Shapes & DOF: on the use of modal concepts in the context of parametric non-linear studies

Abstract

Physical responses tend to lie within restricted subspaces even for parametric problems. For a given subspace, the choice of a basis defines Degree Of Freedom (DOF) and this choice may give interesting meaning to the associated amplitudes. Classical modal analysis builds subspaces combining modeshapes and static responses. Parametric loads for non-linear, damped, variable, ... structures are discussed to extend the theory and illustrated for test and simulation cases. Challenges in shape extraction and basis generation techniques are then detailed. Introducing the ability to manipulate models with variable junction properties, component material and geometry, load and operating conditions, ... opens new questions on the quantification and tracking of changes and objectives throughout design exploration. The definition of a reference linear system and the use of global and/or local modal DOF are shown to provide an interesting perspective.