Discretization and Connectivity Sensitivity of Movable-Node Truss Layout Optimization

Introduction: The GRAND procedure for ground-structure analysis and design of truss layouts generates candidate members between fixed nodal positions and solves a minimum volume linear-programming problem. This study evaluates a movable-node extension in which node positions are varied within predefined cells, while candidate member generation and the linear-programming core remain GRAND-based. The aim is to identify when movable nodes improve structural efficiency and when they mainly increase computational cost.

Methods: The study was carried out on two benchmark problems: an L-shaped domain for the main sensitivity study and a cantilever domain for supporting validation. Fixed-node and movable-node layouts were compared using structural volume, active member count, computational time, topology repeatability, and visual load path characteristics. The movable-node search was varied by number of trials, random seed, and perturbation strategy.

Results: Each L-shaped benchmark movable-node result was compared with the fixed-node GRAND result at the same discretisation density and connectivity level. At connectivity level 1, movable nodes reduced volume by 1.6-3.5% across densities. At connectivity level 2, the main density study showed zero or negligible reduction, although seed screening at medium density found non-centred layouts with reductions up to 0.24%. At connectivity level 3, all tested seeds and strategies retained the centred layout and produced no volume reduction. Search parameter tests at medium density affected the best low-connectivity layout, giving reductions of 2.85-3.68%. The cantilever benchmark confirmed the trend, with 1.20-1.25% reduction at connectivity level 1. Increasing density and connectivity strongly increased computational time, especially for movable-node runs, without proportional volume improvement.

Conclusions: The results show that the movable-node benefit is mainly connectivity-dependent, while the volume-reduction magnitude varies between benchmark geometries. Movable nodes are most effective when the fixed ground structure is connectivity-limited, as observed at connectivity level 1 in both benchmarks. At higher connectivity, the centred solution is often retained and additional search mainly increases computational cost, however, comparable volume cases can still reveal alternative active-member layouts. The movable-node method is useful not only for reducing volume, but also for checking whether similar layouts repeat and for finding alternative truss layouts with nearly the same performance.