On transmissible load formulations in topology optimization

Transmissible loads are external loads defined by their line of action, with actual points of load application chosen as part of the topology optimization process. Although for problems where the optimal structure is a funicular, transmissible loads can be viewed as surface loads, in other cases such loads are free to be applied to internal parts of the structure. There are two main transmissible load formulations described in the literature: a rigid bar (constrained displacement) formulation or, less commonly, a migrating load (equilibrium) formulation. Here, we employ a simple Mohr's circle analysis to show that the rigid bar formulation will only produce correct structural forms in certain specific circumstances. Numerical examples are used to demonstrate (and explain) the incorrect topologies produced when the rigid bar formulation is applied in other situations. A new analytical solution is also presented for a uniformly loaded cantilever structure. Finally, we invoke duality principles to elucidate the source of the discrepancy between the two formulations, considering both discrete truss and continuum topology optimization formulations.

Automated summary

This paper discusses the role of transmissible loads in topology optimization, introducing two main formulations and studying their applicability. Through numerical examples and analytical solutions, the authors demonstrate the potential incorrect structural forms generated by the rigid bar formulation in certain situations. Duality principles are invoked to explain the discrepancy between the two formulations, considering both discrete truss and continuum topology optimization formulations.