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|Title:||Improved dynamic structural analysis for linear and nonlinear systems|
|Doctoral Committee Chair(s):||Pecknold, David A.|
|Department / Program:||Civil and Environmental Engineering|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|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.
|Rights Information:||Copyright 1995 Chang, Shuenn-Yih|
|Date Available in IDEALS:||2011-05-07|
|Identifier in Online Catalog:||AAI9522089|
This item appears in the following Collection(s)
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Civil and Environmental Engineering