Statistical B-spline FEM for predicting effects of geometric uncertainty

Abstract

We address the dimensional analysis of ship structural parts by applying variational simulation using B-spline finite element analysis. The part geometry is defined by B-splines as is common in computer-aided design, and this geometry is then directly used in the variational analysis without model translations or remeshing. We show that the statistical distributions of geometrical imperfections in the parts can be modelled and simulated by statistical B-spline finite elements, as can the statistical correlations of part variations. Similarly, the mean and the variance of forces required to clamp or flatten plate and stiffener parts to the nominal positions can be determined. Thus, we are able to predict the statistical distribution of assembled shapes and stresses involved in assembling imperfect ship structural elements, without computationally expensive Monte Carlo simulation.