Enhancing Structural Design: A Practical Review on Promoting Connectivity in Topology Optimization

By: Vanessa Cool, Niels Aage, Ole Sigmund

Topology optimization revolutionizes the way engineers and designers approach structural design. By automatically determining the most efficient distribution of material within a given space, topology optimization enables the creation of lightweight, high-performance structures that often outperform traditional designs in strength, stiffness, and material efficiency. It serves as a cornerstone in aerospace, automotive, and civil engineering, offering unprecedented freedom to explore novel and non-intuitive design solutions.

However, the full potential of topology optimization is often hindered by a persistent and critical challenge: poor structural connectivity in the optimized results. Without sufficient connectivity, optimized designs can suffer from fragmented regions, unsupported members, or isolated features (Fig. 1) —making them not only difficult or impossible to manufacture but also structurally unreliable. This issue becomes particularly problematic in practical applications, where continuity and robustness are essential for load transfer, durability, and safety.

Figure 1. Definition of connectivity in a topology.

Our recent work addresses this challenge by offering a comprehensive and practical review of methods designed to promote connectivity in topology optimization. Through a systematic analysis and comparative evaluation, we aim to bridge the gap between the theoretical optimization and the real-world manufacturing connectivity requirement, providing valuable guidance to both researchers and practitioners in the field.

Figure 2. Overview of the connectivity constraints. The gray scaling indicates the method is applied for 2D and/or 3D, while T represents the method is theoretically possible but not yet validated in literature.

Key findings

The work first reviews all existing connectivity-enforcing methods in the current state-of-the-art. We categorize and evaluate the existing methods that aim to promote connectivity and divide them into physics-based and geometry-based methodologies (Fig. 2). Secondly, a practical comparison between the key connectivity methodologies is performed on a vibro-acoustic case study where both structural and acoustic performance are of importance. Based on our analysis, we are able to provide guidelines on selecting appropriate connectivity enhancement methods depending on the specific requirements and constraints of the design problem. With Pareto-graph studies, the constraints are evaluated based on computational cost, monotonicity, parameter dependency, and their impact on the optimized designs, their performance, and underlying dynamics  (Fig. 3). From the comparison, practical insights and rule of thumbs emerge. The findings emphasize the critical role of selecting appropriate connectivity constraints, given their significant effect on the optimization results.

Figure 3. Result of the comparison between the key connectivity methodologies with below the applied Pareto-graph results in which each data point is the best result out of several simulations.

Role of high-performance computing

The evaluation of various connectivity constraints involves extensive computational experiments. Utilizing high-performance computing resources, such as those provided by VSC, allows us to perform large-scale simulations and analyses efficiently. The computational power facilitates the efficient comparison of the different methods, leading to robust and generalizable conclusions.

Implications and future work

Improving connectivity in topology optimization has significant implications for the practical application of topology optimization in engineering design. By ensuring that optimized structures are both efficient and manufacturable, these methods bridge the gap between theoretical optimization and real-world implementation. Our work serves as a practical guideline for practitioners to choose the appropriate connectivity constraint for their application and gives inspiration for future research on advanced techniques that can automatically enforce the connectivity during the optimization.

Read the full publication in Springer Nature here

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