稳态热传导下的连续体结构拓扑优化

Topological Optimization of Continuum Structure for Heat Conduction

在稳态热传导连续体拓扑优化中,提出单元总热能、节点温度、区域内节点温度平方和三类不同性能指标,推导三类指标的伴随法敏度分析公式。基于独立连续映射法建立以三类指标为约束的体积最小化模型,应用过滤技术克服拓扑优化的数值不稳定性问题,实现了稳态热传导下的连续体拓扑优化设计。通过数值算例对优化结果进行讨论,其结果验证了方法和模型的可行性和有效性。

Heat energy, temperature and sum of square of temperature in local domain were taken as global, local and regional measures independently in topological optimization of continuous structure for heat conduction. Their sensitivities were derived by using adjoint method. Based on comparison between displacement field and temperature field, structural volumes were taken as objectives and three kinds of measure were taken as constraints, topological optimization model was established by using ICM method. Some numerical examples were provided and results were discussed. Results demonstrate the feasibility and validity of the proposed method.