Towards Bio-Inspired Topology Optimisation in Restricted Design Spaces: Study of Divergences in Structures with Equivalent Stiffness

Biological growth continuously adapts material distribution in response to mechanical stimuli, producing structures that are both lightweight and mechanically efficient. Inspired by this behaviour, this work extends a mechanostat-based topology optimisation framework to restricted (subspace) design domains, allowing structural evolution to be studied under progressively relaxed volume constraints. The proposed methodology is evaluated using two benchmark problems: a top-loaded cantilever beam and an MBB beam. For each case, the evolution of compliance, natural frequency and structural morphology is examined over a range of volume fractions, while representative designs are further assessed using three-dimensional finite element analyses. The results show that the optimisation process is path dependent, with different initial conditions producing distinct topologies that exhibit similar stiffness yet different dynamic responses. Restricting the design space is also found to influence solution fidelity, particularly for low initial volume fractions where exclusion regions limit the natural evolution of the structure. These observations indicate that biologically inspired growth laws can generate multiple mechanically viable designs from the same optimisation problem, providing additional flexibility for selecting structures according to both static and dynamic performance requirements.