Lu, H., Lee, T.U., Ma, J., Chen, D. and Xie, Y.M., 2023. Composite Structures, p.117305. [Link]
Functionally graded porous materials have superior properties such as high strength, low thermal conductivity and high energy absorption. More importantly, their density distribution can be customised to best suit different objectives, thus having a wide range of applications. With different manufacturing approaches, the geometry of functionally graded porous materials can be deterministic (e.g., lattice structure) or stochastic (e.g., metal foam). Whilst the design of the former has been extensively studied leveraging the long-established topology optimisation approach, the latter is rarely investigated despite its widespread use in industrial fields, such as aerospace and biomedical.
In this study, we propose a novel two-step topology optimisation framework to design 2D stochastic porous structures. In the first step, topology optimisation based on compliance minimisation (or stiffness maximisation) is carried out to obtain the homogenised material density distribution. In the second step, a new de-homogenisation approach is developed to transform the homogenised materials into stochastic porous structures. Several numerical examples are presented to demonstrate the effectiveness of the proposed approach. As a result of employing stochastic materials and the associated density constraint, the optimised porous structures demonstrate higher compliance compared to the optimised structures made of solid materials. Nevertheless, the results indicate that the difference in compliance values between the homogenised structures and de-homogenised porous structures is minor (i.e., less than 6.99%). Furthermore, it is observed that the structural stiffness is only minimally affected by the introduction of geometric stochasticity during de-homogenisation, with variations of less than 1.94%. Therefore, the developed topology optimisation is numerically robust. Various constraints have also been developed, enabling designers to choose structures with the desired stiffness and geometric complexity from a diverse range of novel designs.