Abstract as per original application
(English/Chinese): |
Additive manufacturing, also known as 3D printing, is a fast-growing technology that is making an appearance in various businesses and industries. It has the advantage of creating complex-shaped objects in a rapid, flexible and cheap manner, but despite its potential in a variety of areas such as biomedical implants, automotive and aerospace components, and even jewellery and food, it is held back by several factors that prevent real integration with commercial production line assemblies.
One of these factors which we plan to explore in this project is a design issue related to support structures. As the name implies, support structures are used to prop up the 3D object during printing to maintain its intended shape and prevent deformations caused by external factors. However, support structures obviously add to the material costs, printing time, and there is a risk of inflicting damage to the object during their removal. Since support structures are absolutely necessary for general object designs, previous researchers have employed the framework of optimisation, particularly in the context of structural topology optimisation, with the aim of finding optimal designs that address some of the issues arising from support structures.
The goal of this proposal is to develop an alternative optimisation approach for the design of support structures based on the concept of phase fields, which in the past has seen successful applications in tackling problems motivated from shape and topology optimisation. We believe our proposed phase field approach can offer both mathematical and numerical advantages over current methods; such as a rigorous analysis of the optimisation problem, derivation of optimality conditions, convergence of the numerical iterations, and an overall improvement in computational effort. Furthermore, we envision the ideas developed in this proposal can be extended beyond the issue of support structures, and begin to contribute towards resolving other challenges faced by the additive manufacturing industries.
增材製造，俗稱3D打印，是各行各業快速發展的製造技術。它具有以快速、靈活和廉價的方式創建複雜形狀物體的優勢，儘管它在生物醫學植入物、汽車和航空航天部件，甚至珠寶和食品等各個領域具有潛力，但現在仍未完全成為商業生產線主要的一部分。
在這個項目中，我們探討了與支撐結構相關的設計問題。顧名思義，支撐結構用於在打印過程中支撐正在印刷的部分，以保持其預期形狀並防止由外部因素引起的變形。然而，支撐結構顯然會增加材料成本、打印時間，並且在移除過程中存在對物體造成損壞的風險。由於支撐結構對於一般設計是絕對必要的，以前的研究採用了優化方法，特別是在拓撲優化的背景下，目的是找到解決支撐結構引起的一些問題的最佳設計。
我們的目標是開發一種使用相場設計支撐結構的替代方法，該方法過去已成功應用於解決形狀優化和拓撲優化引起的問題。我們相信我們提出的相場方法可以提供優於當前方法的數學和數值優勢；例如對優化問題的嚴格分析、優化條件的推導、數值迭代的收斂以及計算工作的整體改進。此外，我們設想本提案中提出的想法可以擴展到支持結構問題之外，並開始為解決增材製造行業面臨的其他挑戰做出貢獻。
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