Statistical methods in finite element analysis

Finite element analysis (FEA) is a commonly used tool within many areas of engineering and can provide useful information in structural analysis of mechanical systems. However, most analyses within the field of biomechanics usually take no account either of the wide variation in material properties and geometry that may occur in natural tissues or manufacturing imperfections in synthetic materials. This paper discusses two different methods of incorporating uncertainty in FE models. The first, Taguchi's robust parameter design, uses orthogonal matrices to determine how to vary the parameters in a series of FE models, and provides information on the sensitivity of a model to input parameters. The second, probabilistic analysis, enables the distribution of a response variable to be determined from the distributions of the input variables. The methods are demonstrated using a simple example of an FE model of a beam that is assigned material properties and geometry over a range similar to an orthopaedic fixation plate. In addition to showing how each method may be used on its own, we also show how computational effort may be minimised by first identifying the most important input variables before determining the effects of imprecision.