Improved dynamic structural analysis for linear and nonlinear systems
Chang, Shuenn-Yih
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/20737
Description
Title
Improved dynamic structural analysis for linear and nonlinear systems
Author(s)
Chang, Shuenn-Yih
Issue Date
1995
Doctoral Committee Chair(s)
Pecknold, David A.
Department of Study
Civil and Environmental Engineering
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Civil
Language
eng
Abstract
A new family of higher-order implicit, one-step integration algorithms has been developed and evaluated with respect to stability, accuracy, convergence, dissipation, dispersion and overshoot behavior. These algorithms have minimum order of accuracy two, and maximum order of accuracy four. In general, they have order of accuracy three. All the algorithms are unconditionally stable, do not overshoot in displacements or in velocities and possess desirable numerical dissipation which can be continuously controlled. In particular, these schemes possess better dissipative and dispersive characteristics than the commonly used second-order methods.
A useful characteristic of these algorithms is that they do not increase the dimension of implicit system, which has been a major disadvantage for the available higher-order integration methods. In addition, the time integration of external force has been used in the formulation of these algorithms to avoid numerical differentiation of the loading and also to avoid the use of a very small time step to capture any rapid change of dynamic loading.
The most important results of this study is the finding that the algorithm with x = 2 and y = 1/3 can provide an appropriate amplitude compensation effect for nonlinear systems. This amplitude compensation effect can effectively suppress the linearization errors which are introduced by the assumption that the structural properties remain constant during each time step.
The upper bounds on $\Delta\ t/T$ for accurate integration of single-degree-of-freedom nonlinear systems have been established for this algorithm. It is also verified that this algorithm will not cause any unbounded growth of amplitude when $\Delta\ t/T$ is greater than the upper bounds on $\Delta\ t/T$ which will result in accurate integration of nonlinear systems. Therefore, when the responses of a nonlinear system are dominated by the low-frequency modes only, the use of this algorithm will lead to accurate solutions if the dominant modes are integrated accurately.
Because of the excellent properties possessed by the algorithm with x = 2 and y = 1/3, especially the amplitude compensation effect and no growth of high-frequency response, a time step as large as two orders of magnitude greater than what is needed for the average acceleration method can be used, leading to a very significant saving of computational effort.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
