Optimization of the Spatially Graded Superelastic Lattice in a Morphing Structure
The aerodynamic efficiency in different flight conditions can be increased by morphing the wings. Morphing wings require high deformability and high strain recoverability, both of which can be achieved by using optimized structures made of additive manufactured superelastic lattice materials. To obtain an optimized structure of such a wing for certain flight conditions, a mechanical structural optimization of the corresponding trailing edge is presented.
The optimization of the wing is challenging due to the geometric nonlinearities resulting from the desired large geometric deformations as well as the highly nonlinear relationship between stress and strain of the superelastic material. The latter requires adequate material models to capture the response of the experimentally characterized parent material, which often deviates from the idealized constitutive relations. For the optimization, additional complexity arises from the large difference in scale between the desired structure and a single lattice cell.
The resulting multiscale optimization problem is addressed by first optimizing the design of the single lattice cell, where both shape and topology optimization methods are employed. The unit cell is then parametrized, to allow a grading over the whole structure. To handle the nonlinear structural response, the capabilities of the commercial tools ABAQUS 2023/Standard (Dassault Systemes Simulia Corp., Providence, RI, USA) and Tosca 2023 (Dassault Systemes Simulia Corp., Providence, RI, USA) are used. Further optimization of the macroscopic structure is limited in Tosca. However, the use of beam elements, which is often more efficient than the use of continuum elements, is an initial step toward a custom optimization process. To give adequate predictions using beam-based models, a user-defined uniaxial hypoelastic material model is implemented to account for the superelastic constitutive behavior. The results show that superelastic materials can be used in the optimization-driven design of parts of a morphing wing. Furthermore, the capabilities of analyzing the mechanical response of lattice materials by means of beam-based representations in combination with hypoleastic material models are investigated.
ACKNOWLEDGEMENT: The funding of the project ”Building Actions in Smart Aviation with Environmental Gains” by the European Union Programme Horizon Europe under grant agreement no. 101079091 is gratefully acknowledged. The computational results presented have been achieved using the Vienna Scientific Cluster (VSC).
