Topology optimisation with an adaptive design domain
Creators: name: Rong, Yi
Publisher: name: RMIT University
Year: 2024
Subjects: classificationCode: 400510
subject: Structural engineering

description: Topology optimisation has undergone tremendous development in the past decades. In the conventional optimisation techniques, the design space is usually fixed and predefined. In this thesis, a subdomain-based method, named the adaptive design domain (ADD) method, is proposed to optimise structures with an adaptive design space. Through a systematic study, this method is established for both engineering structural design and biomechanical morphogenesis. The thesis consists of four research components. First, the ADD method is developed based on the bi-directional evolutionary structural optimisation (BESO) technique. In the ADD method, the initial design domain is divided into a certain number of subdomains. Different evolution strategies are proposed for updating the design space.

In the second research component, the ADD method is used for engineering structural design. In this application, the evolution of the subdomains depends on their efficiency. Through the automatic, flexible and intelligent adaptation of the design domain, the ADD method is capable of generating diverse high-performance designs with distinctly different topologies. Several represented examples are provided to demonstrate the effectiveness of the ADD method. The results show that, compared with conventional approaches, the ADD method can improve the structural performance substantially by optimising the layout of material while reshaping the design domain. In addition, the loads and boundary conditions can also be simultaneously updated along with the design domain evolution.

In the third research component, the ADD method is used for biomechanical morphogenesis. In past centuries, the growth of plants has attracted extensive attention from scientists. However, there still remains a challenge to quantitatively decipher the biomechanical mechanisms underlying the morphological evolution of plant organs. The ADD method is applied to the simulation of the growth of plant roots. The taproot and the fibrous systems are selected as two typical root systems for the present study. It is found that both systems tend to maximise the transport efficiency of water and nutrients. The evolution of the subdomains depends on the coupling effects of biomechanical and environmental factors. According to the simulations, the lateral roots in the taproot systems develop hierarchically branched layouts from the main roots, while the growth directions of root caps are regulated by geotropism, hydrotropism and growth inertia. The thickness and concentration of roots depend on the growth history, and root hairs are generated to promote water and nutrient absorption. These results are consistent with our experimental observations. This research component not only helps understand the topological formation of root systems, but also provides a quantitative tool for exploring the structure–property–function interrelations of living systems.

In the fourth research component, a subdomain-based parallel strategy is developed to improve the efficiency of the ADD method. In this strategy, matrix calculation is used to calculate weight functions in each subdomain efficiently. Besides, the calculations in multiple subdomains can be executed simultaneously by multiprocessors, which makes the most of the computing resources. This strategy is integrated into an efficient and compact Python code, which can be used for a design domain with an arbitrary shape. Through comparisons with the previous topology optimisation codes, the proposed strategy is shown to have the advantages of higher efficiency, better flexibility and simpler implementation. Therefore, this parallel strategy is used in the second and third components in this thesis.

In summary, this thesis has established an effective, flexible and efficient optimisation method with an adaptive design space. The main contributions of this thesis are outlined below. First, the ADD method is developed based on the BESO technique. Second, the ADD method is successfully implemented into engineering structural designs, where high-performance structures can be achieved. Third, a trans-disciplinary computational framework for plant root growth has been developed based on the ADD method. Various taproot and fibrous root systems can be simulated and the corresponding underlying biomechanisms are revealed. Finally, a simple parallel strategy is developed to improve the efficiency of both the ADD method and general three-dimensional topology optimisation.