Variational motion design for adaptive structures

Abstract

In this thesis, a novel approach to support the design of motions for adaptive structures is presented and gradually developed: the so-called method of motion design. It is based on the observation that, depending on the control of the actuation, the same deformation state of a structure can be reached through various motion processes. The method of motion design allows to calculate optimal deformation paths with defined properties between the initial geometry and a given deformed end geometry of a structure in a formalized way. In order to motivate the efficiency of a movement and to make it mathematically quantifiable, the so-called cost of deformation is introduced as an exemplary target value based on the strain energy. By integration over the deformation path, the motion process is considered in its entirety in this optimization problem. The method of motion design is developed based on a variational formulation using the cost of deformation as underlying functional and the displacement field as the unknown function. One of the decisive features in this work is the discretization of the motion path, i.e., the deformation process. Due to the special structure of the functional with the integration of the strain energy, analytical sensitivities can be calculated by using quantities that are generally available in finite element software. The presented basic method is particularly well suited for the identification and design of kinematic and energy-minimal motion mechanisms, which emphasizes the potential for application to deployable shape changing structures. The motion design method is extended by the use of constraints such that the actuation can be prescribed, e.g., by actuator elements, or the entire motion can be stabilized. Finally, possibilities for enhancement of the motion design method and combinations with other methods to increase the efficiency of adaptive structures are investigated. They include a combination with shape optimization of the initial geometry, an integration within an actuator placement algorithm and variations of the underlying objective function.