Modern advanced manufacturing techniques, such as additive manufacturing and automated fiber placement, empower the creation of composite structures with precisely customized properties. To take full advantage of these variable-stiffness composites, during the design phase, careful attention must be paid to both the manufacturability of the structure and the anisotropic nature of the material. In previous studies, we developed a method to optimize linear elastic fiber-reinforced composite structures produced through additive manufacturing. We designed for maximum stiffness subject to a mass restriction and considered direct ink writing manufacturing constraints. In this study, we design manufacturable variable-stiffness composite laminates by incorporating strength failure criteria such as Tsai-Hill and Tsai-Wu. Since these criteria are local, we employ aggregation techniques to compute the global smooth maximum failure index of the entire composite structure. We investigate and compare several smooth maximum functions, including the p-norm+, p-mean+, Kreisselmeier–Steinhauser (KS), mellowmax, and Boltzmann formulations, highlighting their numerical behavior and impact on optimization. We show that small smoothing parameters <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> lead to overly smooth approximations that may fail to effectively reduce the true maximum failure index. Conversely, larger <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> values yield sharper approximations but may cause numerical overflow. We define upper bounds for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> to avoid such overflow, and demonstrate that values below these limits are numerically stable and effective. Building on our prior research, we leverage level-set functions to define towpaths, facilitating the optimization of material properties while adhering to manufacturing constraints for automated fiber placement like no-gaps and no-overlaps, and minimum turning radius. To enforce the manufacturing constraints, we incorporate a smooth ramp function; and, in this study we further investigate the impact of its parameters on optimization performance. Our approach utilizes a conforming classical plate theory finite element for composite laminate analysis, with the adjoint method enabling efficient sensitivity analysis computations. By employing a gradient-based optimization scheme, we aim to find optimal designs that are readily fabricable by automated fiber placement. Our results confirm that the proposed method consistently produces manufacturable designs with low failure indices and high structural performance.

Optimal design strategy for variable-stiffness composite laminates addressing strength and manufacturing challenges

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发表日期：

2025年7月31日

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Felipe Fernández

摘要

Modern advanced manufacturing techniques, such as additive manufacturing and automated fiber placement, empower the creation of composite structures with precisely customized properties. To take full advantage of these variable-stiffness composites, during the design phase, careful attention must be paid to both the manufacturability of the structure and the anisotropic nature of the material. In previous studies, we developed a method to optimize linear elastic fiber-reinforced composite structures produced through additive manufacturing. We designed for maximum stiffness subject to a mass restriction and considered direct ink writing manufacturing constraints. In this study, we design manufacturable variable-stiffness composite laminates by incorporating strength failure criteria such as Tsai-Hill and Tsai-Wu. Since these criteria are local, we employ aggregation techniques to compute the global smooth maximum failure index of the entire composite structure. We investigate and compare several smooth maximum functions, including the p-norm+, p-mean+, Kreisselmeier–Steinhauser (KS), mellowmax, and Boltzmann formulations, highlighting their numerical behavior and impact on optimization. We show that small smoothing parameters $\alpha $ $α$ lead to overly smooth approximations that may fail to effectively reduce the true maximum failure index. Conversely, larger $\alpha $ $α$ values yield sharper approximations but may cause numerical overflow. We define upper bounds for $\alpha $ $α$ to avoid such overflow, and demonstrate that values below these limits are numerically stable and effective. Building on our prior research, we leverage level-set functions to define towpaths, facilitating the optimization of material properties while adhering to manufacturing constraints for automated fiber placement like no-gaps and no-overlaps, and minimum turning radius. To enforce the manufacturing constraints, we incorporate a smooth ramp function; and, in this study we further investigate the impact of its parameters on optimization performance. Our approach utilizes a conforming classical plate theory finite element for composite laminate analysis, with the adjoint method enabling efficient sensitivity analysis computations. By employing a gradient-based optimization scheme, we aim to find optimal designs that are readily fabricable by automated fiber placement. Our results confirm that the proposed method consistently produces manufacturable designs with low failure indices and high structural performance.