Additive manufacturing (AM) has and continues to experience considerable market and technological growth with many forecasting a tripling in market value over the next decade. One of the primary drivers for this growth is the increased freedom afforded to the design of both the external form and internal structure of fabricated parts. This freedom presents greater opportunities in optimising a parts mechanical properties, (such as strength, stiffness and mass), which in turn leads to enhanced performance whilst potentially reducing material use and hence, environmental impact. Realising this potential will further increase the viability of AM for a greater range of engineering contexts. Correspondingly, the contribution of this paper lies in the creation and validation of a method for the topological optimisation of the infill structure of fused deposition modelled (FDM) components. The proposed method uses results attained from finite element analysis (FEA) to influence the design of the internal structure (i.e. infill) by locally varying the composition of the infill based upon the associated stress values. This paper presents and discusses the proposed method, and demonstrates the generalisability of the method through its ability to handle complex geometries and loading conditions, and manufacturing process constraints. In addition, the paper validates the method through testing of FDM beams comprised of FEA influenced and standard honeycomb infill designs undergoing four different loading scenarios. The validation reveals that a three and a half times increase in strength can be achieved where the stress profiles are well defined within the structure. In addition, the FEA-influenced beams exhibited more consistent failure mode profiles, which maybe desirable for designing parts with specific failure mode characteristics.