A level set method for topology optimization of heat conduction problem under multiple load cases
A level set method for topology optimization of heat conduction problem under multiple load cases
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DOI：
10.1016/j.cma.2006.08.005
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发表时间：
2007
影响因子：
7.2
通讯作者：
Chungang Zhuang;Z. Xiong;H. Ding
中科院分区：
文献类型：
--
作者：
Chungang Zhuang;Z. Xiong;H. Ding
本文提出了一种多工况热传导问题拓扑优化的数值方法。该框架是基于椭圆方程组的拓扑导数和形状导数理论。我们采用水平集模型来隐式表示导热材料的几何边界。拓扑导数的引入将在设计域中产生新的拓扑，在一定程度上抑制了对初始拓扑猜测的依赖性。将形状导数与水平集方法相结合，得到了形状优化结果。分析中以二次温度梯度泛函为目标函数，以稳态热传导状态方程为约束条件，以体积为约束条件。将材料域形状作为设计变量，通过逐步更新水平集函数得到最终结果。我们发展了一种有效的数值技术来实现多工况热传导问题的优化设计。数值算例表明，该方法对热传导问题的拓扑优化是有效的和鲁棒的。
In this paper we present a numerical approach of topology optimization under multiple load cases for heat conduction problem. This framework is based on the theories of topological derivative and shape derivative for elliptic system. We employ level set model to implicitly represent geometric boundary of thermal conductive material. Introducing topological derivative will generate new topology in the design domain, which suppresses the dependence of initial topology guess to some extent. The shape optimization is obtained by combining shape derivative with level set method. The functional of quadratic temperature gradient is taken as the objective function in our analysis, which is subjected to the state equation of steady heat conduction and volume constrain. The shape of material domain is treated as the design variable and the final result is achieved by updating level set function gradually. We develop an effective numerical technique to implement the optimal design with multiple load cases for heat conduction problem. Numerical examples demonstrate that our proposed approach is effective and robust for topology optimization of heat conduction problem.