基于骨骼重建机理的连续体结构仿生拓扑优化方法

Bionic Topology Optimization Method for Continuum Structures Based on Bone Remodeling Mechanism

骨重建是一种持续进行的新骨替代旧骨的过程,它通过具有骨吸收能力的破骨细胞和具有骨成形能力的成骨细胞来实现。在陆地脊椎动物中这两种细胞活动是严格平衡的,并且骨的拓扑形状是适应局部力学环境的。本文以Turing反应-扩散模型为基础,通过骨成形与骨吸收机理耦合建立了骨重建模型。该模型通过有限元方法和像素单元的添加和删除准则提出了连续体结构仿生拓扑优化计算方法,该方法将结构看成生长的骨骼,将寻找最优拓扑的过程比拟为骨骼的重建过程,应变能密度的均匀分布作为优化准则更新材料分布,直至达到一个平衡状态,并由此获得最优拓扑结构。最后通过典型的算例验证了所提方法的可行性和有效性。

Bone remodeling is the process of ongoing replacement of old bone by new. The remodeling process is achieved by bone-resorbing osteoclasts and bone-forming osteoblasts. In terrestrial vertebrates, activities of these two types of cells are strictly balanced and adapt the shape of bone to mechanical stress. A simple bone remodeling model by coupling the bone formation and resorption based on Turing reaction-diffusion system weighed by local mechanical stress was proposed. This model was coupled with finite element method by using the element adding and removing process, and a new bionic topology optimization model was established. The major idea of this approach is to consider the continuum structure to be optimized as a piece of bone, and the process of finding the optimum topology of a structure was equivalent to the bone remodeling process. Uniform distribution of strain-energy density as a guideline updated the material distribution, until equilibrium was reached and then the optimal topology structure was obtained. The effectiveness of the present method is demonstrated by some numerical examples.