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.

可传递负载是由其作用线定义的外部负载，在拓扑优化过程中选择了实际的负载应用点。虽然对于最佳结构是索道的问题，可传递载荷可以视为表面载荷，但在其他情况下，此类载荷可以自由施加到结构的内部部分。文献中描述了两种主要的传递载荷公式：刚性杆（约束位移）公式或不太常见的迁移载荷（平衡）公式。在这里，我们采用简单的莫尔圆分析来表明刚性杆公式只会在某些特定情况下产生正确的结构形式。数值示例用于演示（和解释）在其他情况下应用刚性杆公式时产生的不正确拓扑。还为均匀加载的悬臂结构提供了一种新的解析解。最后，考虑离散桁架和连续拓扑优化公式，我们调用对偶原理来阐明两种公式之间差异的来源。