This study aims to incorporate directional gradient constraints into the Bruns and Tortorelli density method to control local material gradients and convert continuous density fields into manufacturable discrete lattice parameters. By developing a gradient-constrained density-to-lattice conversion and optimized weighting function, the method enhances structural stiffness under equal mass conditions, providing a robust framework for lightweight, high-strength lattice-solid hybrid structure optimization.
This paper designs lattice structures based on topology optimization, modifications to the density method proposed by Bruns and Tortorelli. To validate the advantages of the proposed theoretical design, the method is compared with existing approaches under the same working conditions. A simulation model was developed, and the results were analyzed.
The analysis of the simulation results shows that the density gradient method establishes a density gradient-driven topology optimization framework, which converts the intermediate density into a lattice structure. By introducing directional gradient constraints, the density method of Bruns and Tortorelli is redesigned to achieve the AM-oriented mapping mechanism: A density-based lattice parameter mapping function is established to convert the continuous density field into discrete strut diameters, which improves the overall performance of the additive manufacturing (AM) structure, especially in terms of stiffness and manufacturability.
This study introduces a paradigm-shifting design strategy for AM, establishing a density gradient-driven topology optimization framework to achieve mechanics-oriented lattice design. Departing from conventional passive mapping methods, developing a gradient-constrained density-lattice conversion function that transforms continuous density fields into manufacturable discrete strut diameter distributions, effectively eliminating pseudo-density artifacts and lattice continuity issues inherent to traditional approaches. Make its performance designable and the structure manufacturable. Moreover, it can enhance the structural stiffness under the condition of equivalent mass.
