Abstract
In this paper, design strategies are developed to explore better approaches of enforcing local layer-wise curvature constraints in the optimization of variable stiffness laminates in order to ensure the manufacturability of optimized designs based on the limitations of automated fiber placement. The methods developed here aim to improve an existing approach of imposing the curvature constraint directly on the fiber angles (i.e., direct control method) and are suitable for a design framework that uses lamination parameters as primary design variables. One approach developed here, termed the indirect control method, enforces the curvature constraint indirectly with better computational efficiency through the spatial gradient of the lamination parameters. It is shown that the curvature constraint on the actual fiber angles can also be satisfied with a sufficiently stringent upper bound albeit it produces overly conservative designs. Alternatively, an enhanced approach, termed the hybrid control method, is developed by combining the direct method and a relaxed version of the indirect control method. The case studies of minimum compliance design indicate that it provides the best manufacturable design among the three methods in the context of variable stiffness laminates using lamination parameters.
Highlights
Robotic-driven manufacturing techniques for composite materials, such as Automated Fiber Placement (AFP), allow to manufacture laminates that have non-homogeneous stiffness, commonly known as variable stiffness laminates (VSLs) [1]
The Step 1 corresponds to the primary objective functional, with or without gradient constraints on the lamination parameters depending on the method
The proposed hybrid control method consists of minimizing the normalized compliance C=C0 of the VSL using the gradient constraints on the lamination parameters in Step 1 but with a relaxed upper bound factor d 2 1⁄2dÃ; 1Þ and, subsequently, minimizing the difference D with local steering constraints on the fiber angles in Step 2 using fmax 1⁄4 1=rmin
Summary
Robotic-driven manufacturing techniques for composite materials, such as Automated Fiber Placement (AFP), allow to manufacture laminates that have non-homogeneous stiffness, commonly known as variable stiffness laminates (VSLs) [1]. In a second step, the optimal homogenized parameters are used to retrieve physical and/or geometrical information about the optimal laminate These multistep methods are usually efficient in terms of exploring a large design space at a minimal computational cost. It has been challenging to impose this type of constraint in multistep methods without a significant performance loss This is problematic in methods where the retrieval step is carried out by matching the physical and geometrical properties of the laminate to the optimal homogenized parameters without considering the mechanical performance. In the context of a multi-step method [22], the existing direct control method [20] induces large performance loss between the consecutive steps by imposing local curvature constraints on fiber angles in the intermediate step.
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