Different from the way we have been looking in the past at developments encompassing
linear and nonlinear dynamics applications via time stepping methods, and
significantly different from the manner in which past developments have attempted to
explain and/or justify the algorithms and their design, this is the first time we provide
clear and concise advances to the field. The research and subsequent developments
address: 1) How to properly integrate the equations of motion and the accurate treatment
of the underlying time levels at which the computations should occur, 2) How
to precisely conduct acceleration computations for general nonlinear dynamic situations
and the significance of failure to follow the present propositions, and 3) Proof
of concept strategies and studies to enable long term nonlinear dynamics simulations
for conservative systems such that the approaches foster completion of analysis to the
desired time duration of interest. All these are described in the context of illustrations
to the class of LMS methods as an example to simply demonstrate the basic ideas.
The proposed results help achieve required order of time accuracy of computational
algorithms, required order of accuracy of acceleration fields, and foster long term
dynamics of stiff nonlinear dynamics applications. Numerous numerical illustrations
demonstrate the proposed developments, therein provide significant advances to the
field of computational structural dynamics.
University of Minnesota Master of Science thesis. November 2009. Major: Mechanical Engineering. Advisor: Dr. K. Tamma. 1 computer file (PDF); xi, 263 pages.
Hoitink, Andrew J..
Investigations Encompassing the Equations of Motion and Proper and Accurate Treatment of Algorithmic Variables: Computational Structural Dynamics and Stiff Systems.
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