An Investigation on Shape Morphing by Modulus Variation: Forward Approach

Structural shape deformation, in its conventional way, includes applying forces to a fixed-compliance structure to deform it to certain shapes. Rather than addressing shape control in the established way (applying forces to elastically or plastically deform a structure), this work studies the use of shape morphing, which involves combining applied forces and local modulus changes. Specifically in this paper, a simply supported elastic beam that can exhibit variable compliance behavior is selected as the model. This study focuses on the forward approach of morphing, that is, determining possible beam shapes due to the applied force and modulus variability. The goal is to incorporate variable-modulus materials into a structure model and utilize the controllable modulus change to quantify the morphing of the structure with limited actuator numbers, locations, and force levels. The resulting morphed shapes are quantified in terms of various characteristic parameters. The study demonstrates that a larger, and in some cases nonintuitive, space of shapes becomes possible when modulus change is utilized, for the same set of applied forces. 1. Introduction The spatial orientation of a structure to one or several desired shapes may need to change in order to accommodate new geometry or stress requirements or to expand the performance capabilities and preserve energy metrics of the system. Traditional shape control methods have long been applied to a diverse range of structural materials, such as plastics, ceramics, metals, polymers, and composites whose mechanical properties are constant. For example, Reed et al. [1] developed a wing structure with capability of change in chord and wing’s planform area, resulting in optimizing flight efficiency throughout the entire mission. Others used telescopic [2] and inflatable wings [3] for shape control. These methods accomplished a change in a structure’s shape by continuously varying the magnitude, location, and number of actuation forces over the spatial domain to finally morph the system to the required geometry. Due to fixed material properties, the expected controlled shapes that arise from these methods are significantly limited to the actuators’ capabilities as well as the material’s range of stability. Lately, various adaptive materials have been extensively implemented in shape control applications. A group [4] developed a small-scale flying wing with active winglets via a distribution of piezo- or thermostrain actuators. Others [5] investigated the problem of determining the optimum piezoceramic actuator