Constrained motion design with distinct actuators and motion stabilization

Abstract

The design of adaptive structures is one method to improve sustainability of buildings. Adaptive structures are able to adapt to different loading and environmental conditions or to changing requirements by either small or large shape changes. In the latter case, also the mechanics and properties of the deformation process play a role for the structure's energy efficiency. The method of variational motion design, previously developed in the group of the authors, allows to identify deformation paths between two given geometrical configurations that are optimal with respect to a defined quality function. In a preliminary, academic setting this method assumes that every single degree of freedom is accessible to arbitrary external actuation forces that realize the optimized motion. These (nodal) forces can be recovered a posteriori. The present contribution deals with an extension of the method of motion design by the constraint that the motion is to be realized by a predefined set of actuation forces. These can be either external forces or prescribed length chances of discrete, internal actuator elements. As an additional constraint, static stability of each intermediate configuration during the motion is taken into account. It can be accomplished by enforcing a positive determinant of the stiffness matrix.

Motion Design with Efficient Actuator Placement for Adaptive Structures that Perform Large Deformations

“…In such cases, it is possible to formulate suitable constraints so that the motion is controlled through a prescribed number of internal or external actuators. This approach has been presented in Sachse et al (2021) and it is summarized in the following.…”

“…In addition to external actuation, which is modeled through external point forces, also internal actuation is considered by using linear actuators installed in series with structural elements (Sachse et al, 2021). An actuator element formulation is employed that is based on a bar element (tension/ compression) but includes an additional parameter for the length change.…”

“…This example has shown that through the inverse greedy algorithm it is possible to identify the location of external actuation forces to perform an efficient motion between two prescribed geometries. This way, it is possible to further reduce the integrated strain energy compared to that required for a motion obtained with a predefined set of actuation force locations (as in Sachse et al, 2021).…”

“…In this publication, heuristic algorithms for actuator placement are combined with an existing method for motion design presented in Sachse and Bischoff (2020) and further extended in Sachse et al (2021). This method produces optimal deformation paths between two prescribed geometric configurations that might differ significantly from each other to meet varying demands during service.…”

“…This limitation has been surpassed by adding suitable constraints to the motion design formulation so that resulting deformation paths can be realized through a specific number of external or internal actuators. The constrained motion design formulation is given in Sachse et al (2021) and is summarized in Motion Design of Structures With Constraints of this paper for completeness. A method for optimal placement of external actuation forces to control the structure into required deformation paths is given in Motion Through External Actuation.…”