Concurrent Shape and Fiber Path Optimization for Composites
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Solution Overview
Problem
Optimizing the shape and fiber path in continuous fiber composites is challenging due to their anisotropic properties and sensitivity to initial fiber configurations, which affects their structural performance and manufacturability, especially in stress-based optimization where local non-linearity and abrupt fiber path changes complicate the design process.
Innovation Solution
A novel strength-based structural optimization technique using a level-set method to concurrently design shape and fiber paths, incorporating a higher-order function for shape evolution and fiber placement, with a thickness control term to ensure manufacturability, and combining fixed and adaptive finite element meshes to smooth boundaries and reduce stress concentrations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Strength
If conventional fiber path optimization methods are used, then fiber orientation can be improved, but the method is sensitive to initial fiber configurations and produces non-convex problems that are difficult to manufacture
Solution Approach 1:
The patent transforms the fiber path optimization from a non-convex problem with sensitivity to initial configurations into a convex optimization problem by changing the mathematical formulation. The level-set method introduces a new parameter space where fiber paths are represented as level sets of a scalar function, converting the complex non-convex fiber orientation problem into a convex shape optimization problem that is less sensitive to initial conditions and more manufacturable.
Solution Approach 2:
The level-set function acts as an intermediary between the desired fiber path and the manufacturable shape. Instead of directly optimizing fiber orientations which are sensitive to initial conditions, the level-set method uses an intermediate scalar field to define both the shape boundaries and fiber path trajectories, creating a bridge between optimization goals and manufacturing feasibility.
2Shape
If shape optimization is performed without fiber path consideration, then shape can be optimized, but fiber path changes become abrupt and stress concentrations increase
Solution Approach 1:
The patent merges shape optimization and fiber path optimization into a single concurrent optimization process. The level-set method simultaneously defines both the external shape boundaries and internal fiber path trajectories through the same scalar function, ensuring that shape changes and fiber path changes are coupled and smooth rather than abrupt, thereby reducing stress concentrations.
Solution Approach 2:
The level-set method naturally produces smooth curved transitions in both shape boundaries and fiber paths, avoiding abrupt angular changes. The mathematical formulation inherently favors smooth level-set contours, creating curved transition zones that distribute stresses more uniformly compared to sharp angular transitions.
3Manufacturing precision
If higher-order level-set methods are used for shape evolution, then boundary smoothness is improved, but computational complexity increases
Solution Approach 1:
The patent uses higher-order terms in the level-set expansion (including curvature and higher derivatives) to capture smooth boundary evolution more accurately. By changing the mathematical representation to include these higher-order parameters, the method achieves smoother boundaries with fewer iterations, and the computational complexity increase is offset by reduced iteration counts and improved convergence.
Data Source
AI summary
A computer-implemented method of optimizing a computer model including a shape and a fiber path for a continuous fiber composite can include initializing a fixed finite element mesh. The method can also include creating an updated version of the shape and the fiber path by iterating updates of the shape and the fiber path using the fixed finite element mesh. The method can also include initializing an adapted finite element mesh on the updated version of the shape and the fiber path. The method can also include creating an optimized version of the shape and the fiber path by iterating optimizations of the shape and the fiber path using the adapted finite element mesh. The method can also include generating a specified design of the continuous fiber composite using the optimized version of the shape and the fiber path.