Derivation of a superelement with deformable interfaces – applied to model flexure joint

Design and optimization, as well as real time control, of flexure mechanisms require efficient but accurate models. The flexures can be modelled using beam elements and the frame parts can be modelled using superelements. Such a superelement efficiently models arbitrarily shaped bodies by few coordinates, using models obtained by model order reduction. The interfaces between the frame parts and the flexures often experience considerable deformation which affects the stiffness. To define the interface deformation in a reduced order model, this paper derives a multipoint constraint formulation, which relates the nodes on the deformable interface surface of a finite element model to a few coordinates. The multipoint constraints are imposed using a combination of the Lagrange multiplier method and master–slave elimination for efficient model order reduction. The resulting reduced order models are used in the generalized-strain multi-node superelement (GMS) that was defined in (Dwarshuis et al. in Multibody Syst. Dyn. 56(4):367–399, 2022). The interface deformations can be coupled to the cross-sectional deformation of higher order beam elements (i.e. beam elements of which the deformation of the cross-sections is explicitly taken into account). This paper applies this technique to model flexure joints, where the flexures are modelled with beam elements, and the frame components and critical connections using the GMS. This approach gives generally over 94% accurate stiffness, compared to nonlinear finite element models. The errors were often more than 50% lower than errors of models which only contain beam elements.