| 蔡坤,张洪武,周强,陈飙松.几何非线性连续体结构拓扑优化仿生方法[J].,2008,(1):6-11 |
| 几何非线性连续体结构拓扑优化仿生方法 |
| Topology optimization of geometrical nonlinear continuum structures based on a bionics approach |
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| DOI：10.7511/dllgxb200801002 |
| 中文关键词: 拓扑优化 几何非线性 Wolff法则 构造张量 |
| 英文关键词: topology optimization geometrical nonlinearity Wolff′s Law fabric tensor |
| 基金项目:国家自然科学基金与创新群体基金资助项目(10225212；10421202；10402005)；长江学者和创新团队发展计划以及国家基础性发展规划资助项目(2005CB321704). |
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| 中文摘要: |
| 利用基于Wolff法则的仿生方法对几何非线性、线弹性连续体进行拓扑优化. 该仿生方法中引入构造张量作为设计变量用于描述设计域内各点处材料微结构的几何特征及其宏观弹性本构. 同时，引入参考应变区间并结合Wolff法则用于确定结构中某点处材料的更新方案. 考查了结构最优拓扑的网格依赖性以及参考应变区间对结构的最优拓扑及材料分布的影响. 数值算例表明，结构的最优拓扑无网格依赖性. 几何非线性线弹性连续体结构的最优拓扑明显地依赖于参考应变区间的选取. 如果参考应变区间长度为零且荷载为指定位移时，按同比例改变荷载及参考应变区间上确界，可得到相近的最优拓扑和材料的分布. |
| 英文摘要: |
| The topology optimization of geometrical nonlinear and linear elastic continuum structures is investigated by the bionics method based on Wolff′s Law in biomechanics. In the present approach, the design variable is called as fabric tensor, which is introduced to express both of geometry of the microstructure and the elasticity properties of a material point in the design domain. Simultaneously, the interval of reference strain for the structure is adopted and is applied to renew the fabric tensor of a point together with Wolff′s Law. The mesh-dependence of optimal topology of a structure and the influences of the interval of reference strain on the optimal topology are investigated. By numerical examples, several conclusions are drawn as follows: Firstly, the optimal topology of a structure is not dependent on the mesh-refine. Secondly, the optimal topology of a structure with geometric nonlinearity obviously depends on the specified interval of reference strain. Thirdly, if the length of the interval of reference strain equals to zero and the loading conditions are specified displacements on structure, then changing the superimum of the interval and the given displacements proportionally, the optimal topology and the amount of material of the final structure are approximately identical. |
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