The determination and enhancement of compliant modes for actuation in structural assemblies

Abstract

Linear algebra methods for determining modes of kinematic and static indeter- minacy in jointed frames are extended to reveal modes of compliance in oth- erwise rigid assemblies. These modes are extracted from a structural model, based on nite elements, via a singular value decomposition and yield the ways in which a structure can be most easily deformed. This modal approach also allows for the formulation of a reduced-order structural model, whereby relevant modes are selected and used as the basis for the optimisation of a complaint structure. The method detailed is shown to be a useful design tool, demon- strated by its application to a structure based on the Kagome lattice geometry. For certain frameworks, rst order e ects produce tightening under actuation. As a result, a scheme to adjust the modes to take nonlinear e ects into account is also given.