Novel PartStiff and PartFlex methods for modeling and solving without assembling: How can it be possible?

At LMSSC, Paris, March 25th 2024, 1.30 p.m.

K.C. Park
Professor Emeritus, Aerospace Mechanics Research Center (AMReC),
Ann and H. J. Smead Aerospace Engineering Sciences,
College of Engineering and Applied Science, University of Colorado, Boulder, USA

An initial outcome from this curiosity led us to develop a PartStiff (unassembled stiffness) method which has been successfully applied, in a proof-of-concept stage, to efficient implicit-explicit transient algorithms, new parallel solution algorithms, reduced-order modeling, structural health monitoring, and topology optimization, among others. We will first present the PartStiff method and its applications.

Pursuing my curiosity further, I have revisited the efficacies of the century-old force method in terms of unassembled context. This is because the force (flexibility) method was effectively abandoned in 1967 when NASA eliminated it from its further developments due to “the greater complexity of its mathematics and the greater density of its matrices” even though the force method was viewed as “more efficient for analyzing the effects of design changes”.

I am happy to present the PartFlex (unassembled flexibility) method as a dual of the PartStiff method. As expected, the PartFlex method is shown to alleviate the mathematical complexities of the classical force method and its flexibility matrix yields the same matrix profile as that of its dual PartStiff method while possessing the very telling advantage of efficiently analyzing the effects of design changes.

Applications of both the PartStiff and PartFlex method are illustrated for a variety of mechanics problems, including localized damage detection, reduced-order modeling(CMS), design modifications, topology optimization, data-driven NN modeling, efficient solution of large heterogeneous systems, among others.