This work proposes a systematic topology optimization approach for simultaneously designing the morphing functionality and actuation in three-dimensional wing structures. The actuation was modeled by a linear-strain-based expansion in the actuation material. A three-phase material model was employed to represent structural and actuating materials and voids. To ensure both structural stiffness with respect to aerodynamic loading and morphing capabilities, the optimization problem was formulated to minimize structural compliance, while the morphing functionality was enforced by constraining a morphing error between the actual and target wing shape. Moreover, a feature-mapping approach was utilized to constrain and simplify the actuator geometries. A trailing edge wing section was designed to validate the proposed optimization approach. Numerical results demonstrated that three-dimensional optimized wing sections utilize a more advanced structural layout to enhance structural performance while keeping the morphing functionality better than two-dimensional wing ribs. The work presents the first step towards the systematic design of three-dimensional morphing wing sections.

This work presents an 808-line Matlab educational code for combined multi-scale topology optimisation and phasor-based dehomogenisation titled . The multi-scale formulation utilises homogenisation of optimal microstructures to facilitate efficient coarse-scale optimisation. Dehomogenisation allows for a high-resolution single-scale reconstruction of the optimised multi-scale structure, achieving minor losses in structural performance, at a fraction of the computational cost, compared to its large-scale topology optimisation counterpart. The presented code utilises stiffness optimal Rank-2 microstructures to minimise the compliance of a single-load case problem, subject to a volume fraction constraint. By exploiting the inherent efficiency benefits of the phasor-based dehomogenisation procedure, on-the-fly dehomogenisation to a single-scale structure is obtained. The presented code includes procedures for structural verification of the final dehomogenised structure by comparison to the multi-scale solution. The code is introduced in terms of the underlying theory and its major components, including examples and potential extensions, and can be downloaded from Github.

This work proposes a systematic topology optimization approach to simultaneously design the morphing functionality and actuation in three-dimensional wing structures. The actuation is assumed to be a linear strain-based expansion in the actuation material and a three-phase material model is employed to represent structural and actuating materials, and void. To ensure both structural stiffness with respect to aerodynamic loading and morphing capabilities, the optimization problem is formulated to minimize structural compliance while morphing functionality is enforced by constraining a morphing error between actual and target wing shape. Moreover, a feature mapping approach is utilized to constrain and simplify actuator geometries. A trailing edge wing section is designed to validate the proposed optimization approach. Numerical results demonstrate that three-dimensional optimized wing sections utilize a more advanced structural layout to enhance structural performance while keeping morphing functionality than two-dimensional wing ribs. The work presents the first step towards systematic design of three-dimensional morphing wing sections.

Homogenisation-based topology optimisation offers a computationally efficient approach to inverse design of 3D high-resolution lightweight mechanical structures. By considering a homogenised representation of periodic microstructures the optimisation can be applied on a coarser mesh, and the optimised multi-scale result allows for up-sampling to a single-scale geometry in a post-processing step termed dehomogenisation. Existing methods for performing 3D dehomogenisation are challenged by high computational complexity or, due to their global nature, a lack of robustness with respect to orientation singularity and discontinuity. Phasor noise is a compactly parameterised pattern-generating algorithm that has been proven to offer significant improvements for 2D dehomogenisation in terms of the trade-off between computational efficiency and solution quality. The representation of the design is continuous and periodic at each intermediate step of the dehomogenisation procedure. This maintains the computational advantage of the phasor noise formulation throughout the procedure, as well as ensures a finalised multi-scale design with appropriate length scale and thicknesses. The phasor-based formulation is based on spatial locations and distances, making it inherently mesh-independent. This paper extends the 2D phasor-based dehomogenisation procedure to 3D. Adaptions are required to improve performance for the more general case of 3D optimised results, where ensuring appropriate structural connectivity is especially addressed. Additionally, a novel method for introducing local infill in the dehomogenised design, improving the design process for additive manufacturing further, is presented. The proposed dehomogenisation procedure has been implemented in collaboration with the software company nTopology, using the implicit geometry kernel of the nTop software to exploit the implicit and continuous nature of the phasor noise framework.