基于骨骼重建机理的连续体结构仿生拓扑优化方法研究

项目名称： 基于骨骼重建机理的连续体结构仿生拓扑优化方法研究

项目编号： No.11461069

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 开依沙尔·热合曼

作者单位： 新疆大学

项目金额： 40万元

中文摘要： 骨骼具有适应力学环境的功能，它将根据周围的力学环境调整自身的拓扑结构和形状，以最小的重量实现最优的结构和最大的强度。骨骼的这种功能适应性是通过具有骨形成能力的成骨细胞和具有骨吸收能力的破骨细胞的连续重建来实现。本研究首先从骨骼功能适应性原理出发，以种群动力学模型为基础, 耦合成形骨与吸收骨机理拟建立了骨骼重建数学模型。然后通过有限元方法和像素单元的添加和删除准则，把骨重建过程转化为材料形成和吸收过程对连续体结构拟提出拓扑优化仿生方法。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，并由此获得结构的最优拓扑形状。最后通过典型的算例进行拓扑优化计算，以及将其结果与其它几种传统的拓扑优化方法进行比较，验证本研究所提的拓扑优化方仿生法的可行性和有效性。

中文关键词： 骨骼重建；种群动力学模型；有限元方法；连续体结构；仿生拓扑优化

英文摘要： Bone has ability to adapt itself to mechanical environment. It adjusts its topological structure and shape according to the surrounding mechanical environment and establishes optimized structure and maximal strength with minimal weight. This bone adaptation process is controlled by continuous remodeling of bone-forming osteoblasts and bone-resorbing osteoclasts. In this study firstly according to bone adaptation theory to establish simple mathematical model of bone remodeling by coupling bone forming and resorbing activities based on population dynamics model. Secondly this model is coupled with finite element method the bone remodeling mechanisms is translated to material formation and absorption process by using element adding and removing process, to propose bionic topology optimization of continuum structures. 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 is equivalent to the bone remodeling process, uniform distribution of strain-energy density is as a guideline updates the material distribution, until equilibrium is reached and then the optimal topology structure is obtained. Widely used examples in continuum structural topology optimization are carried out by using presented bionic approach and results are compared with other traditional topology optimization techniques to confirm the validity of the proposed method.

英文关键词： bone remodeling;population dynamics model;finite element method;continuum structures;bionic topology optimization