Symbolic Finite Element Analysis for Parametric Studies
Robert W. Johnstone, M. Ash Parameswaran, Tatsujirô Shimizu · TechConnect Briefs · 2005
This paper presents the theory behind the development of a computer representation of symbolic expressions suitable for use in finite element analysis. This representation is used to replace standard floating-point calculations so that the result of the analysis, instead of being a numeric result, is an equation relating the design variables to system behaviour. Representations based on rational multivariate polynomials and rational multivariate orthogonal polynomials are discussed. Some preliminary results on the accuracy of our initial implementations are presented.