Geometric misfitting in trusses and frames: an interval-based approach

Abstract

In this work, the issue of predicting structural behaviour in the presence of geometric uncertainty arising out of fabrication errors and/or thermal changes in trusses and frames is addressed. Geometric uncertainty is expressed as deviations of actual dimensions of system components from their corresponding nominal dimensions (misfitting) and is expressed in interval form. Such geometric uncertainty is converted into an equivalent nodal load uncertainty. The present work eliminates the element force overestimation resulting in the previous formulation of Muhanna et al. The mixed interval finite element formulation developed earlier by Rama Rao et al. is utilised to obtain sharp bounds to displacements and element forces in the presence of geometric, material and load uncertainties. The present work also computes an exact enclosure to the final system geometry. Results are illustrated in example problems. Dependency due to the presence of geometric uncertainty is eliminated using the M matrix approach developed earlier by Mullen and Muhanna.