Computational cost is one of the challenges in the field of fracture resistance topology optimization. An efficient topology optimization approach is proposed for enhancing resistance to structural fracture based on the adaptive isogeometric–meshfree method. The mesh can be adaptively refined in the computational and design domains simultaneously to capture the fracture and structural boundary delicately, which significantly reduces the degree of freedom and improves the efficiency of the topology optimization problems related to crack propagation. The proposed approach naturally inherits the advantages of both the computer-aided design and continuity of the higher-order basis functions, where the geometry and the analysis models in the process of topology optimization are integrated. The problem is formulated to maximize the absorbed energy throughout the crack process using the solid isotropic material with penalization method under volume constraints. The phase field method is used for modeling crack propagation, thereby eliminating the need of an explicit representation of the crack surface and complex tracking procedures, while a delicate mesh is still required. With this approach, the external work required during the fracture process is maximized, and the crack growth is delayed remarkably. Several representative examples are demonstrated to verify the effectiveness of the present approach in fracture-resistance-enhanced topology optimization, and the computational cost shows remarkable improvement.

中文翻译：

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使用相场模型增强抗脆性断裂的自适应拓扑优化


计算成本是抗断裂拓扑优化领域的挑战之一。基于自适应等几何无网格方法，提出了一种有效的拓扑优化方法来增强结构的抗断裂能力。网格可以在计算域和设计域同时自适应细化，以精细地捕获断裂和结构边界，从而显着降低自由度并提高与裂纹扩展相关的拓扑优化问题的效率。该方法自然继承了计算机辅助设计和高阶基函数连续性的优点，其中集成了拓扑优化过程中的几何和分析模型。该问题的公式化是为了在体积约束下使用固体各向同性材料和惩罚方法最大化整个裂纹过程中的吸收能量。相场方法用于对裂纹扩展进行建模，从而消除了裂纹表面的显式表示和复杂的跟踪程序的需要，但仍然需要精细的网格。通过这种方法，断裂过程中所需的外部功最大化，并且裂纹扩展显着延迟。几个代表性的例子验证了该方法在抗断裂增强拓扑优化中的有效性，并且计算成本得到了显着的改善。