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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.
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This content will become publicly available on February 1, 2026
A geometry projection method for the topology optimization of additively manufactured variable-stiffness composite laminates
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.
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- Award ID(s):
- 1751211
- PAR ID:
- 10562172
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Computer Methods in Applied Mechanics and Engineering
- Volume:
- 435
- Issue:
- C
- ISSN:
- 0045-7825
- Page Range / eLocation ID:
- 117663
- Subject(s) / Keyword(s):
- Topology optimization Geometry projection Continuous fiber-reinforced polymers Variable-stiffness laminates Fused filament fabrication
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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