A qualitative evaluation and structural analysis of multiple and additive load cases for two-dimensional Multi-Material Topology Optimisation in Grasshopper using the Generalised SIMP method

Abstract In the physical world, it is common for Multiple Load Cases (MLC) to act on a body either simultaneously or at different points in time. While MLC has been widely addressed in the literature, it has been identified that MLC in 2D Multi-Material Topology Optimised (MMTO) examples using the Solid Isotropic Material with Penalisation (SIMP) method is understudied, with the majority of examples not evaluating their structural performance. It is also identified that there are currently no MLC-ready MMTO software tailored to Architects that can perform Finite Element Analysis (FEA). The current research investigates how MLC can be addressed within “Stag”, our newly developed MMTO plugin for Grasshopper, and how its results compare topologically to benchmark examples from the literature. Furthermore, an overlaying method (ALC) of individual load case results is compared to MLC. This study addresses the identified gap in the literature by evaluating and comparing the structural performance of Stag’s MMTO MLC and ALC results with those from the literature by performing FEA within the same platform using the Grasshopper plugin “Karamba3D”. It is found that Stag produces MMTO MLC results that have a similar topology and structural performance to the benchmark examples from the literature. While the ALC result surpasses the target volume fraction, it performs structurally better than the MLC result.