In this paper, considering the porosity defects of Additive Manufacturing (AM), a level set topology optimization method for AM with porosity constraints is proposed. The concept of topological sensitivity is used to formulate a global porosity constraint function in the proposed method, and a level set topology optimization model considering porosity defects is obtained. To improve the robustness of the algorithm, the topology optimization model is solved in two phases. At first, the classical level set method without the porosity constraint is used to initially optimize the structure. During this process, the hole nucleation method combining bi-directional evolutionary structural optimization (BESO) and the topological sensitivity is used. Secondly, the topology optimization considering the effects of porosity is implemented on the preliminary optimization results. After performing the two-step optimization, a robust structure that alleviates the harmful impact of porosity defects is obtained. Finally, the robustness and effectiveness of the proposed method are validated by several two-dimensional numerical examples.

As is known to all, the incapacity to nucleate holes automatically in the design domain is one of the main issues of the classical level set topology optimization method. To solve the issue of hole nucleation, this paper employs the bi-directional evolutionary structural optimization (BESO) method based on the material removal scheme and the frequently used topological sensitivity and proposes the combining BESO and topological sensitivity (CBT) method for level set topology optimization. This method can replace the existing hole nucleation method for level set topology optimization. First, the topological sensitivity is combined with BESO, and the BESO method based on topological sensitivity is proposed. Second, the method is integrated into level set topology optimization to solve the issue of hole nucleation. Two sensitivity thresholds are defined depending on the evolutionary volume ratio and boundary topological sensitivity, respectively, and the smaller one is used as the sensitivity threshold for hole nucleation. The material is removed from the design domain to nucleate holes based on this threshold. Three classical two-dimensional numerical examples are used to validate the proposed hole nucleation method.