(6), 1387–1401.
Wilson, E. L., Farhoomand, I., and Bathe, K. J. (1972). “Nonlinear dynamic analysis of complex structures.” Int. J. Earthquake Eng. Struct. Dyn., 1(3), 241–252.
Information & Authors
Information
Published In
Practice Periodical on Structural Design and Construction
Volume 17 • Issue 1 • February 2012
Pages: 30 - 34
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Oct 8, 2010
Accepted: Mar 29, 2011
Published online: Mar 31, 2011
Published in print: Feb 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.