3D Topology Optimization of Spatially Reinforced Composites

Topology optimization is a numerical design tool used to generate structural concepts that present optimal load paths for a given set of functional requirements. This functional generative design capability has been used to lightweight high performance structures with 1D, 2D and 3D stress states. On the other hand, fiber-reinforced composites are the perfect candidate material to use in high performance structures due to the tailorability of their stiffness and strength properties. Although numerical tools that simultaneously tailor the composite material properties while optimizing the structural topology exist, these tools are inherently limited to 1D and 2D stress states. This work aims to address this limitation by presenting a new topology optimization framework for 3D design of fiber-reinforced composites. Such computational design framework is composed of three key elements: (i) a macromechanical model, called multi-thread theory, that estimates the stiffness properties of 3D fiber reinforced composites; (ii) a stable coupling algorithm between macro-mechanics and structural analysis codes; and (iii) a scalable optimization algorithm. To evaluate the feasibility of this framework, 2D and 3D topology optimization results are presented. The 2D numerical results are used to investigate the benefits of the new continuation scheme formulated within the optimization algorithm. Moreover, by optimizing 3D topologies with geometric conditions such that the stress state is approximately plane stress, the 2D results are used to show consistency between this computational design framework and other 2D approaches based on classical laminate theory. Finally, to demonstrate the capability of this framework a 3D MBB-beam is simultaneously optimized for both topology and fiber reinforcement orientation. This problem optimized 249,452 design variables to yield an optimized MBB 3D-beam that is 75% lighter, yet only 16.5% more flexible. Such step-change improvement in performance was due to the complex geometry of the optimized MBB 3D-beam (and its aligned reinforcement) involving structural elements such as curvilinear arches, variable-thickness sidewalls and uni-axial struts connecting these walls