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Continuous fiber fused filament fabrication (CF4) is a layer-by-layer additive manufacturing technique that deposits continuous fiber fused filaments (CFFFs) with a significant in-plane variation of the fiber trajectory, thereby offering great flexibility in fabricating variable-stiffness composite laminates (VSCLs). We introduce a topology optimization method for the design of additively manufactured VSCLs made of overlapping, fiber-reinforced bars. The proposed method is based on geometry projection (GP) techniques, whereby the bars are represented by high-level geometric primitives. As in other GP techniques, this high-level parameterization is mapped onto a fixed structured finite element mesh for conducting analysis, as in densitybased topology optimization techniques. However, unlike previous GP techniques that have demonstrated their applicability in designing structures as assemblies of individual fiberreinforced components, this work focuses on the design of composite structures that adhere to CF4 manufacturing processes. Therefore, we first formulate a material interpolation scheme that better captures the stiffness at the composite’s joints obtained from bar overlaps as a stack. Second, the proposed material interpolation employs composite laminate theory to capture the in-plane and out-of-plane behavior of the structure. Third, to produce designs that conform to the CF4 process, we also proposed a novel length constraint formulation in the form of penalization on the projection scheme, which ensures a minimum length for all the bars. This minimum length limit does not require adding a constraint to the optimization problem. The efficacy and efficiency of the proposed method are demonstrated by a series of compliance minimization problems with in-plane and/or out-of-plane loading. The methodology is also applied to the design of a displacement inverter compliant mechanism. 

Geometry projection-based topology optimization has attracted a great deal of attention because it enables the design of structures consisting of a combination of geometric primitives and simplifies the integration with computer-aided design (CAD) systems. While the approach has undergone substantial development under the assumption of linear theory, it remains to be developed for non-linear hyperelastic problems. In this study, a geometrically non-linear explicit topology optimization approach is proposed in the framework of the geometry projection method. The energy transition strategy is adopted to mitigate excessive distortion in low-stiffness regions that might cause the equilibrium iterations to diverge. A neo-Hookean hyperelastic strain energy potential is used to model the material behavior. Design sensitivities of the functions passed to the gradient-based optimizer are detailed and verified. The proposed method is used to solve benchmark problems for which the output displacement in a compliant mechanism is maximized and the structural compliance is minimized. 

We present a topology optimization method based on the geometry projection technique for the design of frames made of structural shapes. An equivalent-section approach is formulated that represents the cross-section of the structural shapes as a homogeneous rectangular section. The accuracy of this approach is demonstrated by comparison to analyses performed using body-fitted meshes of the original sections for different loads and boundary conditions. A novel geometric representation is also introduced to represent the equivalent section as a cuboid. Like offset solids, this representation is endowed with an explicit expression for the computation of the signed distance to the boundary of the primitive and of its sensitivities, allowing for an efficient implementation. An overlap constraint is imposed via the formulation of auxiliary primitives associated to the structural members, which guarantees the resulting designs do not exhibit impractical intersections of primitives that would preclude their construction. The efficacy and efficiency of the method is demonstrated via 2D and 3D design examples. The examples demonstrate that the proposed method renders optimal designs and exhibits good convergence. They also illustrate the ability to design structures with far lower optimal volume fractions than those typically employed in continuum topology optimization techniques. 

Abstract This work presents a method for the topology optimization of welded frame structures to minimize the manufacturing cost. The structures considered here consist of assemblies of geometric primitives such as bars and plates that are common in welded frame construction. A geometry projection technique is used to map the primitives onto a continuous density field that is subsequently used to interpolate material properties. As in density-based topology optimization techniques, the ensuing ersatz material is used to perform the structural analysis on a fixed mesh, thereby circumventing the need for re-meshing upon design changes. The distinct advantage of the representation by geometric primitives is the ease of computation of the manufacturing cost in terms of the design parameters, while the geometry projection facilitates the analysis within a continuous design region. The proposed method is demonstrated via the manufacturing-cost-minimization subject to a displacement constraint of 2D bar, 3D bar, and plate structures. 

Topology optimization problems are typically non-convex, and as such, multiple local minima exist. Depending on the initial design, the type of optimization algorithm and the optimization parameters, gradient-based optimizers converge to one of those minima. Unfortunately, these minima can be highly suboptimal, particularly when the structural response is very non-linear or when multiple constraints are present. This issue is more pronounced in the topology optimization of geometric primitives, because the design representation is more compact and restricted than in free-form topology optimization. In this paper, we investigate the use of tunneling in topology optimization to move from a poor local minimum to a better one. The tunneling method used in this work is a gradient-based deterministic method that finds a better minimum than the previous one in a sequential manner. We demonstrate this approach via numerical examples and show that the coupling of the tunneling method with topology optimization leads to better designs.