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中文核心期刊

基于智能优化算法的梯度点阵结构承载性能优化设计

Optimization Design Method for Load-Bearing Performance of Gradient Lattice Structures Based on Intelligent Optimization Algorithm

  • 摘要: 作为一种新兴的轻质多功能材料,点阵结构因其高比强度与比刚度等优异的力学性能,在航空航天、医疗器械以及汽车等多个高技术领域获得了广泛应用。然而现有的点阵结构单胞分布大多基于均布式假设设计,在不同边界条件和载荷下不能充分发挥其力学性能。针对上述问题,本文基于智能优化算法提出一种梯度分层点阵优化设计方法。首先,基于水平集函数构建点阵结构单胞显式拓扑描述模型,并通过引入形状插值技术保证不同层间的连接性;其次,通过构建Kriging代理模型建立点阵单胞的单胞相对密度与等效力学性能之间的函数关系;然后,以点阵结构整体柔度最小化为目标,结构体积分数和边界条件为约束条件,建立梯度分层点阵结构优化模型,并采用蜣螂优化算法实现对上述模型高效求解,同时引入形状插值技术对最终的优化结构进行几何连续性优化;最后,通过若干数值算例和仿真实验共同验证了所提方法的有效性,并与相同条件下均匀点阵结构和拓扑梯度点阵结构的承载性能进行对比。结果表明:所提方法能够实现点阵结构的梯度分层优化设计,优化后的梯度分层点阵结构柔度相较均匀点阵和拓扑优化得到的梯度点阵可分别降低70.72%和10.27%。研究结果可为高承载轻量化点阵结构提供新的设计思路。

     

    Abstract: As an emerging lightweight multifunctional material, graded lattice structures have gained extensive applications in various high-technology fields, including aerospace, medical devices, and automotive industries, owing to their exceptional mechanical properties, such as high specific strength and specific stiffness. However, the unit cell distributions of most existing lattice structures are predominantly designed based on uniform distribution assumptions, consequently limiting their ability to fully exploit mechanical performance under diverse boundary and loading conditions. To address these limitations, this paper proposes a graded hierarchical lattice optimization design method based on intelligent optimization algorithms. Initially, an explicit topology description model for lattice unit cells is constructed using level-set functions, with shape interpolation techniques introduced to ensure geometric continuity between hierarchical layers. Subsequently, a functional relationship between the relative density of unit cells and their equivalent mechanical properties is established through a Kriging surrogate model. An optimization model for graded hierarchical lattice structures is then formulated, aiming to minimize overall structural compliance while constrained by structural volume fraction and boundary conditions. The Dung Beetle Optimizer algorithm is employed to solve this model efficiently. Concurrently, shape interpolation techniques refine geometric continuity in the final optimized structure. Validation via numerical examples and simulation experiments confirms the method’s effectiveness. The load-bearing performance of the optimized graded hierarchical lattice structure is compared with uniform lattices and topology-optimized graded lattices under identical conditions. Results demonstrate a compliance reduction of 70.72% and 10.27%, respectively, proving superior mechanical performance. This approach provides a novel design paradigm for high-load-bearing lightweight lattice structures.

     

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