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Symbolic Finite Element Analysis for Parametric Studies

R.W. Johnstone, T. Shimizu and M. Parameswaran
Simon Fraser University, CA

finite element analysis, symbolic computational software, parametric analysis

In our paper, we will present a method of performing finite element analysis using a symbolic kernel. The representation of numbers used in analysis is symbolic expressions instead of floating point numbers. Unlike standard finite element analysis, the end product of symbolic finite element analysis is an equation [5]. We have developed a number of methods of measuring and limiting symbolic growth. We can thus use finite element methods to determine equations capable of predicting system parameters based on the design parameters. This allows us to perform symbolic FEA are much larger systems. Although the symbolic FEA does require more computational effort, the results of symbolic FEA are also considerably more useful. With the results in hand, design parameters can be changed and the results of the analysis computed with minimal effort. This situation contrasts sharply with traditional FEA methods, which requires the entire analysis to done. Such equations have many uses. In particular, they could speed multiple evaluations of similar models. This would aid many important in many types of analysis, such as probabilistic design studies (PDS), design optimization problems, and reduced order modelling (ROM).

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