Multivariable Analysis using Isoparametric Finite Elements

Abstract

A new technique for multivariable analysis of empirical data, based on the isoparametric formulation commonly used with the finite element method, is described. Traditional two- and three-dimensional isoparametric shape functions have been extended for use in the interpolation and extrapolation of higher-order multivariable functions, based on a set of known data points. Elements are formed to make predictions by choosing groups of nodes (known data points) close to the point in the function space where the prediction is required. The proposed model was tested by making predictions based on a set of hypervelocity impact data with four independent variables. For comparison, the same predictions were also made using a linear least-squares approach. Similar predictions were obtained from both techniques.