基于Wolff法则连续体拓扑优化方法中的参数分析

Parameter Analysis in Wolff's Law Based Approach of Continuum Structural Topology Optimization

Wolff法则是指骨骼在外部荷载变化时,骨骼内部小梁骨保持沿主应力方向分布以更好抵抗外部荷载。基于Wolff法则的连续体拓扑优化方法是模仿骨骼重建规律的一种新的连续体优化方法。基本思想是将待优化的结构看成是遵从Wolff法则的“骨骼”,仿照骨骼重建过程,连续体的拓扑优化过程即为“骨骼”重建过程。该方法中利用用于描述材料微结构几何及弹性性质的构造张量作为设计变量,采用参考应变区间确定构造张量特征主值的更新规律。本文通过对仿生过程中各因素的分析,解释了优化模型中各参数的物理意义。通过数值分析,给出了参数选取规律以保证算法稳定和快速收敛,从而使得本文优化方法更具实际应用价值。

Wolff's law indicates that bone is endowed with the ability to adapt its internal structure to the load environment and trabecular bone distributes along the trajectories of the principal stresses, which motivates to propose for continuum structural topology optimization. The structure is cosidered as a piece of bone obeying Wolff's law and the process of finding the optimum structural topology is simulated as the bone remodeling/growth, where a second rank positive and definite fabric tensor as the design variable of a material point is introduced to express the geometry and elasticity of the material point in design domain. An interval of reference strain corresponding to the dead zone in biomechanics, is presented to determine the update rule of the eigenvalues of fabric tensors. And, the physical significations of the parameters, i.e. the initial design variables, increments of the design variable and the interval of reference strain, as well their effects on the convergence behaviour of the optimization algorithm are discussed. Some useful conclusions for setting the parameters are presented to improve the convergence behaviour.