Composite number

Engineering

Curvature

Materials science

Constraint (computer-aided design)

Curl (programming language)

Computer science

Mathematical optimization

Manufacturing engineering

Mechanical engineering

Design for manufacturability

Finite element method

Mathematics

Path (computing)

Geometry

Composite material

Structural engineering

Programming language

Engineering drawing

Topology (electrical circuits)

Composite laminates

Electrical engineering

Composite Structures

Automatic fiber placement machines have made it viable to manufacture composites where fiber angles vary continuously—tow-steered composites. The additional freedom provided by tow-steered composites has the potential to increase structural performance; however, this approach comes with added design complexity. Numerical optimization can address this complexity, though it is critical that constraints are enforced to ensure that the resulting optimal tow-steered designs are manufacturable using current automatic fiber placement machines. In this work, we consider two manufacturing constraints: tow path curvature and gaps/overlaps. To develop these constraints, we consider a general tow-steered layer pattern as a 2D unit vector field, where the field streamlines represent the tow paths laid down by the automated fiber placing machine. This mathematical formulation provides a relationship between tow path curvature, gap/overlap propagation rate, vector curl, and divergence. These relationships also lead to a constraint on the minimum cut/add length of a tow for a given tow-steered pattern. We demonstrate the developed constraint formulations on two analytical examples, as well as on a structural optimization. We also explore the relationship between curl and divergence of rotated tow patterns. This analysis leads to the conclusion that layups featuring such patterns require strict constraints on bounds to ensure satisfaction of manufacturability requirements. Finally, we use these relationships to motivate a family of gap/overlap-free and curvature-free tow-steered patterns.

On manufacturing constraints for tow-steered composite design optimization