Constrained motion design with distinct actuators and motion stabilization

TL;DR

This paper extends variational motion design for adaptive structures by incorporating predefined actuation forces and ensuring static stability throughout the deformation process, enhancing energy efficiency and control.

Contribution

It introduces a method to design deformation paths using specific actuators while maintaining static stability at all intermediate steps.

Findings

Incorporates actuator constraints into motion design.

Ensures static stability via stiffness matrix positivity.

Applicable to adaptive, energy-efficient structures.

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.