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An Application of Space and Time Finite Element Method for Two-Dimensional Transient Vibration  

Kim, Chi-Kyung (Department of Safety Engineering, University of Incheon)
Publication Information
Journal of the Korean Society of Safety / v.21, no.2, 2006 , pp. 143-149 More about this Journal
Abstract
This paper deals with the space-time finite element analysis of two-dimensional vibration problem with a single variable. The method of space-time finite elements enables the simpler solution than the usual finite element analysis with discretization in space only. We present a discretization technique in which finite element approximations are used in time and space simultaneously for a relatively large time period. The weighted residual process is used to formulate a finite element method for a space-time domain. A stability problem is described and some investigations for chosen type of rectangular space-time finite elements are carried out. Instability is caused by a too large time step of successive time steps in the traditional time-dependent problems. It has been shown that the numerical stability of time-stepping on the larger time steps is quite good. The unstructured space-time finite element not only overcomes the shortcomings of the stability in the traditional numerical methods, but it is also endowed with the features of an effective computational technique. Some numerical examples have been presented to illustrate the efficiency of the described method.
Keywords
space-time finite element; weighted residual; vibration; stability; unstructured;
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